Maths Answers Class 10 Ncert
ANSWERS/HINTS
345
APPENDIX 1 ANSWERS/ HINTS
EXERCISE 1.1
1. (i) 45 3. 8 columns 4. An integer can be of the form 3q, 3q + 1 or 3q + 2. Square all of these integers. 5. An integer can be of the form 9q, 9q + 1, 9q + 2, 9q + 3, . . ., or 9q + 8. (ii) 196 (iii) 51 2. An integer can be of the form 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4 or 6q + 5.
EXERCISE 1.2
1. 2. 3. (i) 2 × 5 × 7 (iv) 5 × 7 × 11 × 13 (i) LCM = 182; HCF = 13 (i) LCM = 420; HCF = 3
2
(ii) 22 × 3 × 13 (v) 17 × 19 × 23 (ii) LCM = 23460; HCF = 2 (ii) LCM = 1139; HCF = 1 7. 36 minutes
(iii) 32 × 52 × 17 (iii) LCM = 3024; HCF = 6 (iii) LCM = 1800; HCF = 1
4. 22338
EXERCISE 1.4
1. (i) Terminating (iii) Non-terminating repeating (v) Non-terminating repeating (vii) Non-terminating repeating (ix) Terminating 2. (i) 0.00416 (vi) 0.115 (ii) 2.125 (viii) 0.4 (ii) Terminating (iv) Terminating (vi) Terminating (viii) Terminating (x) Non-terminating repeating (iv) 0.009375 (ix) 0.7
346 3. (i) Rational, prime factors of q will be either 2 or 5 or both only. (ii) Not rational (iii) Rational, prime factors of q will also have a factor other than 2 or 5.
MATHEMATICS
EXERCISE 2.1
1. (i) No zeroes (ii) 1 (iii) 3 (iv) 2 (v) 4 (vi) 3
EXERCISE 2.2
1. (i) –2, 4 (iv) –2, 0 2. (i) 4x2 – x – 4 (iv) x2 – x + 1 (ii)
1 1 , 2 2
1 3 (iii) − , 3 2
(v) − 15, 15 (ii) 3 x2 − 3 2 x + 1 (v) 4x2 + x + 1
(vi) –1,
4 3
(iii) x2 + 5 (vi) x2 – 4x + 1
EXERCISE 2.3
1. (i) Quotient = x – 3 and remainder = 7x – 9 (ii) Quotient = x2 + x – 3 and remainder = 8 (iii) Quotient = – x2 – 2 and remainder = – 5x + 10 2. 5. (i) Yes (ii) Yes (iii) No 3. –1, 1 4. g(x) = x2 – x + 1 (i) p(x) = 2x2 – 2x + 14, g(x) = 2, q(x) = x2 – x + 7, r(x) = 0 (ii) p(x) = x3 + x2 + x + 1, g(x) = x2 – 1, q(x) = x + 1, r(x) = 2x + 2 (iii) p(x) = x3 + 2x2 – x + 2, g(x) = x2 – 1, q(x) = x + 2, r(x) = 4 There can be several examples in each of (i), (ii) and (iii).
EXERCISE 2.4 (Optional)*
2. x3 – 2x2 – 7x + 14 4. – 5, 7 3. a = 1, b = ± 2 5. k = 5 and a = –5
EXERCISE
345
APPENDIX 1 ANSWERS/ HINTS
EXERCISE 1.1
1. (i) 45 3. 8 columns 4. An integer can be of the form 3q, 3q + 1 or 3q + 2. Square all of these integers. 5. An integer can be of the form 9q, 9q + 1, 9q + 2, 9q + 3, . . ., or 9q + 8. (ii) 196 (iii) 51 2. An integer can be of the form 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4 or 6q + 5.
EXERCISE 1.2
1. 2. 3. (i) 2 × 5 × 7 (iv) 5 × 7 × 11 × 13 (i) LCM = 182; HCF = 13 (i) LCM = 420; HCF = 3
2
(ii) 22 × 3 × 13 (v) 17 × 19 × 23 (ii) LCM = 23460; HCF = 2 (ii) LCM = 1139; HCF = 1 7. 36 minutes
(iii) 32 × 52 × 17 (iii) LCM = 3024; HCF = 6 (iii) LCM = 1800; HCF = 1
4. 22338
EXERCISE 1.4
1. (i) Terminating (iii) Non-terminating repeating (v) Non-terminating repeating (vii) Non-terminating repeating (ix) Terminating 2. (i) 0.00416 (vi) 0.115 (ii) 2.125 (viii) 0.4 (ii) Terminating (iv) Terminating (vi) Terminating (viii) Terminating (x) Non-terminating repeating (iv) 0.009375 (ix) 0.7
346 3. (i) Rational, prime factors of q will be either 2 or 5 or both only. (ii) Not rational (iii) Rational, prime factors of q will also have a factor other than 2 or 5.
MATHEMATICS
EXERCISE 2.1
1. (i) No zeroes (ii) 1 (iii) 3 (iv) 2 (v) 4 (vi) 3
EXERCISE 2.2
1. (i) –2, 4 (iv) –2, 0 2. (i) 4x2 – x – 4 (iv) x2 – x + 1 (ii)
1 1 , 2 2
1 3 (iii) − , 3 2
(v) − 15, 15 (ii) 3 x2 − 3 2 x + 1 (v) 4x2 + x + 1
(vi) –1,
4 3
(iii) x2 + 5 (vi) x2 – 4x + 1
EXERCISE 2.3
1. (i) Quotient = x – 3 and remainder = 7x – 9 (ii) Quotient = x2 + x – 3 and remainder = 8 (iii) Quotient = – x2 – 2 and remainder = – 5x + 10 2. 5. (i) Yes (ii) Yes (iii) No 3. –1, 1 4. g(x) = x2 – x + 1 (i) p(x) = 2x2 – 2x + 14, g(x) = 2, q(x) = x2 – x + 7, r(x) = 0 (ii) p(x) = x3 + x2 + x + 1, g(x) = x2 – 1, q(x) = x + 1, r(x) = 2x + 2 (iii) p(x) = x3 + 2x2 – x + 2, g(x) = x2 – 1, q(x) = x + 2, r(x) = 4 There can be several examples in each of (i), (ii) and (iii).
EXERCISE 2.4 (Optional)*
2. x3 – 2x2 – 7x + 14 4. – 5, 7 3. a = 1, b = ± 2 5. k = 5 and a = –5
EXERCISE