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CGBSE | 9 | Mathematics | 1 | History of Mathematics | Page9 Q2 | Find the digit sum (Beejank) of the following numbers: 15, 38, 88, 99, 412, 867, 4852, 9875, 24601, 48956701. | 15: 1+5=6. 38: 3+8=11 -> 1+1=2. 88: 8+8=16 -> 1+6=7. 99: 9+9=18 -> 1+8=9. 412: 4+1+2=7. 867: 8+6+7=21 -> 2+1=3. 4852: 4+8+5+2=19 -> 1+9=10 -> 1+0=1. 9875: 9+8+7+5=29 -> 2+9=11 -> 1+1=2. 24601: 2+4+6+0+1=13 -> 1+3=4. 48956701: 4+8+9+5+6+7+0+1=40 -> 4+0=4. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-1-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-1/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | गणित का इतिहास | निम्नलिखित संख्याओं के बीजांक ज्ञात कीजिए। 15, 38, 88, 99, 412, 867, 4852, 9875, 24601, 48956701 | 15: 1+5=6। 38: 3+8=11 -> 1+1=2। 88: 8+8=16 -> 1+6=7। 99: 9+9=18 -> 1+8=9। 412: 4+1+2=7। 867: 8+6+7=21 -> 2+1=3। 4852: 4+8+5+2=19 -> 1+9=10 -> 1+0=1। 9875: 9+8+7+5=29 -> 2+9=11 -> 1+1=2। 24601: 2+4+6+0+1=13 -> 1+3=4। 48956701: 4+8+9+5+6+7+0+1=40 -> 4+0=4। | Hindi | dual_sourced_no_translation | 7fdaea3f49 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 1 | History of Mathematics | Page9 Q3 | What should be added to the following numbers to make them divisible by 9: 241, 861, 4441, 83504? | 241: digit sum = 7, so add 2 (9-7=2). 861: digit sum = 6, so add 3 (9-6=3). 4441: digit sum = 4, so add 5 (9-4=5). 83504: digit sum = 2, so add 7 (9-2=7). | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-1-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-1/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | गणित का इतिहास | निम्नलिखित संख्याओं में क्या जोड़ दिया जाए कि संख्या 9 से विभाजित हो जाए:- 241, 861, 4441, 83504 | 241: बीजांक = 7, अतः 2 जोड़ना होगा (9-7=2)। 861: बीजांक = 6, अतः 3 जोड़ना होगा (9-6=3)। 4441: बीजांक = 4, अतः 5 जोड़ना होगा (9-4=5)। 83504: बीजांक = 2, अतः 7 जोड़ना होगा (9-2=7)। | Hindi | dual_sourced_no_translation | 7946053636 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 1 | History of Mathematics | Page23 Q(1-4) | Find the square root of the following numbers using Vilokanam Vidhi (observation method): (1) 9409 (2) 7569 (3) 8281 (4) 3249. | (1) √(9409): unit digit must be 3 or 7; since 95²=9025 < 9409, the answer is 97 (97²=9409). (2) √(7569): unit digit 3 or 7; since 85²=7225 < 7569, the answer is 87 (87²=7569). (3) √(8281): unit digit 1 or 9; since 8281 < 95²=9025, the answer is 91 (91²=8281). (4) √(3249): unit digit 3 or 7; since 3249 > 55²=3025, the a... | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-1-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-1/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | गणित का इतिहास | वर्गमूल विलोकनम् विधि से ज्ञात कीजिए। (1) 9409 (2) 7569 (3) 8281 (4) 3249 | (1) 9409 का वर्गमूल: इकाई अंक 3 या 7 होगा; चूँकि 95²=9025 < 9409, अतः उत्तर 97 है (97²=9409)। (2) 7569 का वर्गमूल: इकाई अंक 3 या 7; चूँकि 85²=7225 < 7569, अतः उत्तर 87 है (87²=7569)। (3) 8281 का वर्गमूल: इकाई अंक 1 या 9; चूँकि 8281 < 95²=9025, अतः उत्तर 91 है (91²=8281)। (4) 3249 का वर्गमूल: इकाई अंक 3 या 7; चूँकि 3249... | Hindi | dual_sourced_no_translation | 59fa730c5f | dual_sourced_independent |
CGBSE | 9 | Mathematics | 2 | Real Numbers | Page53 Q2 | Find 3 rational numbers between 6 and 7. | Multiply 6 and 7 by 4/4 to get 24/4 and 28/4. Three rational numbers between them are 25/4, 26/4, 27/4. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-2-real-numbers-exercise-2-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-2/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वास्तविक संख्याएँ | 6 व 7 के बीच 3 परिमेय संख्याएँ ज्ञात करें। | 6 और 7 को 4/4 से गुणा करने पर 24/4 और 28/4 प्राप्त होता है। इनके बीच की 3 परिमेय संख्याएँ हैं: 25/4, 26/4, 27/4। | Hindi | dual_sourced_no_translation | f381d6e4ce | dual_sourced_independent |
CGBSE | 9 | Mathematics | 2 | Real Numbers | Page53 Q4 | Find 3 rational numbers between 2/3 and 3/4. | LCM of denominators 3 and 4 is 12, so 2/3 = 32/48 and 3/4 = 36/48 (using a common denominator of 48). Three rational numbers between them are 33/48, 34/48, 35/48. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-2-real-numbers-exercise-2-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-2/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वास्तविक संख्याएँ | 2/3 व 3/4 के बीच 3 परिमेय संख्याएँ ज्ञात करें। | हरो 3 और 4 का ल.स. = 12, अतः 2/3 = 32/48 और 3/4 = 36/48 (हर 48 लेने पर)। इनके मध्य की 3 परिमेय संख्याएँ हैं: 33/48, 34/48, 35/48। | Hindi | dual_sourced_no_translation | c9f77a2d01 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 2 | Real Numbers | Page53 Q9(i) | Express the following decimal in p/q form: 0.53 | 0.53 = 53/100. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-2-real-numbers-exercise-2-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-2/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वास्तविक संख्याएँ | निम्नलिखित दशमलव रूप को p/q के रूप में व्यक्त कीजिए। (i) 0.53 | 0.53 = 53/100। | Hindi | dual_sourced_no_translation | 29db4ffd89 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 2 | Real Numbers | Page53 Q9(iv) | Express the following decimal in p/q form: 7.36 | 7.36 = 736/100 = 184/25. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-2-real-numbers-exercise-2-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-2/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वास्तविक संख्याएँ | निम्नलिखित दशमलव रूप को p/q के रूप में व्यक्त कीजिए। (iv) 7.36 | 7.36 = 736/100 = 184/25। | Hindi | dual_sourced_no_translation | 18f61899b9 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q5 | In triangle PQR, PQ = PR and angle R = 28°. Find the remaining angles. | Since PQ=PR, the opposite angles are equal, so angle Q = angle R = 28°. Angle P = 180 - (28+28) = 124°. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | यदि ΔPQR में PQ = PR और ∠R = 28० हो तो त्रिभुज के शेष कोणों को ज्ञात कीजिए। | चूँकि PQ=PR, अतः सम्मुख कोण बराबर होंगे, इसलिए ∠Q = ∠R = 28०। ∠P = 180० - (28०+28०) = 124०। | Hindi | dual_sourced_no_translation | 817b4ac6bc | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q6 | A triangle has two sides of equal length. If the angle opposite one of them is 30°, find the third angle. | Since two sides are equal, the opposite angles are equal, each 30°. Third angle = 180 - (30+30) = 120°. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | किसी त्रिभुज की दो भुजाओ बराबर माप की है। यदि उनका एक सम्मुख कोण 30० हो तो शेष अन्य कोण की माप ज्ञात कीजिए। | चूँकि दो भुजाएँ बराबर हैं, अतः सम्मुख कोण भी बराबर होंगे, प्रत्येक 30०। तीसरा कोण = 180० - (30०+30०) = 120०। | Hindi | dual_sourced_no_translation | baf6e3cb9f | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q7 | In an isosceles triangle, the vertex angle is 70°. Find the other two angles opposite the equal sides. | The two angles opposite the equal sides are equal. Sum of other two angles = 180 - 70 = 110°. Each angle = 110/2 = 55°. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | किसी समद्विबाहु त्रिभुज का शीर्ष कोण 70० का है। समान भुजाओं के सम्मुख कोण ज्ञात कीजिए। | समान भुजाओं के सम्मुख दोनों कोण बराबर होते हैं। शेष दोनों कोणों का योग = 180० - 70० = 110०। प्रत्येक कोण = 110०/2 = 55०। | Hindi | dual_sourced_no_translation | f9d1b94a10 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q8 | Triangle ABC is a right triangle with angle C = 90° and CA = CB. Find the value of x (angle A = angle B = x). | Since angle C = 90, angle A + angle B = 90. Since CA=CB, angle A = angle B = x, so x = 90/2 = 45°. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | ΔABC एक समकोण त्रिभुज है जिसमें ∠C = 90० और CA = CB है। x का मान ज्ञात कीजिए। | चूँकि ∠C = 90०, अतः ∠A + ∠B = 90०। चूँकि CA=CB, ∠A = ∠B = x, अतः x = 90०/2 = 45०। | Hindi | dual_sourced_no_translation | 220c724408 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q9 | In triangle ABC, AB = AC and angle B is twice angle A. Find all three angles of the triangle. | Let angle A = x. Then angle B = 2x and angle C = angle B = 2x (since AB=AC). So x + 2x + 2x = 180, 5x = 180, x = 36. Angle A = 36°, angle B = angle C = 72° each. