Explore topic-wise MCQs in Mathematics.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

What is the relation between f(x) and ℓ when the minimum value or least value function f is defined on a set A and ℓ ∈ f(A)?

A. f(x) < &ell; ∀ x ∈ A
B. f(x) ≤ &ell; ∀ x ∈ A
C. f(x) ≥ &ell; ∀ x ∈ A
D. f(x) > &ell; ∀ x ∈ A
Answer» D. f(x) > &ell; ∀ x ∈ A
Discussion
2.

What is the relation between f(x) and &ell; when the maximum value or greatest value function f is defined on a set A and &ell; ∈ f(A)?

A. f(x) < &ell; ∀ x ∈ A
B. f(x) ≤ &ell; ∀ x ∈ A
C. f(x) = &ell; ∀ x ∈ A
D. f(x) > &ell; ∀ x ∈ A
Answer» C. f(x) = &ell; ∀ x ∈ A
Discussion
3.

What is the mathematical expression for monotonically non-increasing function?

A. x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)c) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)d) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,
B. x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
Answer» C. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
Discussion
4.

What is the mathematical expression of non-decreasing function?

A. x1 > x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b) ∀ c ∈ ab) x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)c) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)d) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,
B. ∀ c ∈ ab) x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
Answer» C. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
Discussion
5.

What is the condition for a function f to be constant if f be continuous and differentiable on (a,b)?

A. f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)d) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,
B. ?a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)
C. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
D. f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)
Answer» D. f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)
Discussion
6.

What is the condition for a function f to be strictly decreasing if f be continuous and differentiable on (a,b)?

A. f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)d) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,
B. ?a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)
C. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
D. f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)
Answer» C. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
Discussion
7.

What is the condition for a function f to be strictly increasing if f be continuous and differentiable on (a,b)?

A. f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)c) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)d) f’(x) = 0 ∀ x1, x2 ∈ (a,
B. ?a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)
C. f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)
D. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
Answer» B. ?a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)
Discussion
8.

What is the condition for a function f to be decreasing if f be continuous and differentiable on (a,b)?

A. f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)d) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,
B. ?a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)
C. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
D. f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)
Answer» E.
Discussion
9.

What is the condition for a function f to be increasing if f be continuous and differentiable on (a,b)?

A. f’(x) < 0 ∀ x1, x2 ∈ (a,b)b) f’(x) > 0 ∀ x1, x2 ∈ (a,b)c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)d) f’(x) ≥ 0 ∀ x1, x2 ∈ (a,
B. ?a) f’(x) < 0 ∀ x1, x2 ∈ (a,b)b) f’(x) > 0 ∀ x1, x2 ∈ (a,b)
C. f’(x) = 0 ∀ x1, x2 ∈ (a,b)
D. f’(x) ≥ 0 ∀ x1, x2 ∈ (a,b)
Answer» E.
Discussion
10.

Monotonically increasing functions are usually referred to as decreasing functions.

A. True
B. False
Answer» C.
Discussion
11.

A monotonic function on [a,b] is either a monotonically increasing or monotonically decreasing function.

A. False
B. True
Answer» C.
Discussion
12.

What is the mathematical expression for a function to be strictly decreasing on (a,b)?

A. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) > f(x2) ∀ x1, x2 ∈ (a,b)c) x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)d) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,
B. ?a) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) > f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
Answer» C. x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)
Discussion
13.

What is the mathematical expression for a function to be strictly increasing on (a,b)?

A. x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)c) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)d) x1 = x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,
B. ?a) x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 = x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)
Answer» B. ?a) x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)
Discussion
14.

What is the mathematical expression for monotonically decreasing function?

A. x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)c) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)d) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,
B. x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
Answer» C. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
Discussion
15.

What is a monotonically increasing function?

A. x1 > x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b) ∀ c ∈ ab) x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)c) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)d) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,
B. ∀ c ∈ ab) x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
C. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
D. x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)
Answer» C. x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)
Discussion