MATHEMATICS

 1 If  f ( x ) = 2x + 3 , g ( x ) = 1 – x2  then the values of x that satisfy the equation   g o f ( x ) = 0 are (a)    2, -2            ( b )   1, -2           ( c )   0 , 3              ( d )  -1 , -2 2 Which one of the following is the solution of the equation  sec2 x – 2 tan x = 4 ?   (a)     π / 2           ( b )    π / 3           ( c )   - π / 4           ( d )    π  / 6 3 If the argument of the complex number is π / 2 then the value of a is ............................... 4 Which of the following statements is not true ? (a)  2n > n for all positive integers  n. (b)  For every positive integer n , 8n  – 5n  is divisible by 3. (c)  12 + 22 +32+ ... + n2  > for all  natural numbers n. (d)  n (n + 1) (n + 5) is  not a multiple of 3 where n is a positive integer. 5 From 7 consonants and 5 vowels, how many words ( with or without meaning ) can be formed consisting of 3 different  consonants and 2 different vowels? (a) 350           (b) 42,000          (c) 4,200            (d) 21, 000 6 If in a sequence the first term is a1 = -3 and the nth term is  an = 1 – 2 an-1 , what is the fourth term of the sequence ? (a)  27           (b)  - 21               (c)  31                (d)   - 25 7 If the mean of the data   9, x, 5, x, 12, 10, 18, 4, 7, 18, 21 is known to be 10, what is the value of x ? (a)  6               (b)  2                  (c)  3                 (d) 1 8 The length of latus rectum of the ellipse  36x2 + 4y2 = 144  is (a)  4/9           (b)  4/3                (c) 8/3              (d)  36 9 If R1 and R2 are two equivalence relations on a non‐empty set A, then (a) R1 U R2 is an equivalence relation on A (b) R1 ∩ R2 is an equivalence relation on A (c) R1– R2 is an equivalence relation on A (d) None of these 10 If  w is a complex cube root of unity and A  = , then A98 is equal to (a) w I            (b) w2                             (c) A2                         (d) A itself 11 If   y = 1 + + ....  to  infinity where  x > 1 then   dy / dx is (a) (b) (c) (d) 12 If a man of height 6 ft walks at a uniform speed of 9 ft / sec  from a lamp  of height  15 ft then the length of his shadow is increasing at the rate of (a ) 6 ft / sec      (b)   12  ft / sec           (c)  10 ft / sec          (d) 15 ft / sec. 13 is  (a)  - ( 2 + cot x ) -1  + c              (b)   - ( 2 + cot x ) -2  + c (c)  ( 2 + cot x ) -1  + c               (d)  -2 ( 2 + cot x ) -1   + c 14 The value of is (a)    π /2           (b)    3 π / 4             (c)   5 π/4          (d)    5 π /2 15 The area of the region bounded by the curve y = 2x − x2 and the line y = x is (a)  6 sq. units         (b)  ½  sq. units    (c)  1/6  sq. units     (d)   1/3  sq. units 16 The solution of the differential equation is  (a)   y =  ( x- 1 ) ex  + c          (b)   xy  = ( x -1 ) ex + c (c)   xy   =  ( x+ 1 ) e –x  + c    ( d )  y =  ( x – 1 ) e –x   + c 17 If a space vector makes angles 150° and 60°  with the positive direction of X and Y axes then the  angle made by the vector with the positive direction of Z‐axis is (a)   60o             (b)   120o          (c)   30o              (d)   90o 18 The equation of the plane passing through the origin and containing the lines whose direction cosines are proportional to 1, 2, 2 and 2, 1, −3 is (a)  8x  - 7 y + 3z  = 0           ( b )   8x  +7y  +3z  = 0 (c)  4x  - 7y – 3z + 2  = 0      (d )  6x  + 7y – 3z = 0 19 The maximum value of z = 10x + 6y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 12,  2x + y ≤ 20 is (a)  100              (b)   104            (c)   72                ( d )   120 20 Suppose that ﬁve good pens and two defective ones have been mixed up. To ﬁnd the defective ones, the pens are tested one-by-one, at random and without replacement. What is the probability that both the defective fuses are found in the first two tests? (a)  1/ 21            (b)  5/ 7              (c)  10 / 21             d)  3/ 7