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | निम्नांकित चित्र में AB = AC यदि ∠B का माप ∠A के माप का दो गुना है तो सभी कोणों के माप ज्ञात कीजिए। | माना ∠A = x। तब ∠B = 2x और ∠C = ∠B = 2x (चूँकि AB=AC)। अतः x + 2x + 2x = 180०, 5x = 180०, x = 36०। ∠A = 36०, ∠B = ∠C = 72० प्रत्येक। | Hindi | dual_sourced_no_translation | 4ffe900bc6 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 3 | Properties of a Triangle | Ex3.1 Q11 | The angles of a triangle are in the ratio 2:3:4. Find all three angles. | Let the angles be 2x, 3x, 4x. Sum = 180, so 9x = 180, x = 20. The angles are 40, 60, and 80°. | https://www.netexplanations.com/chhattisgarh-class-7-math-properties-of-a-triangle-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | त्रिभुज के गुण | किसी त्रिभुज के कोणों में 2:3:4 का अनुपात है। त्रिभुज के तीनों कोणों की माप ज्ञात कीजिए। | माना कोण 2x, 3x, 4x हैं। योग = 180०, अतः 9x = 180०, x = 20०। कोण हैं: 40०, 60०, 80०। | Hindi | dual_sourced_no_translation | f6f6021b7a | dual_sourced_independent |
CGBSE | 7 | Mathematics | 4 | Equations | Ex4.1 Q1(i-iv) | Fill in the blanks: (i) Solution of equation 2x = 4 is x = ? (ii) Solution of x/3 = 3 is x = ? (iii) Solution of 3x + 2 = 8 is x = ? (iv) Solution of 5y = 2y + 15 is y = ? | (i) 2x=4 => x=2. (ii) x/3=3 => x=9. (iii) 3x+2=8 => 3x=6 => x=2. (iv) 5y=2y+15 => 3y=15 => y=5. | https://www.netexplanations.com/chhattisgarh-class-7-math-equations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-4/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समीकरण | रिक्त स्थानों की पूर्ति कीजिये: (i) समीकरण 2x = 4 का हल x = ? (ii) x/3 = 3 का हल x = ? (iii) 3x + 2 = 8 का हल x = ? (iv) 5y = 2y + 15 का हल y = ? | (i) 2x=4 => x=2। (ii) x/3=3 => x=9। (iii) 3x+2=8 => 3x=6 => x=2। (iv) 5y=2y+15 => 3y=15 => y=5। | Hindi | dual_sourced_no_translation | 58b612ea25 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 4 | Equations | Ex4.1 Q2(i-ix) | Solve and verify: (i) 7x+15=3x+31 (ii) 3(x-3)=5(2x-1) (iii) (2y+9)/3=3y+10 (iv) 2(x-1)-3(x-2)=4(x-3)+5(x-4) (v) 2x/3+5/6=13/6 (vi) (x+2)/3+5=17 (vii) 3y+5/8=11/8 (viii) (3m+2)/3=17/3 (ix) 2.5x+3.5=6 | (i) x=4. (ii) x=-4/7. (iii) y=-3. (iv) x=18/5. (v) x=2. (vi) x=34. (vii) y=1/4. (viii) m=5. (ix) x=1. | https://www.netexplanations.com/chhattisgarh-class-7-math-equations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-4/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समीकरण | समीकरण को हल कीजिए एवं उत्तर की जाँच कीजिये: (i) 7x+15=3x+31 (ii) 3(x-3)=5(2x-1) (iii) (2y+9)/3=3y+10 (iv) 2(x-1)-3(x-2)=4(x-3)+5(x-4) (v) 2x/3+5/6=13/6 (vi) (x+2)/3+5=17 (vii) 3y+5/8=11/8 (viii) (3m+2)/3=17/3 (ix) 2.5x+3.5=6 | (i) x=4। (ii) x=-4/7। (iii) y=-3। (iv) x=18/5। (v) x=2। (vi) x=34। (vii) y=1/4। (viii) m=5। (ix) x=1। | Hindi | dual_sourced_no_translation | 3297154aac | dual_sourced_independent |
CGBSE | 7 | Mathematics | 5 | Use of Brackets | Ex5.1 Q1(i-iii) | Write using brackets and simplify: (i) Divide the difference of ten and two by thirty (ii) Multiply the difference of twelve and five by twenty seven (iii) Divide the sum of 4.5 and 2.3 by 3.8 | (i) (10-2)/30 = 8/30 = 4/15. (ii) (12-5)x27 = 7×27 = 189. (iii) (4.5+2.3)/3.8 = 6.8/3.8 = 34/19. | https://www.netexplanations.com/chhattisgarh-class-7-math-use-of-brackets-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | कोष्ठकों का प्रयोग | कोष्ठक का प्रयोग करते हुए हल कीजिए: (i) दस और दो के अंतर को तीस से भाग दिया जावे। (ii) बारह और पांच के अंतर को 27 से गुणा किया जावे। (iii) 4.5 एवं 2.3 के योग में 3.8 का भाग दिया जावे। | (i) (10-2)/30 = 8/30 = 4/15। (ii) (12-5)x27 = 7×27 = 189। (iii) (4.5+2.3)/3.8 = 6.8/3.8 = 34/19। | Hindi | dual_sourced_no_translation | 39551b845c | dual_sourced_independent |
CGBSE | 7 | Mathematics | 9 | Operations on Algebraic Expressions | Ex9.1 Q1 | Find the sum of the following: (a) 2pq and 7pq (b) 2xy-4xy and 8xy (d) 7y+3z and 3x+4y (e) x+y-z, x-y-z and y+z-x (f) 5x+4y-12, 6x+5y and 12z-7x+9y (g) 3x-7xy, 6xy-4y and x+2 (h) x²y²+3x²-7 and -5x²y²-5x+7 | (a) 9pq. (b) 6xy. (d) 3x+11y+3z. (e) x+y-z. (f) 4x+18y+12z-12. (g) 4x-4y-xy+2. (h) 3x²-4x²y²-5x. | https://www.netexplanations.com/chhattisgarh-class-7-math-operations-on-algebraic-expressions-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-9/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | बीजीय व्यंजकों का संक्रियाएँ | निम्नलिखित का योग ज्ञात कीजिए: (a) 2pq और 7pq (b) 2xy-4xy और 8xy (d) 7y+3z और 3x+4y (e) x+y-z, x-y-z और y+z-x (f) 5x+4y-12, 6x+5y और 12z-7x+9y (g) 3x-7xy, 6xy-4y और x+2 (h) x²y²+3x²-7 और -5x²y²-5x+7 | (a) 9pq। (b) 6xy। (d) 3x+11y+3z। (e) x+y-z। (f) 4x+18y+12z-12। (g) 4x-4y-xy+2। (h) 3x²-4x²y²-5x। | Hindi | dual_sourced_no_translation | 1882c12328 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 9 | Operations on Algebraic Expressions | Ex9.1 Q2 | Subtract the second expression from the first: (a) 3x from 8x (b) -4x from 12x (d) -8x from -5x (e) -3x²-4x-2 from x²-3x+7 (g) 3ab+2a-3b from xy-5a-9b | (a) 5x. (b) 16x. (d) 3x. (e) 4x²+x+9. (g) xy-7a-6b-3ab. | https://www.netexplanations.com/chhattisgarh-class-7-math-operations-on-algebraic-expressions-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-9/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | बीजीय व्यंजकों का संक्रियाएँ | निम्नलिखित में प्रथम व्यंजक से द्वितीय व्यंजक को घटाइए: (a) 8x में से 3x को (b) 12x में से (-4x) को (d) (-5x) में से (-8x) को (e) x²-3x+7 में से -3x²-4x-2 को (g) xy-5a-9b में से 3ab+2a-3b को | (a) 5x। (b) 16x। (d) 3x। (e) 4x²+x+9। (g) xy-7a-6b-3ab। | Hindi | dual_sourced_no_translation | ce69453b71 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 9 | Operations on Algebraic Expressions | Ex9.1 Q3 | Simplify: (1) 5ab-7b²c-6ab+2bc²-4b²c-3bc² (2) m²-2n²+7mn-5m²-11mn-3n²+2n² | (1) -ab-11b²c-bc². (2) -4m²-3n²-4mn. | https://www.netexplanations.com/chhattisgarh-class-7-math-operations-on-algebraic-expressions-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-9/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | बीजीय व्यंजकों का संक्रियाएँ | सरल कीजिए: (1) 5ab-7b²c-6ab+2bc²-4b²c-3bc² (2) m²-2n²+7mn-5m²-11mn-3n²+2n² | (1) -ab-11b²c-bc²। (2) -4m²-3n²-4mn। | Hindi | dual_sourced_no_translation | 7e58ba8a33 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.2 Q1(a,e) | Convert the following decimals to rational (p/q) form: (a) 0.2 (e) 14.53 | (a) 0.2 = 1/5. (e) 14.53 = 1453/100. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | निम्न संख्याओं को परिमेय संख्या (p/q) में परिवर्तित कीजिए: (a) 0.2 (e) 14.53 | (a) 0.2 = 1/5। (e) 14.53 = 1453/100। | Hindi | dual_sourced_no_translation | 6f6994c160 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.2 Q2(a) | Convert the repeating decimal 0.444... (0.4 recurring) to rational (p/q) form. | Let x = 0.444... Then 10x = 4.444... Subtracting, 9x = 4, so x = 4/9. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | मान लीजिए p/q = 0.4444... (अर्थात 0.4 आवर्ती), इसे परिमेय संख्या के रूप में व्यक्त कीजिए। | माना x = 0.444...। तब 10x = 4.444...। घटाने पर, 9x = 4, अतः x = 4/9। | Hindi | dual_sourced_no_translation | b016a88c23 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.3 Q1(i,iii) | Add: (i) 1.0087 + 0.321 (iii) 3.81 + 0.009 + 10.0023 | (i) 1.0087 + 0.321 = 1.3297. (iii) 3.81 + 0.009 + 10.0023 = 13.8213. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | योग कीजिए: (i) 1.0087 + 0.321 (iii) 3.81 + 0.009 + 10.0023 | (i) 1.0087 + 0.321 = 1.3297। (iii) 3.81 + 0.009 + 10.0023 = 13.8213। | Hindi | dual_sourced_no_translation | 5fa156b3bc | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.3 Q2(i,iii) | Find the value: (i) 7.89 - 2.324 (iii) 1.01 - 0.1 - 0.001 + 10.001 | (i) 7.89 - 2.324 = 5.566. (iii) 1.01 - 0.1 - 0.001 + 10.001 = 10.91. