TEST PAPER 1
Total Questions: 75
1. The set of all integers x such that |x – 3| < 2 is equal to (a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4} (c) {2, 3, 4} (d) {-4, -3, -2} The Range of the function f(x) = (a) R (c) (-1) 3. The value of (i)i is (a) ω (c) e-π/2
x−2 is 2−x
Time allotted 90 minutes
2.
(b) R – {1} (d) R – {-1} (b) ω2 (d) 2√2
4.
( cos θ + isin θ ) is equal to 5 ( i cos θ + sin θ )
4
(a) cos − isin θ (c) sin θ − i cos θ 5.
(b) cos9θ − isin 9θ (d) sin 9θ − i cos9θ
The roots of the quadratic equation ax 2 + bx + c = 0 will be reciprocal to each other if (a) a = 1/c (b) a = c (c) b = ac (d) a = b If α, β are the roots of ax 2 − 2bx + c = 0 then α3β3 + α 2β3 + α 3β2 is
c 2 ( c + 2b ) a3 2 c (c) 3 a
6.
(a)
(b)
bc3 a3
(d) None of these
7.
The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is (a) 1/39 (b) 1/28 (c) 1/17 (d) 1/6 Let Sn denote the sum of first n terms of an A.P.. If S2n = 3Sn, then the ratio S3n / 5n is equal to (a) 4 (b) 6 (c) 8 (d) 10 Solution of |3 – x| = x – 3 is (a) x < 3 (b) x > 3 (c) x > 3 (d) x < 3 If the product of n positive numbers in 1, then their sum is (a) a positive integer (b) divisible by n (c) equal to n +
1 n
8.
9.
10.
(d) never less than n
11.
A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
(a) 112 (c) 164 12.
(b) 140 (d) None of these
For 1 ≤ r ≤ n, the value of nCr + n −1 Cr + n − 2 Cr + _ _ _ + r Cr is (a) nC r +1 (c) n +1 Cr +1 (b) n +1 Cr (d) None of them.
13.
2.42n +1 + 33n +1 is divisible by
(a) 2 (c) 11 14.
(b) 9 (d) 27
Pn +1 equals Pn
If Pn denotes the product of the binomial coefficients in the expansions of (1 + x)n, the (a) (c)
n +! n!
(b)
n +1
nn n!
( n + 1)
n!
(d)
( n + 1) ! ( n + 1)
n +1
15.
If x is very large and n is a negative integer or...