Explore topic-wise MCQs in Engineering Mathematics.

This section includes 20 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the value of \(\int \frac{1}{4x^2+4x+5} dx\).

A. 1⁄8 sin(-1)⁡(x + 1⁄2)
B. 1⁄4 tan(-1)⁡(x + 1⁄2)
C. 1⁄8 sec(-1)⁡(x + 1⁄2)
D. 1⁄4 cos(-1)⁡(x + 1⁄2)
Answer» C. 1⁄8 sec(-1)⁡(x + 1⁄2)
Discussion
2.

Find the value of \(\int \frac{sec^4⁡(x)}{\sqrt{tan⁡(x)}} dx\).

A. \(\frac{2}{5}\sqrt{tan⁡(x)}[5+sec^2⁡(x)]\)
B. \(\frac{2}{5}\sqrt{sec⁡(x)}[5+tan^2⁡(x)]\)
C. \(\frac{2}{5}\sqrt{tan⁡(x)}[6+tan^2⁡(x)]\)
D. \(\frac{2}{5}\sqrt{tan⁡(x)}[5+tan^2⁡(x)]\)
Answer» E.
Discussion
3.

Find the value of ∫ cot3(x) cosec4 (x).

A. –\([\frac{cot^4⁡(x)}{4}+\frac{cosec^6⁡(x)}{6}]\)
B. –\([\frac{cosec^4⁡(x)}{4}+\frac{cosec^6⁡(x)}{6}]\)
C. –\([\frac{cot^4⁡(x)}{4}+\frac{cot^6⁡(x)}{6}]\)
D. –\([\frac{cosec^4⁡(x)}{4}+\frac{cot^6⁡(x)}{6}]\)
Answer» D. –\([\frac{cosec^4⁡(x)}{4}+\frac{cot^6⁡(x)}{6}]\)
Discussion
4.

Find the value of ∫t⁄(t+3)(t+2) dt, is?

A. 2 ln⁡(t+3)-3 ln⁡(t+2)
B. 2 ln⁡(t+3)+3 ln⁡(t+2)
C. 3 ln⁡(t+3)-2 ln⁡(t+2)
D. 3 ln⁡(t+3)+2ln⁡(t+2)
Answer» D. 3 ln⁡(t+3)+2ln⁡(t+2)
Discussion
5.

Find the value of ∫ ln⁡(x)⁄x dx.

A. 3a2
B. a2
C. a
D. 1
Answer» B. a2
Discussion
6.

Integration of function y = f(x) from limit x1 < x < x2 , y1 < y < y2, gives ___________

A. Area of f(x) within x1 < x < x2
B. Volume of f(x) within x1 < x < x2
C. Slope of f(x) within x1 < x < x2
D. Maximum value of f(x) within x1 < x < x2
Answer» B. Volume of f(x) within x1 < x < x2
Discussion
7.

If differentiation of any function is infinite at any point and constant at other points then it means ___________

A. Function is parallel to x-axis at that point
B. Function is parallel to y-axis at that point
C. Function is constant
D. Function is discontinuous at that point
Answer» B. Function is parallel to y-axis at that point
Discussion
8.

If differentiation of any function is zero at any point and constant at other points then it means?

A. Function is parallel to x-axis at that point
B. Function is parallel to y-axis at that point
C. Function is constant
D. Function is discontinuous at that point
Answer» B. Function is parallel to y-axis at that point
Discussion
9.

Value of ∫ Cos2 (x) Sin2 (x)dx.

A. \(\frac{1}{8} [x-\frac{Cos(2x)}{2}]\)
B. \(\frac{1}{4} [x-\frac{Cos(2x)}{2}]\)
C. \(\frac{1}{8} [x-\frac{Sin(2x)}{2}]\)
D. \(\frac{1}{4} [x-\frac{Sin(2x)}{2}]\)
Answer» D. \(\frac{1}{4} [x-\frac{Sin(2x)}{2}]\)
Discussion
10.

Integration of (Sin(x) – Cos(x))ex is ___________

A. -ex Cos(x)
B. ex Cos(x)
C. -ex Sin(x)
D. ex Sin(x)
Answer» B. ex Cos(x)
Discussion
11.

Integration of (Sin(x) + Cos(x))ex is______________

A. ex Cos(x)
B. ex Sin(x)
C. ex Tan(x)
D. ex (Sin(x)+Cos(x))
Answer» C. ex Tan(x)
Discussion
12.

Integration of function is same as the ___________

A. Joining many small entities to create a large entity
B. Indefinitely small difference of a function
C. Multiplication of two function with very small change in value
D. Point where function neither have maximum value nor minimum value
Answer» B. Indefinitely small difference of a function
Discussion
13.