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | मान ज्ञात कीजिए: (i) 7.89 - 2.324 (iii) 1.01 - 0.1 - 0.001 + 10.001 | (i) 7.89 - 2.324 = 5.566। (iii) 1.01 - 0.1 - 0.001 + 10.001 = 10.91। | Hindi | dual_sourced_no_translation | 0a4d69966c | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.3 Q3(i,iii) | Solve: (i) 243 × 0.15 (iii) 0.1 × 0.1 × 0.1 × 0.1 | (i) 243 × 0.15 = 36.45. (iii) 0.1 × 0.1 × 0.1 × 0.1 = 0.0001. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | हल कीजिए: (i) 243 × 0.15 (iii) 0.1 × 0.1 × 0.1 × 0.1 | (i) 243 × 0.15 = 36.45। (iii) 0.1 × 0.1 × 0.1 × 0.1 = 0.0001। | Hindi | dual_sourced_no_translation | 37615a6264 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 11 | Decimal Representation of Rational Numbers and Operations | Ex11.3 Q4(i) | Divide: 2.25 / 15 | 2.25 / 15 = 0.15. | https://www.netexplanations.com/chhattisgarh-class-7-math-decimal-representation-of-rational-numbers-and-operations-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-11/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | परिमेय संख्याओं का दशमलव निरूपण एवं संक्रियाएँ | भाग दीजिए: 2.25 / 15 | 2.25 / 15 = 0.15। | Hindi | dual_sourced_no_translation | a7998ae3a6 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q2(i-iv) | Which of the following groups of angles are possible for a quadrilateral: (i) 60°,70°,80°,145° (ii) 102°,150°,40°,68° (iii) 75°,75°,75°,135° (iv) 90°,90°,90°,90°? | (i) Sum=355°, not possible. (ii) Sum=360°, possible. (iii) Sum=360°, possible. (iv) Sum=360°, possible. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | दिए गए कोणों में अन्तः कोणों के मान के आधार पर कौन-कौन सा समूह किसी चतुर्भुज के लिए संभव हो सकते है: (i) 60०,70०,80०,145० (ii) 102०,150०,40०,68० (iii) 75०,75०,75०,135० (iv) 90०,90०,90०,90०? | (i) योग=355०, संभव नहीं। (ii) योग=360०, संभव। (iii) योग=360०, संभव। (iv) योग=360०, संभव। | Hindi | dual_sourced_no_translation | 9c5b3453ea | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q3 | Two angles of a quadrilateral are supplementary to each other. If one of the remaining angles is 65°, find the fourth angle. | Supplementary angles sum to 180. Fourth angle = 360 - 180 - 65 = 115°. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | एक चतुर्भुज के दो कोण एक दूसरे के संपूरक है। यदि शेष कोणों में एक कोण 65० का हो तो चौथे कोण का मान ज्ञात कीजिए। | संपूरक कोणों का योग 180० होता है। चौथा कोण = 360० - 180० - 65० = 115०। | Hindi | dual_sourced_no_translation | f40b050228 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q4 | In a quadrilateral, two angles are each 70° and the remaining two angles are equal. Find the value of each equal angle. | 70+70+2x=360, so 2x=220, x=110° each. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | किसी चतुर्भुज में दो कोण प्रत्येक 70० के है तथा शेष दो कोण बराबर है तो बराबर कोणों में प्रत्येक का मान ज्ञात कीजिए। | 70+70+2x=360, अतः 2x=220, x=110० प्रत्येक। | Hindi | dual_sourced_no_translation | 471f3b04b1 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q5 | All angles of a quadrilateral are equal in measure. Find the measure of each angle. | 4x = 360, so x = 90° each. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | किसी चतुर्भुज के सभी कोणों के माप बराबर है तो प्रत्येक कोण का माप ज्ञात कीजिए। | 4x = 360, अतः x = 90० प्रत्येक। | Hindi | dual_sourced_no_translation | 814d15d77b | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q6 | Two angles of a quadrilateral are 65° and 105° respectively. The remaining two angles are equal. Find each equal angle. | 65+105+2x=360, so 2x=190, x=95° each. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | किसी चतुर्भुज के दो कोण क्रमशः 65० एवं 105० के है। शेष दो कोण आपस में बराबर है, बराबर कोणों में प्रत्येक का मान ज्ञात कीजिए। | 65+105+2x=360, अतः 2x=190, x=95० प्रत्येक। | Hindi | dual_sourced_no_translation | 376f529f46 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q7 | The angles of a quadrilateral are in the ratio 3:5:7:9. Find the measure of each angle. | Let angles be 3x,5x,7x,9x. Sum=24x=360, x=15. Angles are 45,75,105,135°. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | किसी चतुर्भुज के कोणों का अनुपात 3:5:7:9 है। उसके प्रत्येक कोण की मान ज्ञात कीजिए। | माना कोण 3x,5x,7x,9x हैं। योग=24x=360, x=15। कोण हैं: 45०,75०,105०,135०। | Hindi | dual_sourced_no_translation | 23af565f2c | dual_sourced_independent |
CGBSE | 7 | Mathematics | 13 | Quadrilateral | Ex13.1 Q9 | Three angles of a quadrilateral are each equal to 80°. Find the fourth angle. | 3×80 + x = 360, so 240+x=360, x=120°. | https://www.netexplanations.com/chhattisgarh-class-7-math-quadrilateral-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-13/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | चतुर्भुज | एक चतुर्भुज के तीन कोण प्रत्येक 80० के बराबर है। चौथा कोण ज्ञात कीजिए। | 3×80० + x = 360०, अतः 240०+x=360०, x=120०। | Hindi | dual_sourced_no_translation | b93923363d | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.1 Q3(i-iii) | Fill in the blanks so that the ratios on both sides are equal: (i) 32 : ___ = 6 : 12 (ii) 22 kg : 26 kg = ___ : 260 metres (iii) 45 km : 60 km = ___ : 12 hours | (i) 64 (since 32:64=6:12=1:2). (ii) 220 metres (22:26=220:260). (iii) 9 hours (45:60=9:12). | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | रिक्त स्थानों को इस प्रकार भरें कि दोनों पक्षों के अनुपात समान हों: (i) 32 : ___ = 6 : 12 (ii) 22 किग्रा : 26 किग्रा = ___ : 260 मीटर (iii) 45 किमी : 60 किमी = ___ : 12 घंटे | (i) 64 (चूँकि 32:64=6:12=1:2)। (ii) 220 मीटर (22:26=220:260)। (iii) 9 घंटे (45:60=9:12)। | Hindi | dual_sourced_no_translation | 85f84e8c9f | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.1 Q4 | The cost of 8 kilograms of sugar is Rs 72. Find the cost of 15 kilograms. | Cost per kg = 72/8 = Rs 9. Cost of 15 kg = 9 × 15 = Rs 135. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | 8 किलोग्राम चीनी का मूल्य 72 रु. है, तो 15 किलोग्राम चीनी का मूल्य ज्ञात कीजिए। | प्रति किग्रा मूल्य = 72/8 = 9 रु.। 15 किग्रा का मूल्य = 9 × 15 = 135 रु.। | Hindi | dual_sourced_no_translation | 8c1a889318 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.1 Q5 | The ratio of length to width of a playground is 5:2. Find the length if the width is 40 metres. | Length/width = 5/2. Length = 40 × 5/2 = 100 metres. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | किसी मैदान की लम्बाई एवं चौड़ाई का अनुपात 5:2 है मैदान की लम्बाई मीटर में ज्ञात कीजिए यदि चौड़ाई 40 मीटर है। | लम्बाई/चौड़ाई = 5/2। लम्बाई = 40 × 5/2 = 100 मीटर। | Hindi | dual_sourced_no_translation | ec4f37c7ea | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.1 Q6 | A person bought 3 copies of a book for Rs 75. How many copies can be bought for Rs 300? | Cost per copy = 75/3 = Rs 25. Copies for Rs 300 = 300/25 = 12 copies. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | किसी व्यक्ति ने एक पुस्तक की तीन प्रतियां 75 रु. में खरीदी। बताईये कि 300 रु. में वह व्यक्ति पुस्तक की कितनी प्रतियां खरीद सकता है? | प्रति प्रति मूल्य = 75/3 = 25 रु.। 300 रु. में प्रतियां = 300/25 = 12 प्रतियां। | Hindi | dual_sourced_no_translation | 5e2571512d | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.2 Q1 | Three copies cost Rs 16.50. What will be the cost of 7 copies? | Cost per copy = 16.50/3 = Rs 5.50. Cost of 7 copies = 5.50 × 7 = Rs 38.50. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | तीन कॉपियों की कीमत 16.50 रु. है। तो 7 कॉपियों की कीमत ज्ञात कीजिए। | प्रति कॉपी मूल्य = 16.50/3 = 5.50 रु.। 7 कॉपियों का मूल्य = 5.50 × 7 = 38.50 रु.। | Hindi | dual_sourced_no_translation | fa85fa7889 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.2 Q2(i,ii) | A car moves 165 km in 3 hours. Find: (i) time needed to move 440 km (ii) distance covered in 6.5 hours. | Speed = 165/3 = 55 km/h. (i) Time = 440/55 = 8 hours. (ii) Distance = 55 × 6.5 = 357.5 km. