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.

Find ’C’ using Lagrange’s mean value theorem, if f(x) = ex, a = 0, b = 1.

A. ee-1
B. e-1
C. log\(_e^{e+1}\)
D. log\(_e^{e-1}\)
Answer» E.
Discussion
2.

What is the formula for Lagrange’s theorem?a) f’(c) = \(\frac {f(a)+f(b)}{b-a}\) b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\) c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\) d) f’(c) = \(\frac {f(

A. f’(c) = \(\frac {f(a)+f(b)}{b-a}\) b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\) c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\) d) f’(c) = \(\frac {f(a)-f(
B. }{b-a}\) b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\) c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\) d) f’(
C. = \(\frac {f(a)+f(b)}{b-a}\) b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\) c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\)
D. f’(c) = \(\frac {f(a)-f(b)}{b+a}\)
Answer» C. = \(\frac {f(a)+f(b)}{b-a}\) b) f’(c) = \(\frac {f(b)-f(a)}{b-a}\) c) f’(c) = \(\frac {f(a)+f(b)}{b+a}\)
Discussion
3.

Is Rolle’s theorem applicable to f(x) = tan x on [ \(\frac {\pi }{4}, \frac {5\pi }{4}\) ]?

A. Yes
B. No
Answer» C.
Discussion
4.

Rolle’s theorem is a special case of _____

A. Euclid’s theorem
B. another form of Rolle’s theorem
C. Lagrange’s mean value theorem
D. Joule’s theorem
Answer» D. Joule’s theorem
Discussion
5.

Lagrange’s mean value theorem is also called as _____

A. Euclid’s theorem
B. Rolle’s theorem
C. a special case of Rolle’s theorem
D. the mean value theorem
Answer» E.
Discussion
6.

Function f is differentiable on [a,b] to satisfy Lagrange’s mean value theorem.

A. True
B. False
Answer» B. False
Discussion
7.

What are/is the conditions to satify Lagrange’s mean value theorem?

A. f is continuous on [a,b] b) f is differentiable on (a,b)c) f is differentiable and continuous on (a,b)d) f is differentiable and non-continuous on (a,
B. f is differentiable on (a,b)
C. f is differentiable and continuous on (a,b)
D. f is differentiable and non-continuous on (a,b)
Answer» D. f is differentiable and non-continuous on (a,b)
Discussion
8.

Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.

A. False
B. True
Answer» B. True
Discussion
9.

What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?a) f(a) < f(a+h)b) f(a) = f(a+h)c) f(a) = f(a-h)d) f(

A. and f(h) according to another form of Rolle’s theorem?a) f(a) < f(a+h)
B. f(a) = f(a+h)
C. f(a) = f(a-h)
D. f(a) > f(a+h)
Answer» C. f(a) = f(a-h)
Discussion
10.

Another form of Rolle’s theorem for the continuous condition is _____

A. f is continuous on [a,a-h]
B. f is continuous on [a,h]
C. f is continuous on [a,a+h]
D. f is continuous on [a,ah]
Answer» D. f is continuous on [a,ah]
Discussion
11.

Another form of Rolle’s theorem for the differential condition is _____

A. f is differentiable on (a,ah)
B. f is differentiable on (a,a-h)
C. f is differentiable on (a,a/h)
D. f is differentiable on (a,a+h)
Answer» E.
Discussion
12.

Does Rolle’s theorem applicable if f(a) is not equal to f(b)?

A. is not equal to f(b)?a) Yes
B. ?a) Yesb) No
C. Under particular conditions
D. May be
Answer» C. Under particular conditions
Discussion
13.

What is the relation between f(a) and f(b) according to Rolle’s theorem?

A. and f(b) according to Rolle’s theorem?a) Equals to
B. according to Rolle’s theorem?a) Equals tob) Greater than
C. Less than
D. Unequal
Answer» B. according to Rolle’s theorem?a) Equals tob) Greater than
Discussion
14.

Function f is differential on (a,b) according to Rolle’s theorem.

A. True
B. according to Rolle’s theorem.a) Trueb) False
Answer» B. according to Rolle’s theorem.a) Trueb) False
Discussion
15.

Function f should be _____ on [a,b] according to Rolle’s theorem.

A. continuous
B. non-continuous
C. integral
D. non-existent
Answer» B. non-continuous
Discussion