Mathematics Test 156

Result

Mathematics Test 156

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Question 1
4 / -1

The domain of the function

A
[–2, –1) ∪ (1, 2]

B
(–2, –1] ∪ [1, 2]

C
[–2, –1] ∪ [1, 2]

D
(–2, –1), ∪ (1, 2)

Solution
Question 2
4 / -1

The number of integral values of ‘a’ for which the system of linear equations x sin θ – 2y cos θ – az = 0, x + 2y + z = 0, –x + y + z = 0 may have non-trivial solutions, then which of the following is incorrect :

A
at a = 2 the given system will have finite solutions for θ ∈ R

B
number of possible integral values of a is 3

C
for a = 1 the system can have infinite solutions

D
for a = 3 the system will have unique solution

Solution
Question 3
4 / -1

then 4S is equal to

A
5

B
10

C
1

D
15

Solution
Question 4
4 / -1

If n is a factor of 72, such that xy = n, then number of ordered pairs (x, y) are (where x, y ∈ N) :

A
40

B
50

C
60

D
70

Solution

Let xyz = 72 = 2³ × 3²

then number of solutions are

^3+3–1C_3–1 × ^2+3–1C_3–1

= ⁵C₂ × ⁴C₂ = 10 × 6 = 60
Question 5
4 / -1

Letwhere α ∈ R, suppose Q = [q_ij]_3×3 matrix such that PQ = kl₃ for some non-zero k ∈ R. If q₂₃

A
Even number

B
Prime number

C
Composite number

D
a number divisible by 3

Solution
Question 6
4 / -1

Suppose a population X has 50 observations 51, 52, 53 ... 100 and another population Y has 50 observations 151, 152, 153 ... 200. If V_x and V_y be variances of the sets X and Y respectively such that V_x = λV_y, then λ is equal to

A
0

B
1

C
3

D
None of these

Solution

X : 51, 52, 53 ...100

Y : 151, 152, 153 ... 200

V_x = V_y hence λ = 1
Question 7
4 / -1

Let A and B be two events such that

A

B

C
A and B are independent events

D
P(A) < P(B)

Solution
Question 8
4 / -1

A
f(x) is continuous and differentiable for all x ∈ R

B
f(x) is continuous but not differentiable for all x ∈ R

C
f(x) is discontinuous at infinite number of points.

D
f(x) is discontinuous at finite number of points.

Solution

x² + 2x + 3 + sin πx = (x + 1)² + 2 + sin π x > 1

∴ f(x) = 1 ∀ x ∈ R
Question 9
4 / -1

x ∈ [0, 1] and a ∈ [2, 3] then which of the following is correct :

A
Minimum value of f(x) is at x = 0 in interval [0, 1]

B
Maximum value of f(x) in [0, 1] is at x = 1

C
Minimum value of f(x) in [0, 1] is

D
Maximum value of f(x) in [0, 1] is

Solution

f′(x) is –ve

⇒ f(x) is decreasing function
Hence maximum value is at x = 0
Question 10
4 / -1

Given f(x) = x ℓn x. Let Δ denotes the area bounded by y = f(x), x = a, x = a³ and x-axis, for 0 < a < 1. Mark the correct statement :

A
Δ is maximum when

B
Δ is minimum when a = 1/2

C
Δ is maximum when

D
None of these

Solution