FIND_THE_AREA_INSIDE_A_FUNCTION_F(T)_=_T/(T+3)(T+2)_FROM_T_=_-1_TO_0?$

A. 4 ln⁡(3) – 5ln⁡(2)
B. 3 ln‚Å°(3)
C. 3 ln⁡(3) – 4ln⁡(2)
D. 3 ln⁡(3) – 5 ln⁡(2)
Answer» E.
Discussion
14.

Find the value of
A. <sup>1</sup>‚ÅÑ<sub>8</sub> sin<sup>-1</sup>(x + <sup>1</sup>‚ÅÑ<sub>2</sub>)
B. <sup>1</sup>‚ÅÑ<sub>8</sub> tan<sup>-1</sup>(x + <sup>1</sup>‚ÅÑ<sub>2</sub>)
C. <sup>1</sup>‚ÅÑ<sub>8</sub> sec<sup>-1</sup>(x + <sup>1</sup>‚ÅÑ<sub>2</sub>)
D. <sup>1</sup>‚ÅÑ<sub>4</sub> cos<sup>-1</sup>(x + <sup>1</sup>‚ÅÑ<sub>2</sub>)
Answer» C. <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>8</sub> sec<sup>-1</sup>(x + <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>)
Discussion
15.

Temperature of a rod is increased by moving x distance from origin and is given by equation T(x) = x2 + 2x , where x is the distance and T(x) is change of temperature w.r.t distance.If,at x = 0,temperature is 40 C,find temperature at,x=10 .
A. 473 C
B. 472 C
C. 474 C
D. 475 C
Answer» B. 472 C
Discussion
16.

Find the area ln(x)‚ÅÑx from x = x = aeb to ?#

A. <sup>b<sup>2</sup></sup>‚ÅÑ<sub>2</sub>
B. <sup>b</sup>‚ÅÑ<sub>2</sub>
C. b
D. 1
Answer» B. <sup>b</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>
Discussion
17.

Find the area of a function f(x) = x2 + xCos(x) from x = 0 to a, where , a>0,

A. <sup>a<sup>2</sup></sup>⁄<sub>2</sub> + aSin(a) + Cos(a) – 1
B. <sup>a<sup>3</sup></sup>‚ÅÑ<sub>3</sub> + aSin(a) + Cos(a)
C. <sup>a<sup>3</sup></sup>⁄<sub>3</sub> + aSin(a) + Cos(a) – 1
D. <sup>a<sup>3</sup></sup>⁄<sub>3</sub> + Cos(a) + Sin(a) – 1
Answer» D. <sup>a<sup>3</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>3</sub> + Cos(a) + Sin(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 1
Discussion
18.

Find the value of ‚à´x3 Sin(x)dx$

A. x<sup>3</sup> Cos(x) + 3x<sup>2</sup> Sin(x) + 6xCos(x) – 6Sin(x)
B. – x<sup>3</sup> Cos(x) + 3x<sup>2</sup> Sin(x) – 6Sin(x)
C. – x<sup>3</sup> Cos(x) – 3x<sup>2</sup> Sin(x) + 6xCos(x) – 6Sin(x)
D. – x<sup>3</sup> Cos(x) + 3x<sup>2</sup> Sin(x) + 6xCos(x) – 6Sin(x)
Answer» E.
Discussion
19.

Integration of (Sin(x) + Cos(x))ex is
A. e<sup>x</sup> Cos(x)
B. e<sup>x</sup> Sin(x)
C. e<sup>x</sup> Tan(x)
D. e<sup>x</sup> (Sin(x) + Cos(x))
Answer» C. e<sup>x</sup> Tan(x)
Discussion
20.

Find the value of ‚à´tan-1‚Å°(x)dx

A. sec<sup>-1</sup> (x) – <sup>1</sup>⁄<sub>2</sub> ln⁡(1 + x<sup>2</sup>)
B. xtan<sup>-1</sup> (x) – <sup>1</sup>⁄<sub>2</sub> ln⁡(1 + x<sup>2</sup>)
C. xsec<sup>-1</sup> (x) – <sup>1</sup>⁄<sub>2</sub> ln⁡(1 + x<sup>2</sup>)
D. tan<sup>-1</sup> (x) – <sup>1</sup>⁄<sub>2</sub> ln⁡(1 + x<sup>2</sup>)
Answer» C. xsec<sup>-1</sup> (x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1 + x<sup>2</sup>)
Discussion