1) The value of 1/log4120 + 1/log5120 + 1/log6120 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 = ay2 and y = ax2 , 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 3rd, 6th & 11th 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[sin4(3π/2 – a) + sin4(3π + a)] – 2[sin6(π/2 + a) + sin6(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 20C0 – 20C1 + 20C2 – … + 20C10 is
a) 0 b) 20C10 c) -1/2 20C10 d) 1/2 20C10
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 logx(16/9) = -1/2 , then the value of x is equal to
a) 3/4 b) 4/3 c) 81/256 d) 256/81