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | एक कार 3 घंटे में 165 किलोमीटर चलती है। ज्ञात कीजिए: (i) 440 किमी चलने में लगा समय (ii) 6.5 घंटे में तय की गई दूरी। | चाल = 165/3 = 55 किमी/घंटा। (i) समय = 440/55 = 8 घंटे। (ii) दूरी = 55 × 6.5 = 357.5 किमी। | Hindi | dual_sourced_no_translation | 672dfd9d74 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.2 Q3(i,ii) | 72 books weigh 9 kilograms. Find: (i) weight of 80 books (ii) how many books weigh 6 kg. | Weight per book = 9/72 = 1/8 kg. (i) Weight of 80 books = 80/8 = 10 kg. (ii) Number of books in 6 kg = 6 × 8 = 48 books. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | 72 किताबों का वजन 9 किलोग्राम है। ज्ञात कीजिए: (i) 80 किताबों का वजन (ii) 6 किग्रा में कितनी किताबें होंगी। | प्रति पुस्तक भार = 9/72 = 1/8 किग्रा। (i) 80 किताबों का वजन = 80/8 = 10 किग्रा। (ii) 6 किग्रा में किताबें = 6 × 8 = 48 किताबें। | Hindi | dual_sourced_no_translation | b0dbc225c3 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.2 Q4 | A worker earns Rs 1500 in 25 days. Find the income in 30 days. | Income per day = 1500/25 = Rs 60. Income in 30 days = 60 × 30 = Rs 1800. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | किसी मजदूर की 25 दिनों की आय 1500 रु. है। उसकी 30 दिनों की आय ज्ञात कीजिए। | प्रतिदिन आय = 1500/25 = 60 रु.। 30 दिनों की आय = 60 × 30 = 1800 रु.। | Hindi | dual_sourced_no_translation | 383c0076a2 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 14 | Proportion | Ex14.2 Q5 | If 22 metres of cloth costs Rs 704, what would be the cost of 20 metres? | Cost per metre = 704/22 = Rs 32. Cost of 20 metres = 32 × 20 = Rs 640. | https://www.netexplanations.com/chhattisgarh-class-7-math-proportion-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | समानुपात | यदि 22 मीटर कपड़े का मूल्य 704 रु है तो 20 मीटर कपड़े का मूल्य क्या होगा? | प्रति मीटर मूल्य = 704/22 = 32 रु.। 20 मीटर का मूल्य = 32 × 20 = 640 रु.। | Hindi | dual_sourced_no_translation | 56a3fc85f4 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 16 | Percentage | Ex16.2 Q4 | The cost price of an item is Rs 120 and the selling price is Rs 150. What is the percentage profit? | Profit = 150-120 = Rs 30. Profit% = 30/120 × 100 = 25%. | https://www.netexplanations.com/chhattisgarh-class-7-math-percentage-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-16/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | प्रतिशतता | किसी वस्तु का क्रय मूल्य 120 रु. है तथा विक्रय मूल्य 150 रु. है, तो उसे कितने प्रतिशत लाभ हुआ? | लाभ = 150-120 = 30 रु.। लाभ% = 30/120 × 100 = 25%। | Hindi | dual_sourced_no_translation | b631808740 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 16 | Percentage | Ex16.2 Q5 | Jyotsna bought a watch for Rs 380 and sold it for Rs 342. What percentage loss did she incur? | Loss = 380-342 = Rs 38. Loss% = 38/380 × 100 = 10%. | https://www.netexplanations.com/chhattisgarh-class-7-math-percentage-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-16/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | प्रतिशतता | ज्योत्सना ने एक घड़ी 380 रु. में खरीदी और उसे 342 रु. में बेच दी तो उसे कितने प्रतिशत हानि हुई? | हानि = 380-342 = 38 रु.। हानि% = 38/380 × 100 = 10%। | Hindi | dual_sourced_no_translation | 441457ad47 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 16 | Percentage | Ex16.2 Q9 | A person sells a chair for Rs 144 incurring a 4% loss. At what price should he sell the chair to gain 10% profit? | Cost price = 144/0.96 = Rs 150. Selling price for 10% profit = 150 × 1.10 = Rs 165. | https://www.netexplanations.com/chhattisgarh-class-7-math-percentage-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-16/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | प्रतिशतता | एक कुर्सी 144 रु. में बेचने पर एक व्यक्ति को 4% की हानि होती है। 10% लाभ प्राप्त करने के लिए उसे कुर्सी को कितने रुपये में बेचना चाहिए? | क्रय मूल्य = 144/0.96 = 150 रु.। 10% लाभ हेतु विक्रय मूल्य = 150 × 1.10 = 165 रु.। | Hindi | dual_sourced_no_translation | 64fb9281b6 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 16 | Percentage | Ex16.2 Q10 | A shopkeeper buys a TV set for Rs 5000 and spends Rs 500 on its repair. If he wants to sell it at 5% profit, find the selling price. | Total cost = 5000+500 = Rs 5500. Selling price = 5500 × 1.05 = Rs 5775. | https://www.netexplanations.com/chhattisgarh-class-7-math-percentage-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-16/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | प्रतिशतता | एक दुकानदार एक टीवी सेट 5000 रु. खरीदता है। वह उसके मरम्मत पर 500 रु. खर्च करता है। अब यदि वह 5% लाभ लेकर उसे बेचना चाहता है तो विक्रय मूल्य ज्ञात कीजिए। | कुल लागत = 5000+500 = 5500 रु.। विक्रय मूल्य = 5500 × 1.05 = 5775 रु.। | Hindi | dual_sourced_no_translation | c909f5c534 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 16 | Percentage | Ex16.2 Q15 | An item was bought for Rs 900. At what price should it be sold to gain 15% profit? | Selling price = 900 × 1.15 = Rs 1035. | https://www.netexplanations.com/chhattisgarh-class-7-math-percentage-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-16/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | प्रतिशतता | किसी वस्तु को 900 रु. में ख़रीदा गया वस्तु को कितने में बेचा जाये कि 15% का लाभ हो। | विक्रय मूल्य = 900 × 1.15 = 1035 रु.। | Hindi | dual_sourced_no_translation | 467a7b632a | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.1 Q2(i-vi) | Solve the following equations: (i) 5x+2=17 (ii) 5p+1=24 (iii) 4x+8x=17x-9-1 (iv) -7+3t-9t=12t-5 (v) 3(z-2)+5z=2 (vi) -2+(x+4)=8x | (i) x=3. (ii) p=23/5. (iii) x=2. (iv) t=-1/9. (v) z=1. (vi) x=2/7. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | नीचे दिए गए समीकरणों को हल कीजिए: (i) 5x+2=17 (ii) 5p+1=24 (iii) 4x+8x=17x-9-1 (iv) -7+3t-9t=12t-5 (v) 3(z-2)+5z=2 (vi) -2+(x+4)=8x | (i) x=3। (ii) p=23/5। (iii) x=2। (iv) t=-1/9। (v) z=1। (vi) x=2/7। | Hindi | dual_sourced_no_translation | eba78885a5 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.1 Q4(i,ii,iii,v,vi,vii) | Solve the following equations: (i) 6+(4-m)=8(3m+5) (ii) 2(k-5)+3k=k+6 (iii) 5p+4(3-2p)=2+p-10 (v) m-(m-1)/2=1-(m-2)/3 (vi) (3t-2)/4-(2t+3)/3=2/3-t (vii) x/2-1/5=x/3+1/4 | (i) m=-6/5. (ii) k=4. (iii) p=5. (v) m=7/5. (vi) t=2. (vii) x=27/10. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | निम्नलिखित समीकरणों को हल कीजिए: (i) 6+(4-m)=8(3m+5) (ii) 2(k-5)+3k=k+6 (iii) 5p+4(3-2p)=2+p-10 (v) m-(m-1)/2=1-(m-2)/3 (vi) (3t-2)/4-(2t+3)/3=2/3-t (vii) x/2-1/5=x/3+1/4 | (i) m=-6/5। (ii) k=4। (iii) p=5। (v) m=7/5। (vi) t=2। (vii) x=27/10। | Hindi | dual_sourced_no_translation | dc22a6f0e0 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q1 | A triangle has an area of 36 square metres and its base measures 12 metres. Find its height. | Area = 1/2 x base x height, so 36 = 1/2 × 12 x height, giving height = 6 metres. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | एक त्रिभुज का क्षेत्रफल 36 वर्ग मीटर है और उसके आधार की माप 12 मीटर है। तब उसकी ऊँचाई ज्ञात कीजिए। | क्षेत्रफल = 1/2 x आधार x ऊँचाई, अतः 36 = 1/2 × 12 x ऊँचाई, जिससे ऊँचाई = 6 मीटर। | Hindi | dual_sourced_no_translation | a1a44a43e1 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q2 | A rectangle's length exceeds its width by 5 cm. Its perimeter is five times the width. Find the rectangle's length and width. | Let width = x, length = x+5. Perimeter = 2(2x+5) = 5x, so 4x+10=5x, x=10. Width = 10 cm, length = 15 cm. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | एक आयत की लम्बाई उसकी चौड़ाई से 5 सेमी अधिक है। उसका परिमाप चौड़ाई का पाँच गुना है। आयत की लम्बाई एवं चौड़ाई ज्ञात कीजिये। | माना चौड़ाई = x, लम्बाई = x+5। परिमाप = 2(2x+5) = 5x, अतः 4x+10=5x, x=10। चौड़ाई = 10 सेमी, लम्बाई = 15 सेमी। | Hindi | dual_sourced_no_translation | 39c958a977 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q4 | Find three consecutive odd numbers such that three times their sum is 5 more than eight times the middle number. | Let numbers be x, x+2, x+4. 3(3x+6) = 8(x+2)+5, so 9x+18=8x+21, x=3. The numbers are 3, 5, 7. