Page 5 - ISC-12
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2Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
1 1
00
5. If f : R → R is a twice differentiable function such that f (x) > 0 for all x ∈ R, and f = ,
2 2
f(1) = 1, then
1 1
0
0
0
0
(A) f (1) ≤ 0. (B) 0 < f (1) ≤ . (C) < f (1) ≤ 1. (D) f (1) > 1.
2 2
[JEE 2017]
6. How many 3 × 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal
T
entries of M M is 5?
(A) 126. (B) 198. (C) 162. (D) 135.
[JEE 2017]
7. Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x+y+z = 10.
Then the probability that z is even, is
36 6 1 5
(A) . (B) . (C) . (D) .
55 11 2 11
[JEE 2017]
8. A computer producing factory has only two plants T 1 and T 2 . Plant T 1 produces 20% and plant T 2
produces 80% of the total computers produced. 7% of computers produced in the factory turn out to
be defective. It is known that
P(computer turns out to be defective given that it is produced in plant T 1 )
= 10 P(computer turns out to be defective given that it is produced in plant T 2 ),
where P(E) denotes the probability of an event E. A computer produced in the factory is randomly
selected and it does not turn out to be defective. Then the probability that it is produced in plant T 2 is
36 47 78 75
(A) . (B) . (C) . (D) .
73 79 93 83
[JEE 2016]
1
2
9. The least value of α ∈ R for which 4αx + ≥ 1, for all x > 0, is
x
1 1 1 1
(A) . (B) . (C) . (D) .
64 32 27 25
[JEE 2016]
1 0 0
10. Let P = 4 1 0 and I be the identity matrix of order 3. If Q = [q ij ] is a matrix such that
16 4 1
P 50 − Q = I, then q 31 + q 32 equals
q 21
(A) 52. (B) 103. (C) 201. (D) 205.
[JEE 2016]
