1. If a = 5 + 2 √6, the value of √a - 1/√a is —
(A) 2 √2 (Ans)
(B) 2 √3
(C) 3 - √2
(D) 1 + √5
Explanation :
a = 5 + 2 √6
= (√3)2 + 2 (√3) * (√2) + (√2)2
= (√3 + √2)2
∴ √a = √3 + √2
∴ √a - 1/√a = (√3 + √2) - (1/√3 + √2)
= (√3 + √2)2 - 1 / (√3 + √2) = 5 + 2 √6 - 1 / √3 + √2
= 4 + 2 √6 / √3 + √2 = 2 √2 (√2 + √3) / √3 + √2
= 2 √2
2. Simplify —
√[(12.1)2 - (8.1)2 ÷ [(0.25)2 + (0.25) (19.95)]
(A) 1
(B) 2
(C) 3
(D) 4 (Ans)
Explanation :
√[(12.1)2 - (8.1)2 ÷ [(0.25)2 + (0.25) (19.95)]
= √[(12.1 + 8.1) (12.1 - 8.1)] ÷ [0.25 (0.25 + 19.95)]
= √(20.2 * 4) ÷ (0.25 * 20.2)
= √20.2 * 4 / 0.25 * 20.2 = √16 = 4
3. Simplify —
(2.3)3 - 0.027 / (2.3)2 + 0.69 + 0.09
(A) 0
(B) 1.6
(C) 2 (Ans)
(D) 3.4
4. On simplification of —
1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/100 we get —
(A) 2/27
(B) 1/9
(C) 5/27
(D) 6/55 (Ans)
5. If 0 < a < 1, then the value of a + 1/a is —
(A) Greater than 2 (Ans)
(B) Less than 2
(C) Greater than 4
(D) Less than 4
Explanation :
a + 1/a - 2 = (√a - 1/√a)2 = positive
∴ a + 1/a > 2
6. The simplification of
2.002 + 7.9 {2.8 - 6.3 (3.6 - 1.5) + 15.6} yields —
(A) 2.002
(B) 4.2845
(C) 40.843
(D) 42.845 (Ans)
7. The arrangement of rational numbers -7/10, 5/-8, 2/-3 in ascending order is —
(A) -7/10, 5/-8, 2/-3
(B) -7/10, 2/-3, 5/-8 (Ans)
(C) 2/-3, 5/-8, -7/10
(D) 5/-8, -7/10, 2/-3
Explanation :
-7/10 = -0.7
-5/8 = - 0.625
and 2/-3 = - 0.667
On writing these numbers in ascending order, we get
-7/10, 2/-3, and -5/8
8. Given that log10 2 = 0.3010, then log2 10 is equal to —
(A) 0.3010
(B) 0.6990
(C) 1000/301 (Ans)
(D) 699/301
Explanation : log2 10 = 1/log10 2
= 1/0.3010 = 1000/301
_ _
9. 3.9 + 5.7 is equal to —
_
(A) 9.6
_
(B) 8.6
_
(C) 7.6 (Ans)
_
(D) 1.6
_ _ Explanation : 3.9 + 5.7 = - 3 + .9 - 5 + .7
_
= - 8 + 1.6 = 7.6
10. If 1/6.198 = 0.16134, then the value of 1/0.0006198 is —
(A) 16134
(B) 1613.4 (Ans)
(C) 0.16134
(D) 0.016134
Explanation : 1/6.198 = 0.16134
∴ 1/0.0006198 = 1/6.198 * 10-4
= 1 * 104 / 6.198 = 1/6.198 * 10,000
= 0.16134 * 10,000
= 1613.4