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | तीन क्रमागत विषम पूर्णांक संख्याएँ ज्ञात कीजिए, यदि उनके योग का तीन गुना मध्य संख्या के 8 गुने से 5 अधिक है। | माना संख्याएँ x, x+2, x+4 हैं। 3(3x+6) = 8(x+2)+5, अतः 9x+18=8x+21, x=3। संख्याएँ हैं: 3, 5, 7। | Hindi | dual_sourced_no_translation | 5f27200064 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q6 | The sum of the digits of a two-digit number is 8. When the digits are reversed, the new number exceeds the original by 18. Find the number. | Let tens digit = a, units digit = b, with a+b=8. Reversed number - original = 9(b-a) = 18, so b-a=2. Solving, a=3, b=5. The number is 35. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | दो अंको वाली संख्या के अंको का योग 8 है। अंको का परस्पर क्रम बदलने पर प्राप्त संख्या दी गयी संख्या से 18 अधिक है। यह संख्या ज्ञात कीजिए। | माना दहाई अंक = a, इकाई अंक = b, जहाँ a+b=8। पलटी हुई संख्या - मूल संख्या = 9(b-a) = 18, अतः b-a=2। हल करने पर, a=3, b=5। संख्या है 35। | Hindi | dual_sourced_no_translation | afbcf3dfba | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q8 | Alka thinks of a number. She adds 5 to it, then adds double the original number, then subtracts 10, getting 40. Find the number. | Let the number be x. x + 5 + 2x - 10 = 40, so 3x - 5 = 40, 3x = 45, x = 15. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | अलका एक संख्या सोचती है। वह उसमे 5 जोड़ती है। इसमें सोची गई संख्या के दुगुने की पुनः जोड़कर 10 घटाती है। घटाने पर 40 प्राप्त होता है, तो वह संख्या बताइये। | माना संख्या x है। x + 5 + 2x - 10 = 40, अतः 3x - 5 = 40, 3x = 45, x = 15। | Hindi | dual_sourced_no_translation | 5c44b194c0 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 5 | Linear Equation in One Variable | Ex5.2 Q10 | The sum of three consecutive multiples of 5 is 555. Find these multiples. | Let the multiples be x, x+5, x+10. 3x+15=555, so 3x=540, x=180. The multiples are 180, 185, 190. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-5-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-5/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | एक चर का रैखिक समीकरण | 5 के तीन क्रमागत गुणजो का योगफल 555 है, तो ये गुणज ज्ञात कीजिए। | माना गुणज x, x+5, x+10 हैं। 3x+15=555, अतः 3x=540, x=180। गुणज हैं: 180, 185, 190। | Hindi | dual_sourced_no_translation | ba7895ba4b | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q1 | Mohan saves Rs 3950 after spending 75% of his monthly income. What is his monthly income? | Savings = 25% of income = 3950, so income = 3950/0.25 = Rs 15800. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | मोहन अपनी मासिक आय का 75% खर्च करने के बाद 3950 रु. बचाता है तो उसकी मासिक आय कितनी है? | बचत = आय का 25% = 3950, अतः आय = 3950/0.25 = 15800 रु.। | Hindi | dual_sourced_no_translation | 1f6b19d33a | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q2 | In class 10, 60% are girls and their number is 18. Find the ratio of boys to girls in the class. | Total students = 18/0.6 = 30. Boys = 30-18 = 12. Ratio of boys to girls = 12:18 = 2:3. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कक्षा 10 में 60% लड़किया है और उनकी संख्या 18 है तो कक्षा में लड़के और लड़कियों की संख्या में अनुपात क्या होगा? | कुल विद्यार्थी = 18/0.6 = 30। लड़के = 30-18 = 12। लड़के व लड़कियों का अनुपात = 12:18 = 2:3। | Hindi | dual_sourced_no_translation | 551adb9fcb | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q3 | An item marked at Rs 950 is sold for Rs 760. Find the discount and the discount percentage. | Discount = 950-760 = Rs 190. Discount% = 190/950 × 100 = 20%. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | 950 रु. अंकित मूल्य वाली वस्तु 760 रु. में बेचीं जाती है। बट्टा और बट्टा प्रतिशत कितना है? | बट्टा = 950-760 = 190 रु.। बट्टा% = 190/950 × 100 = 20%। | Hindi | dual_sourced_no_translation | 76d86ec0b5 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q4 | Lalita bought a microwave oven for Rs 9016 including 12% sales tax. Find the price before tax was added. | Pre-tax price = 9016/1.12 = Rs 8050. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | ललिता ने एक माइक्रोवेव ओवन 12% बिक्री कर सहित 9016 रु. में ख़रीदा। बिक्री कर को जोड़ने से पहले का मूल्य ज्ञात कीजिये। | कर-पूर्व मूल्य = 9016/1.12 = 8050 रु.। | Hindi | dual_sourced_no_translation | f35cba3399 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q5 | A flour mill costs Rs 1,30,000 and 7% sales tax is charged. If Shweta buys this flour mill, find the amount she pays. | Amount paid = 130000 × 1.07 = Rs 1,39,100. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | एक आटा चक्की का मूल्य 1,30,000 रु. है। इस पर 7% की दर से बिक्रीकर वसूला जाता है। यदि श्वेता इस आटा चक्की को ख़रीदती है तो उसके द्वारा भुगतान की जाने वाली राशि ज्ञात कीजिए। | भुगतान राशि = 130000 × 1.07 = 1,39,100 रु.। | Hindi | dual_sourced_no_translation | 7bcfe749f0 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q8(i,ii) | (i) A shirt costs Rs 200. Find the selling price if 5% sales tax is added. (ii) 5 kg of sugar is bought at Rs 30 per kg. Find the selling price if 5% sales tax is added. | (i) 200 × 1.05 = Rs 210. (ii) 5 × 30 = Rs 150; 150 × 1.05 = Rs 157.50. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | (i) 200 रु. वाली शर्ट पर 5% विक्रीकर जुड़ता है तो विक्रय मूल्य ज्ञात कीजिए। (ii) 30 रु. प्रति किलोग्राम की दर से 5 किग्रा शक्कर पर 5% विक्रीकर जुड़ता है तो विक्रय मूल्य ज्ञात कीजिए। | (i) 200 × 1.05 = 210 रु.। (ii) 5 × 30 = 150 रु.; 150 × 1.05 = 157.50 रु.। | Hindi | dual_sourced_no_translation | 57ef394af8 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q9 | Sarita bought a cooler for Rs 5750 including 15% tax. Find the price of the cooler before tax was added. | Pre-tax price = 5750/1.15 = Rs 5000. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | सरिता ने एक कूलर 15% कर सहित 5750 रु. में ख़रीदा। कर के जुड़ने से पहले कूलर का मूल्य ज्ञात कीजिए। | कर-पूर्व मूल्य = 5750/1.15 = 5000 रु.। | Hindi | dual_sourced_no_translation | a55d63d628 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.1 Q10 | Suraj bought a television for Rs 10,260 including 8% sales tax. Find its price before tax was added. | Pre-tax price = 10260/1.08 = Rs 9500. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | सूरज ने एक टेलीविजन 8% बिक्री कर सहित 10,260 रु. में ख़रीदा। बिक्री कर को जोड़ने से पहले का उसका मूल्य ज्ञात कीजिए। | कर-पूर्व मूल्य = 10260/1.08 = 9500 रु.। | Hindi | dual_sourced_no_translation | fa621ad50e | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q1(i,ii,iii) | Find the compound interest and amount for: (i) Principal = Rs 7000, Rate = 10% annual, Time = 4 years (ii) Principal = Rs 6250, Rate = 12% annual, Time = 2 years (iii) Principal = Rs 16000, Rate = 5% annual, Time = 3 years | (i) Amount = 7000×1.1⁴ = Rs 10248.70, CI = Rs 3248.70. (ii) Amount = 6250×1.12² = Rs 7840, CI = Rs 1590. (iii) Amount = 16000×1.05³ = Rs 18522, CI = Rs 2522. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | चक्रवृद्धि ब्याज एवं मिश्रधन ज्ञात कीजिए: (i) मूलधन =7000 रु., दर =10% वार्षिक, समय =4 वर्ष (ii) मूलधन =6250 रु., दर =12% वार्षिक, समय =2 वर्ष (iii) मूलधन =16000 रु., दर =5% वार्षिक, समय =3 वर्ष | (i) मिश्रधन = 7000×1.1⁴ = 10248.70 रु., चक्रवृद्धि ब्याज = 3248.70 रु.। (ii) मिश्रधन = 6250×1.12² = 7840 रु., ब्याज = 1590 रु.। (iii) मिश्रधन = 16000×1.05³ = 18522 रु., ब्याज = 2522 रु.। | Hindi | dual_sourced_no_translation | 13512932ef | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q2 | Rahul borrowed Rs 1,25,000 from a bank to buy a car at 12% annual compound interest. Find the amount due and the interest amount after 3 years. | Amount = 125000 × 1.12³ = Rs 1,75,616. Interest = Rs 50,616. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | राहुल ने एक कार ख़रीदने के लिए बैंक से 125000 रु. की राशि 12% वार्षिक चक्रवृद्धि ब्याज की दर से उधार ली, तो 3 वर्ष बाद देय राशि एवं ब्याज की राशि बताईये। | मिश्रधन = 125000 × 1.12³ = 1,75,616 रु.। ब्याज = 50,616 रु.। | Hindi | dual_sourced_no_translation | 59c7381efc | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q3 | Find the interest on a bank deposit of Rs 50,000 at 15% annual compound interest for 2 years. | Amount = 50000 × 1.15² = Rs 66,125. CI = Rs 16,125. