MHT CET 2024 16 May Shift 2 Question Paper : Download PCM Question Paper with Answers PDF

MHT CET 2024 16 May Shift 2 Solution

Question 1:

A vector parallel to the line of intersection of the planes:

Plane 1: r · (3i - j + k) = 1
Plane 2: r · (i + 4j - 2k) = 2

(1) -2i + 7j + 13k
(2) 2i - 7j + 13k
(3) -i + 4j + 7k
(4) i - 4j + 7k

Question 2:

The angle between the lines, whose direction cosines l, m, n satisfy the equations:
l + m + n = 0 and 2l² + 2m² - n² = 0, is:

(1) 60°
(2) 180°
(3) 90°
(4) 30°

Question 3:

If X is a random variable with the probability mass function (p.m.f.) as follows:

P(X = x) =
For x = 0: 5/16
For x = 1: kx/48
For x = 2: 1/4
For x = 3: 1/4

(1) 1.1875
(2) 1.4375
(3) 1.5625
(4) 0.5625

Question 4:

The surface area of a spherical balloon is increasing at the rate of 2 cm²/sec. Then the rate of increase in the volume of the balloon, when the radius of the balloon is 6 cm, is:

(1) 4 cm³/sec
(2) 16 cm³/sec
(3) 36 cm³/sec
(4) 6 cm³/sec

Question 5:

If f(x) = 2x³ - 15x² - 144x - 7, then f(x) is strictly decreasing in:

(1) (-8, 3)
(2) (-3, 8)
(3) (3, 8)
(4) (-8, -3)

Question 6:

If y = (sin x)^y, then dy/dx is:

(1) y² cot x / (1 - y log(sin x))
(2) y² cot x / (1 - y log(x))
(3) y² cot x / (1 + y log(sin x))
(4) y² cot x / (1 + y log(x))

Question 7:

If sin^-1(x) + cos^-1(y) = 3π/10, then the value of cos^-1(x) + sin^-1(y) is:

(1) π/10
(2) 7π/10
(3) 9π/10
(4) 3π/10

Question 8:

sin^-1[sin(-600°)] + cot^-1(-√3) =

(1) π/6
(2) π/4
(3) π/3
(4) 7π/6

Question 9:

If A = [[0, 1, 2], [1, 2, 3], [3, a, 1]] and A^-1 = (1/2) [[1, -1, 1], [-8, 6, 2c], [5, -3, 1]], then values of a and c are respectively:

(1) 1/2, 1/2
(2) -1, 1
(3) 2, -1/2
(4) 1, -1

Question 10:

The p.m.f. of a random variable X is P(X) = 2x / [n(n + 1)], for x = 1, 2, 3, ..., n, and P(X) = 0 otherwise. Then E(X) is:

(1) (n + 1) / 3
(2) (2n + 1) / 3
(3) (n + 2) / 3
(4) (2n - 1) / 2