**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 log

_{10 }2 = 0.3010, then log

_{2}10 is equal to —

(A) 0.3010

(B) 0.6990

(C) 1000/301

**(Ans)**

(D) 699/301

**Explanation :**log

_{2 }10 = 1/log

_{10 }2

= 1/0.3010 = 1000/301

**_ _**

9

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 * 10

^{4}/ 6.198 = 1/6.198 * 10,000

= 0.16134 * 10,000

= 1613.4

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