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | बैंक में जमा धनराशि 50,000 रु. पर 15% वार्षिक चक्रवृद्धि ब्याज की दर से 2 वर्ष के ब्याज की गणना कीजिए। | मिश्रधन = 50000 × 1.15² = 66,125 रु.। ब्याज = 16,125 रु.। | Hindi | dual_sourced_no_translation | 7ac0b7c822 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q5 | Find the difference between the compound interest and simple interest on Rs 8000 at 10% annual rate for 2 years. | Difference = P x r² = 8000 × 0.01 = Rs 80. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | 8,000 रु. का 10% वार्षिक ब्याज की दर से 2 वर्ष के चक्रवृद्धि ब्याज तथा साधारण ब्याज का अंतर ज्ञात कीजिये। | अंतर = P x r² = 8000 × 0.01 = 80 रु.। | Hindi | dual_sourced_no_translation | 386960e9c3 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q6 | Find the compound interest on Rs 3000 at 8% annual rate for 1.5 years, when interest is compounded half-yearly. | Half-yearly rate = 4%, periods = 3. Amount = 3000 × 1.04³ = Rs 3374.59. CI = Rs 374.59. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | 3000 रुपये का 8% वार्षिक ब्याज की दर से 1½ वर्ष के चक्रवृद्धि ब्याज की गणना कीजिए जब ब्याज अर्धवार्षिक संयोजित हो। | अर्धवार्षिक दर = 4%, अवधि = 3। मिश्रधन = 3000 × 1.04³ = 3374.59 रु.। ब्याज = 374.59 रु.। | Hindi | dual_sourced_no_translation | 5499757d5a | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q7 | How much interest will Rs 9000 earn in 1 year at a bank, if the rate is 8% annual and calculated quarterly? | Quarterly rate = 2%, periods = 4. Amount = 9000 × 1.02⁴ = Rs 9741.89. Interest = Rs 741.89. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | 9000 रुपये पर किसी बैंक से 1 वर्ष में कितने ब्याज प्राप्त होगा, यदि ब्याज की दर 8% वार्षिक हो और गणना तिमाही की जाए। | तिमाही दर = 2%, अवधि = 4। मिश्रधन = 9000 × 1.02⁴ = 9741.89 रु.। ब्याज = 741.89 रु.। | Hindi | dual_sourced_no_translation | 76df867ca2 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q9 | A person borrowed Rs 25,000. If the rate of interest is 20% annual, compounded half-yearly, how much amount will be repaid after 1 year? | Half-yearly rate = 10%, periods = 2. Amount = 25000 × 1.1² = Rs 30,250. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | एक व्यक्ति ने 25,000 रुपए उधार लिए। यदि ब्याज की दर 20% वार्षिक हो और ब्याज की गणना अर्धवार्षिक की जाये तो 1 वर्ष बाद कितनी राशि चुकाई जाएगी? | अर्धवार्षिक दर = 10%, अवधि = 2। मिश्रधन = 25000 × 1.1² = 30,250 रु.। | Hindi | dual_sourced_no_translation | a759245175 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q10 | Find the compound interest on Rs 10,000 at 12% annual rate for 6 months, if interest is calculated quarterly. | Quarterly rate = 3%, periods = 2. Amount = 10000 × 1.03² = Rs 10,609. CI = Rs 609. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | 10,000 रु. का 12% वार्षिक ब्याज की दर से 6 माह का चक्रवृद्धि ब्याज ज्ञात कीजिए, यदि ब्याज की गणना तिमाही की जाए। | तिमाही दर = 3%, अवधि = 2। मिश्रधन = 10000 × 1.03² = 10,609 रु.। ब्याज = 609 रु.। | Hindi | dual_sourced_no_translation | a37ad35c6d | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q11 | How much money should Surjeet deposit in Punjab National Bank so that he gets Rs 6615 in 2 years at 5% annual interest? | Principal = 6615/1.05² = 6615/1.1025 = Rs 6000. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | सुरजीत पंजाब नेशनल बैंक में कितना धन जमा करे कि 5% वार्षिक ब्याज की दर से उसे 2 वर्ष में 6615 रु. प्राप्त हो? | मूलधन = 6615/1.05² = 6615/1.1025 = 6000 रु.। | Hindi | dual_sourced_no_translation | 4ae7f6108b | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q12 | What principal will become Rs 18,522 in 1.5 years at 10% annual compound interest, if interest is calculated half-yearly? | Half-yearly rate = 5%, periods = 3. Principal = 18522/1.05³ = 18522/1.157625 = Rs 16,000. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कौन सा धन 1½ वर्ष में 10% की वार्षिक चक्रवृद्धि ब्याज की दर से 18522 रु. हो जाएगा, यदि ब्याज की गणना अर्धवार्षिक की जाए? | अर्धवार्षिक दर = 5%, अवधि = 3। मूलधन = 18522/1.05³ = 18522/1.157625 = 16,000 रु.। | Hindi | dual_sourced_no_translation | eb8f67ade2 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q13 | Kabir borrowed Rs 15,625 from Indian Bank to buy a motorcycle. After 3 years he returned Rs 17,576 to the bank. Find the rate of interest charged by the bank. | 17576/15625 = 1.124864 = 1.04³, so the rate is 4% per annum. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कबीर ने मोटर साइकिल खरीदने हेतु इंडियन बैंक से 15625 रु. उधार लिए। 3 वर्ष बाद उसने बैंक को 17576 रु. लौटाए, तो बैंक द्वारा निर्धारित ब्याज की दर ज्ञात कीजिए। | 17576/15625 = 1.124864 = 1.04³, अतः ब्याज दर 4% वार्षिक है। | Hindi | dual_sourced_no_translation | 5bc2820135 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q14 | At what annual rate of interest will Rs 6000 become Rs 6615 in 2 years? | 6615/6000 = 1.1025 = 1.05², so the rate is 5% per annum. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कितने प्रतिशत वार्षिक ब्याज की दर से 6000 रु. की राशि 2 वर्ष में 6615 हो जाती है? | 6615/6000 = 1.1025 = 1.05², अतः ब्याज दर 5% वार्षिक है। | Hindi | dual_sourced_no_translation | 729f34be97 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q15 | In how much time will Rs 8000 amount to Rs 9261, if compound interest is calculated at 5% annual rate? | 9261/8000 = 1.157625 = 1.05³, so the time is 3 years. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कितने समय में 8,000 रु. का मिश्रधन 9,261 रु. हो जायेगा जबकि ब्याज की गणना 5% वार्षिक चक्रवृद्धि ब्याज की दर पर की जाए? | 9261/8000 = 1.157625 = 1.05³, अतः समय 3 वर्ष है। | Hindi | dual_sourced_no_translation | d7f91408be | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q16 | Ahmed received Rs 5853 interest from the State Bank of India on his deposit of Rs 46875 at 8% annual rate. If the bank calculated the interest half-yearly, find the time. | 1+5853/46875 = 1.124864 = 1.04³ (half-yearly rate 4%), so 3 half-year periods = 1.5 years. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | भारतीय स्टेट बैंक से अहमद को उसके जमा धन 46875 रु. पर 8% वार्षिक ब्याज की दर से 5853 रु. ब्याज प्राप्त हुआ। यदि बैंक द्वारा ब्याज की गणना अर्धवार्षिक की गयी हो, तो समय बताईये। | 1+5853/46875 = 1.124864 = 1.04³ (अर्धवार्षिक दर 4%), अतः 3 अर्ध-वार्षिक अवधि = 1.5 वर्ष। | Hindi | dual_sourced_no_translation | f323d18970 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 7 | Comparing Quantities | Ex7.2 Q17 | Find the principal for which the difference between compound interest and simple interest at 5% annual rate for 2 years is Rs 40. | Difference = P x r² = P x 0.0025 = 40, so P = Rs 16,000. