Surds and Indices
Q11. If x = ya, y = zb, z=xc then abc = ?
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1
z = xc = (ya)c = yac = (zb)ac = zabc
∴ z1 = zabc ⇒ abc = 1
Q12. If x = √3/2 then √(1+x) + √(1-x) = ?
(a) √1
(b) √3
(c) √5
(d) √8
Answer: (b) √3
We have ( √(1+x) + √(1+x) )2 = 1+x+1-x+2√(1+x)(1-x)
= 2 + 2√(1-x2)
= 2 + 2√(1 - 3/4)
= 2 + 2√(1/4)
= 2 + 2 . ½ = 2 + 1 = 3
∴ √(1+x) + √ (1-x) = √3
Q13. The greatest among (√7 - √5), (√5 - √3), (√9 - √7), (√11 - √9) is
(a) √7 - √5
(b) √5 - √3
(c) √9 - √7
(d) √11 - √9
Answer: (b) √5 - √3
√7 - √5 | (√7 - √5)(√7 + √5) | = | 7 - 5 | = | 2 |
(√7 + √5) | (√7 + √5) | (√7 + √5) |
√5 - √3 | (√5 - √3)(√5 + √3) | = | 5 - 3 | = | 2 |
(√5 + √3) | (√5 + √3) | (√5 + √3) |
√9 - √7 | (√9 - √7)(√9 + √7) | = | 9 - 7 | = | 2 |
(√9 + √7) | (√9 + √7) | (√9 + √7) |
√11 - √9 | (√11 - √9)(√11 + √9) | = | 11 - 9 | = | 2 |
(√11 + √9) | (√11 + √9) | (√11 + √9) |
∴ Greatest is √5 - √3
Q14. 23 X 22 X 2-5 = ?
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1
23 X 22 X 2-5 = 23+2-5 = 25-5 = 20 = 1
Q15. The greatest of √2, 6√3, 3√4, 4√5 is
(a) √2
(b) 6√3
(c) 3√4
(d) 4√5
Answer: (c) 3√4
√2 = 2½
6√3 = 31/6
3√4 = 41/3
4√5 = 5¼
LCM of 2, 6, 3, 4 = 12
Now √2 = 2½ = 26.(1/12) = (64)1/12
6√3 = 31/6 = 32.(1/12) = 91/12
3√4 = 41/3 = 44.(1/12) = 2561/12
4√5 = 5¼ = 53.(1/12) = 1251/12
Hence the greatest one is 2561/12 i.e 3√4
Practice Test Exam