**1) The value of 1/log _{4}120 + 1/log_{5}120 + 1/log_{6}120 is**

a) **0** b) **1** c) **24** d) **120**

**2) For a 3×3 matrix A, |A| = 4 and adj A = [(1 p 3) , (1 3 3) , (2 4 4)], then the value of p is**

a) **4 ** b) **11** c) **5** d) **0**

**3) A plane P which is perpendicular to two planes 2x-2y+z = 0 & x-y+2z = 4, passes through (1,-2,1) . The distance of the plane P from the point Q (1,2,2) is**

a) **0 ** b) **1** c) **√2** d) **2√2**

**4) The area enclosed between the curves x = ay ^{2} and y = ax^{2} , a > 0 is 1sq. unit, then the value of ‘a’ is**

a) **1/√3 ** b) **1/3** c) **√3** d) **3**

**5) A fair coin is tossed repeatedly. If the tail appears on first four tosses, then probability of the head appearing in the fifth toss equals**

a) **1/2 ** b) **1/8** c) **1/16** d) **1/32**

**6) The number of arrangements of the letters in the word ‘POTATO’, in which two ‘T’s do not appear adjacently, is**

a) **40 ** b) **60** c) **80** d) **120**

**7) If 3 ^{rd}, 6^{th} & 11^{th} terms of an Arithmetic Progression are in Geometric Progression, then the common ratio of the Geometric Progression is**

a) **4/3 ** b) **5/3** c) **8/3** d) **11/3**

**8) If non-zero numbers a,b,c are in Harmonic Progression, then the straight line x/a + y/b + 1/c = 0 always passes through the fixed point**

a) **(-1,-2) ** b) **(-1,2)** c) **(1,-1/2)** d) **(1,-2)**

**9) The value of ∫ √(1-x)/√(1+x) dx is (interval 0-1)**

a) **π/2 + 1 ** b) **1** c) **π/2 – 1** d) **-1**

**10) The value of 3[sin ^{4}(3π/2 – a) + sin^{4}(3π + a)] – 2[sin^{6}(π/2 + a) + sin^{6}(5π – a)] is**

a) **0 ** b) **1** c) **3** d) **sin4a + cosa**

**11) The number of integral values of k for which the equation 7cosx+5sinx = 2k+1 has a solution is**

a) **4 ** b) **8** c) **10** d) **12**

**12) The orthocenter of the triangle formed by the lines x = 0 , y = 0 and x+y = 1 is **

a) **(1/3 , 1/3) ** b) **(1/2 , 1/2)** c) **(0 , 0)** d) **(1 , 1)**

**13) The sum of the series 20C _{0} – 20C_{1} + 20C_{2} – … + 20C_{10 }is **

a) **0 ** b) **20C _{10}** c)

**-1/2 20C**d)

_{10}**1/2 20C**

_{10}**14) The value of lim x→π/2 (1-tan x/2)(1-sin x)/(1+tan x/2)(π-2x) ^{3 }is **

a) **0 ** b) **1/32** c) **infinity** d) **1/8**

**15) If log _{x}(16/9) = -1/2 , then the value of x is equal to**

a) **3/4 ** b) **4/3** c) **81/256** d) **256/81**