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-7-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-7/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | राशियों की तुलना | कौन सी राशि का 5% वार्षिक ब्याज की दर से 2 वर्ष में साधारण ब्याज और चक्रवृद्धि ब्याज का अंतर 40 रुपए है? | अंतर = P x r² = P x 0.0025 = 40, अतः P = 16,000 रु.। | Hindi | dual_sourced_no_translation | a56740ccfb | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.1 Q2(a-e) | Factorise and write in exponential form: (a) 15⁴ (b) 42⁵ (c) 51³ (d) 21^m (e) 65⁶ | (a) 15=3×5, so 15⁴ = 3⁴ x 5⁴. (b) 42=2×3×7, so 42⁵ = 2⁵ x 3⁵ x 7⁵. (c) 51=3×17, so 51³ = 3³ x 17³. (d) 21=3×7, so 21^m = 3^m x 7^m. (e) 65=5×13, so 65⁶ = 5⁶ x 13⁶. | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | निम्नलिखित को गुणनखंड में तोड़कर घातीय रूप में लिखिए: (a) 15⁴ (b) 42⁵ (c) 51³ (d) 21^m (e) 65⁶ | (a) 15=3×5, अतः 15⁴ = 3⁴ x 5⁴। (b) 42=2×3×7, अतः 42⁵ = 2⁵ x 3⁵ x 7⁵। (c) 51=3×17, अतः 51³ = 3³ x 17³। (d) 21=3×7, अतः 21^m = 3^m x 7^m। (e) 65=5×13, अतः 65⁶ = 5⁶ x 13⁶। | Hindi | dual_sourced_no_translation | 9328789689 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.1 Q4(a-d) | Using the rule (a x b)^n = a^n x b^n, write in exponential form: (a) 6⁸ x 7⁸ (b) a³ x b³ (c) p⁹ x q⁹ x r⁹ (d) a^n x b^n x c^n x d^n | (a) 6⁸ x 7⁸ = (6×7)⁸ = 42⁸. (b) a³ x b³ = (ab)³. (c) p⁹ x q⁹ x r⁹ = (pqr)⁹. (d) a^n x b^n x c^n x d^n = (abcd)^n. | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | नियम (a x b)^n = a^n x b^n का उपयोग कर घातांक रूप में लिखिए: (a) 6⁸ x 7⁸ (b) a³ x b³ (c) p⁹ x q⁹ x r⁹ (d) a^n x b^n x c^n x d^n | (a) 6⁸ x 7⁸ = (6×7)⁸ = 42⁸। (b) a³ x b³ = (ab)³। (c) p⁹ x q⁹ x r⁹ = (pqr)⁹। (d) a^n x b^n x c^n x d^n = (abcd)^n। | Hindi | dual_sourced_no_translation | ff3891d2cf | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.1 Q5(a,c,d,e) | State true or false: (a) 2³ x 2⁴ = 2⁷ (c) 2⁴ x 3² = 2⁶ (d) 27² = (3³)² (e) (2³)⁴ = (2⁴)³ | (a) True, since 2³ x 2⁴ = 2^(3+4) = 2⁷. (c) False, since bases 2 and 3 are different so the terms cannot be combined into a single power of 2. (d) True, since 27 = 3³, so 27² = (3³)². (e) True, since both sides equal 2¹². | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | सही अथवा गलत बताइए: (a) 2³ x 2⁴ = 2⁷ (c) 2⁴ x 3² = 2⁶ (d) 27² = (3³)² (e) (2³)⁴ = (2⁴)³ | (a) सत्य, क्योंकि 2³ x 2⁴ = 2^(3+4) = 2⁷। (c) असत्य, क्योंकि आधार 2 और 3 भिन्न हैं अतः इन्हें एक घात में नहीं मिलाया जा सकता। (d) सत्य, क्योंकि 27 = 3³, अतः 27² = (3³)²। (e) सत्य, क्योंकि दोनों पक्ष 2¹² के बराबर हैं। | Hindi | dual_sourced_no_translation | 0b9063f85b | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.2 Q1(a-e) | Solve using the division rule of exponents: (a) 6⁵ / 6³ (b) 27⁸ / 27² (c) 13^m / 13^n (d) (mn)⁷ / (mn)² (e) x¹¹ / x⁴ | (a) 6⁵ / 6³ = 6^(5-3) = 6². (b) 27⁸ / 27² = 27^(8-2) = 27⁶. (c) 13^m / 13^n = 13^(m-n). (d) (mn)⁷ / (mn)² = (mn)^(7-2) = (mn)⁵. (e) x¹¹ / x⁴ = x^(11-4) = x⁷. | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | नियम–4 की सहायता से घातीय रूप में हल करें: (a) 6⁵ / 6³ (b) 27⁸ / 27² (c) 13^m / 13^n (d) (mn)⁷ / (mn)² (e) x¹¹ / x⁴ | (a) 6⁵ / 6³ = 6^(5-3) = 6²। (b) 27⁸ / 27² = 27^(8-2) = 27⁶। (c) 13^m / 13^n = 13^(m-n)। (d) (mn)⁷ / (mn)² = (mn)^(7-2) = (mn)⁵। (e) x¹¹ / x⁴ = x^(11-4) = x⁷। | Hindi | dual_sourced_no_translation | 271742be1e | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.2 Q7(i-v) | Find the value of x: (i) 2^x = 4 (ii) 4^x = 64 (iii) 8^x = 1 (iv) 3^x = 1/3 (v) 4^x = 1/64 | (i) 2^x = 2², so x = 2. (ii) 4^x = 4³, so x = 3. (iii) 8^x = 8⁰ = 1, so x = 0. (iv) 3^x = 3⁻¹, so x = -1. (v) 4^x = 4⁻³ (since 4³ = 64), so x = -3. | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | x का मान निकालिए: (i) 2^x = 4 (ii) 4^x = 64 (iii) 8^x = 1 (iv) 3^x = 1/3 (v) 4^x = 1/64 | (i) 2^x = 2², अतः x = 2। (ii) 4^x = 4³, अतः x = 3। (iii) 8^x = 8⁰ = 1, अतः x = 0। (iv) 3^x = 3⁻¹, अतः x = -1। (v) 4^x = 4⁻³ (चूँकि 4³ = 64), अतः x = -3। | Hindi | dual_sourced_no_translation | 34e524f706 | dual_sourced_independent |
CGBSE | 7 | Mathematics | 6 | Exponents | Ex6.2 Q8 | World population is about 5×10⁹ and the surface area of the world is about 4×10¹¹ square km. How many persons live per square km? | Persons per sq km = (5×10⁹)/(4×10¹¹) = (5/4) x 10^(9-11) = 1.25 × 10⁻². | https://www.netexplanations.com/chhattisgarh-class-7-math-exponents-solution/ | https://cgbsesolutions.com/class-7-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 7 Ganit, SCERT Chhattisgarh | घातांक | विश्व की जनसंख्या लगभग 5×10⁹ है तथा विश्व का सतही क्षेत्रफल लगभग 4×10¹¹ वर्ग किलोमीटर है तो प्रति वर्ग किलोमीटर कितने व्यक्ति रहते हैं? | प्रति वर्ग किलोमीटर व्यक्ति = (5×10⁹)/(4×10¹¹) = (5/4) x 10^(9-11) = 1.25 × 10⁻²। | Hindi | dual_sourced_no_translation | 5f62ad99c3 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 3 | Exponents | Ex3.1 Q1(i-iii) | Find the value of: (i) (1/2)⁻⁵ (ii) (1/3)⁻⁴ (iii) 6⁷ x 2⁻³ x 3⁻⁷ | (i) (1/2)⁻⁵ = 2⁵ = 32. (ii) (1/3)⁻⁴ = 3⁴ = 81. (iii) 6⁷ = 2⁷ x 3⁷, so 6⁷ x 2⁻³ x 3⁻⁷ = 2⁷ x 3⁷ x 2⁻³ x 3⁻⁷ = 2^(7-3) x 3^(7-7) = 2⁴ x 3⁰ = 16 × 1 = 16. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-3-exponent-exercise-3-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | घातांक | निम्नलिखित के मान ज्ञात कीजिए: (i) (1/2)⁻⁵ (ii) (1/3)⁻⁴ (iii) 6⁷ x 2⁻³ x 3⁻⁷ | (i) (1/2)⁻⁵ = 2⁵ = 32। (ii) (1/3)⁻⁴ = 3⁴ = 81। (iii) 6⁷ = 2⁷ x 3⁷, अतः 6⁷ x 2⁻³ x 3⁻⁷ = 2⁷ x 3⁷ x 2⁻³ x 3⁻⁷ = 2^(7-3) x 3^(7-7) = 2⁴ x 3⁰ = 16 × 1 = 16। | Hindi | dual_sourced_no_translation | e2f8e6f947 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 3 | Exponents | Ex3.1 Q2(i-iii) | Simplify: (i) (-4)³ x (-2)⁻³ (ii) (-3)⁴ x (5/3)⁴ (iii) (-5)³ / (5)⁻⁷ | (i) (-4)³ x (-2)⁻³ = -64 x (-1/8) = 8. (ii) (-3)⁴ x (5/3)⁴ = 81 x (625/81) = 625. (iii) (-5)³ / 5⁻⁷ = -125 × 5⁷ = -125 × 78125 = -9765625. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-3-exponent-exercise-3-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | घातांक | निम्नलिखित को सरल कीजिए: (i) (-4)³ x (-2)⁻³ (ii) (-3)⁴ x (5/3)⁴ (iii) (-5)³ / (5)⁻⁷ | (i) (-4)³ x (-2)⁻³ = -64 x (-1/8) = 8। (ii) (-3)⁴ x (5/3)⁴ = 81 x (625/81) = 625। (iii) (-5)³ / 5⁻⁷ = -125 × 5⁷ = -125 × 78125 = -9765625। | Hindi | dual_sourced_no_translation | 1b950acfcc | dual_sourced_independent |
CGBSE | 9 | Mathematics | 3 | Exponents | Ex3.1 Q5(i-iii) | Write the following numbers in standard form: (i) 0.00000000000852 (ii) 8020000000000000 (iii) 41960000000 | (i) 8.52 × 10⁻¹². (ii) 8.02 × 10¹⁵. (iii) 4.196 × 10¹⁰. | https://www.netexplanations.com/chhattisgarh-class-9-maths-solution-chapter-3-exponent-exercise-3-1/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-3/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | घातांक | निम्नलिखित संख्याओं को मानक रूप में लिखिए: (i) 0.00000000000852 (ii) 8020000000000000 (iii) 41960000000 | (i) 8.52 × 10⁻¹²। (ii) 8.02 × 10¹⁵। (iii) 4.196 × 10¹⁰। | Hindi | dual_sourced_no_translation | 4aa6214838 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 6 | Playing with Numbers | Ex6.2 Q1 | Which of the following numbers are multiples of 5 and of 10: 316, 9560, 205, 311, 800, 7936? | Multiples of 5 (unit digit 0 or 5): 9560, 205, 800. Multiples of 10 (unit digit 0): 9560, 800. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-6-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | संख्याओं में भी है खेल | निम्नलिखित में से कौन-सी संख्याये 5 और 10 की गुणज है? 316, 9560, 205, 311, 800, 7936 | 5 की गुणज (इकाई स्थान पर 0 या 5): 9560, 205, 800। 10 की गुणज (इकाई स्थान पर 0): 9560, 800। | Hindi | dual_sourced_no_translation | 7a632a992a | dual_sourced_independent |
CGBSE | 9 | Mathematics | 6 | Playing with Numbers | Ex6.2 Q3 | If the number 35P is a multiple of 5, find the value of P. | For a number to be a multiple of 5, its unit digit must be 0 or 5. So P = 0 or P = 5. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-6-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | संख्याओं में भी है खेल | संख्या 35P, 5 का एक गुणज है तो P का मान बताईये। | 5 का गुणज होने के लिए इकाई स्थान पर 0 या 5 होना आवश्यक है। अतः P = 0 या P = 5। | Hindi | dual_sourced_no_translation | db7f6fabd8 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 6 | Playing with Numbers | Ex6.2 Q4 | The number 6A3B is divisible by 9. Find the possible values of A and B. | For divisibility by 9, the digit sum must be a multiple of 9: 6+A+3+B = 9+A+B. So A+B must equal 9 (taking the non-trivial case). Possible digit pairs (A,B): (0,9),(1,8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1),(9,0). | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-6-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-6/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | संख्याओं में भी है खेल | 6A3B, 9 से विभाजित एक संख्या है। A तथा B के मान ज्ञात कीजिये। | 9 से विभाज्य होने के लिए अंकों का योग 9 का गुणज होना चाहिए: 6+A+3+B = 9+A+B। अतः A+B = 9 होना चाहिए। संभावित मान (A,B): (0,9),(1,8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1),(9,0)। | Hindi | dual_sourced_no_translation | ee7f71a197 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.1 Q1(i) | In right triangle ABC, angle B = 90°. If AC=5, AB=3, BC=4, find sinA, cosC and tanA. | Check: 3²+4²=9+16=25=5², valid right triangle. sinA = BC/AC = 4/5. cosC = BC/AC = 4/5. tanA = BC/AB = 4/3. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि समकोण त्रिभुज ABC में ∠B समकोण है और AC=5, AB=3, BC=4 हो तो sinA, cosC, tanA का मान ज्ञात कीजिए। | जाँच: 3²+4²=9+16=25=5², अतः यह समकोण त्रिभुज है। sinA = BC/AC = 4/5। cosC = BC/AC = 4/5। tanA = BC/AB = 4/3। | Hindi | dual_sourced_no_translation | bc39a92cd0 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.1 Q1(ii) | In right triangle ABC, angle B = 90°. If AB=12, BC=5, AC=13, find sinA, cosC and tanA. | Check: 12²+5²=144+25=169=13², valid right triangle. sinA = BC/AC = 5/13. cosC = BC/AC = 5/13. tanA = BC/AB = 5/12. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि समकोण त्रिभुज ABC में ∠B समकोण है और AB=12, BC=5, AC=13 हो तो sinA, cosC, tanA का मान ज्ञात कीजिए। | जाँच: 12²+5²=144+25=169=13², अतः यह समकोण त्रिभुज है। sinA = BC/AC = 5/13। cosC = BC/AC = 5/13। tanA = BC/AB = 5/12। | Hindi | dual_sourced_no_translation | ac5c45a353 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.1 Q1(iii) | In right triangle ABC, angle B = 90°. If AB=5, AC=13, BC=12, find sinA, cosC and tanA. | Check: 5²+12²=25+144=169=13², valid right triangle. sinA = BC/AC = 12/13. cosC = BC/AC = 12/13. tanA = BC/AB = 12/5. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि समकोण त्रिभुज ABC में ∠B समकोण है और AB=5, AC=13, BC=12 हो तो sinA, cosC, tanA का मान ज्ञात कीजिए। | जाँच: 5²+12²=25+144=169=13², अतः यह समकोण त्रिभुज है। sinA = BC/AC = 12/13। cosC = BC/AC = 12/13। tanA = BC/AB = 12/5। | Hindi | dual_sourced_no_translation | 698ace4807 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.1 Q1(iv) | In right triangle ABC, angle B = 90°. If BC=12, AB=9, AC=15, find sinA, cosC and tanA. | Check: 12²+9²=144+81=225=15², valid right triangle. sinA = BC/AC = 12/15 = 4/5. cosC = BC/AC = 4/5. tanA = BC/AB = 12/9 = 4/3. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि समकोण त्रिभुज ABC में ∠B समकोण है और BC=12, AB=9, AC=15 हो तो sinA, cosC, tanA का मान ज्ञात कीजिए। | जाँच: 12²+9²=144+81=225=15², अतः यह समकोण त्रिभुज है। sinA = BC/AC = 12/15 = 4/5। cosC = BC/AC = 4/5। tanA = BC/AB = 12/9 = 4/3। | Hindi | dual_sourced_no_translation | adc253bb89 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.2 Q1(i) | If tan(theta) = 3/4, find sin(theta), cos(theta), cosec(theta), sec(theta) and cot(theta). | Using a right triangle with opposite=3, adjacent=4, hypotenuse=5 (3-4-5 triple): sin(theta)=3/5, cos(theta)=4/5, cosec(theta)=5/3, sec(theta)=5/4, cot(theta)=4/3. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि tanθ = 3/4 हो, तो sinθ, cosθ, cosecθ, secθ तथा cotθ ज्ञात कीजिए। | समकोण त्रिभुज में लम्ब=3, आधार=4, कर्ण=5 (3-4-5 त्रिक) लेने पर: sinθ = 3/5, cosθ = 4/5, cosecθ = 5/3, secθ = 5/4, cotθ = 4/3। | Hindi | dual_sourced_no_translation | 6b59985535 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.2 Q1(ii) | If sin(theta) = 5/13, find cos(theta), tan(theta), cot(theta), sec(theta) and cosec(theta). | Using a right triangle with opposite=5, hypotenuse=13, adjacent=12 (5-12-13 triple): cos(theta)=12/13, tan(theta)=5/12, cot(theta)=12/5, sec(theta)=13/12, cosec(theta)=13/5. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि sinθ = 5/13 हो, तो cosθ, tanθ, cotθ, secθ तथा cosecθ ज्ञात कीजिए। | समकोण त्रिभुज में लम्ब=5, कर्ण=13, आधार=12 (5-12-13 त्रिक) लेने पर: cosθ = 12/13, tanθ = 5/12, cotθ = 12/5, secθ = 13/12, cosecθ = 13/5। | Hindi | dual_sourced_no_translation | c7e794500a | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.2 Q1(vi) | If sec(theta) = 2, find cos(theta), sin(theta), cosec(theta), tan(theta) and cot(theta). | cos(theta) = 1/2, so theta = 60° (a standard 30-60-90 triangle: adjacent=1, hypotenuse=2, opposite=√(3)). sin(theta) = √(3)/2, cosec(theta) = 2/√(3), tan(theta) = √(3), cot(theta) = 1/√(3). | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | यदि secθ = 2 हो, तो cosθ, sinθ, cosecθ, tanθ तथा cotθ ज्ञात कीजिए। | cosθ = 1/2, अतः θ = 60 डिग्री (30-60-90 त्रिभुज: आधार=1, कर्ण=2, लम्ब=√3)। sinθ = √3/2, cosecθ = 2/√3, tanθ = √3, cotθ = 1/√3। | Hindi | dual_sourced_no_translation | 3662df74e6 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 8 | Trigonometric Ratios and Identities | Ex8.3 Q3 | State true or false: (i) sin30 cos60 + cos30 sin60 = tan90 (ii) 1 - 2sin²(30) = cos²(60) (iii) 2cos²(45) - 1 = cos90 (iv) sin²(45) = 1 - cos²(45) (v) sin²(60) + cos²(60) = 1 | (i) False: LHS = sin(30+60) = sin90 = 1, but tan90 is undefined. (ii) False: LHS = 1 - 2(1/4) = 1/2, RHS = 1/4, not equal. (iii) True: LHS = 2(1/2) - 1 = 0, RHS = cos90 = 0. (iv) True: both sides equal 1/2 (Pythagorean identity). (v) True: this is the Pythagorean identity, always equal to 1. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-8-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-8/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | त्रिकोणमितीय अनुपात एवं सर्वसमिकाएँ | सही अथवा गलत बताइए: (i) sin30 cos60 + cos30 sin60 = tan90 (ii) 1 - 2sin² 30 = cos² 60 (iii) 2cos² 45 - 1 = cos90 (iv) sin² 45 = 1 - cos² 45 (v) sin² 60 + cos² 60 = 1 | (i) असत्य: LHS = sin(30+60) = sin90 = 1, परंतु tan90 अपरिभाषित है। (ii) असत्य: LHS = 1 - 2(1/4) = 1/2, RHS = 1/4, बराबर नहीं। (iii) सत्य: LHS = 2(1/2) - 1 = 0, RHS = cos90 = 0। (iv) सत्य: दोनों पक्ष 1/2 के बराबर हैं (पाइथागोरस सर्वसमिका)। (v) सत्य: यह पाइथागोरस सर्वसमिका है, सदैव 1 के बराबर। | Hindi | dual_sourced_no_translation | 67830d1238 | dual_sourced_independent |
CGBSE | 9 | Mathematics | 14 | Sector of a Circle and Length of Arc | Q1 | Find the circumference of a circle whose radius is 17.5 cm. (Use π = 22/7) | Circumference = 2 x π x r = 2 x (22/7) x 17.5 = 110 cm. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-14-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वृत्त का त्रिज्याखण्ड एवं चाप की लम्बाई | उस वृत्त की परिधि ज्ञात कीजिए, जिसकी त्रिज्या 17.5 सेमी है। (π = 22/7 लीजिए) | परिधि = 2 x π x r = 2 x (22/7) x 17.5 = 110 सेमी। | Hindi | dual_sourced_no_translation | 75cee4f7fc | dual_sourced_independent |
CGBSE | 9 | Mathematics | 14 | Sector of a Circle and Length of Arc | Q3 | A horse is tied with a 14-metre rope on open ground. Find the area it can graze. | Since the ground is open, the horse can graze a full circle of radius 14 m. Area = π x r² = (22/7) x 14 × 14 = 616 sq metres. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-14-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वृत्त का त्रिज्याखण्ड एवं चाप की लम्बाई | घास के मैदान में एक घोड़ा 14 मीटर लंबी रस्सी से बंधा हुआ है। बताइये वह मैदान के कितने क्षेत्रफल के घास चर सकता है? | चूँकि मैदान खुला है, घोड़ा 14 मीटर त्रिज्या का पूर्ण वृत्त चर सकता है। क्षेत्रफल = π x r² = (22/7) x 14 × 14 = 616 वर्ग मीटर। | Hindi | dual_sourced_no_translation | 7a2271e7fa | dual_sourced_independent |
CGBSE | 9 | Mathematics | 14 | Sector of a Circle and Length of Arc | Q4 | The radius of a bicycle wheel is 35 cm. How much distance will it cover in 500 complete rotations? (Use π = 22/7) | Circumference = 2 x π x r = 2 x (22/7) x 35 = 220 cm. Distance in 500 rotations = 500 × 220 = 110000 cm = 1100 m = 1.1 km. | https://www.netexplanations.com/chhattisgarh-state-class-9-math-chapter-14-solution/ | https://cgbsesolutions.com/class-9-maths-solutions-chapter-14/ | Chhattisgarh Board (CGBSE) Class 9 Ganit, SCERT Chhattisgarh | वृत्त का त्रिज्याखण्ड एवं चाप की लम्बाई | एक साइकिल के पहिये की त्रिज्या 35 सेमी है, 500 पुरे चक्कर लगाने में यह कितनी दूरी तय करेगा? | परिधि = 2 x π x r = 2 x (22/7) x 35 = 220 सेमी। 500 चक्करों में दूरी = 500 × 220 = 110000 सेमी = 1100 मीटर = 1.1 किमी। | Hindi | dual_sourced_no_translation | 95482c6899 | dual_sourced_independent |
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