Explore topic-wise MCQs in Engineering Mathematics.

This section includes 13 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 sqrt{4x^2+4x+5} dx ).

A. (2 left [ frac{1}{2} (x+ frac{1}{2}) sqrt{{(x+ frac{1}{2})^2+1)}} right ]+ln u2061 left [(x+ frac{1}{2})+ sqrt{(x+ frac{1}{2})^2+1} right ] )
B. (2 left [ frac{1}{2} sqrt{(x+ frac{1}{2})^2+1)} right ]+ frac{1}{2} ln u2061 left [(x+ frac{1}{2})+ sqrt{(x+ frac{1}{2})^2+1} right ] )
C. (2 left [ frac{1}{2} (x+ frac{1}{2}) sqrt{(x+ frac{1}{2})^2+1)} right ]+ frac{1}{2} ln u2061 left [(x+ frac{1}{2})+ sqrt{(x+ frac{1}{2})^2+1} right ] )
D. (2 left [(x+ frac{1}{2}) sqrt{{(x+ frac{1}{2})^2+1)}} right ]+ frac{1}{2} ln u2061 left [(x+ frac{1}{2})+ sqrt{(x+ frac{1}{2})^2+1} right ] )
Answer» D. (2 left [(x+ frac{1}{2}) sqrt{{(x+ frac{1}{2})^2+1)}} right ]+ frac{1}{2} ln u2061 left [(x+ frac{1}{2})+ sqrt{(x+ frac{1}{2})^2+1} right ] )
Discussion
2.

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

A. <sup>1</sup> <sub>8</sub> sin<sup>(-1)</sup> u2061(x + <sup>1</sup> <sub>2</sub>)
B. <sup>1</sup> <sub>4</sub> tan<sup>(-1)</sup> u2061(x + <sup>1</sup> <sub>2</sub>)
C. <sup>1</sup> <sub>8</sub> sec<sup>(-1)</sup> u2061(x + <sup>1</sup> <sub>2</sub>)
D. <sup>1</sup> <sub>4</sub> cos<sup>(-1)</sup> u2061(x + <sup>1</sup> <sub>2</sub>)
Answer» C. <sup>1</sup> <sub>8</sub> sec<sup>(-1)</sup> u2061(x + <sup>1</sup> <sub>2</sub>)
Discussion
3.

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

A. ( frac{2}{5} sqrt{tan u2061(x)}[5+sec^2 u2061(x)] )
B. ( frac{2}{5} sqrt{sec u2061(x)}[5+tan^2 u2061(x)] )
C. ( frac{2}{5} sqrt{tan u2061(x)}[6+tan^2 u2061(x)] )
D. ( frac{2}{5} sqrt{tan u2061(x)}[5+tan^2 u2061(x)] )
Answer» E.
Discussion
4.

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

A. ([ frac{cot^4 u2061(x)}{4}+ frac{cosec^6 u2061(x)}{6}] )
B. ([ frac{cosec^4 u2061(x)}{4}+ frac{cosec^6 u2061(x)}{6}] )
C. ([ frac{cot^4 u2061(x)}{4}+ frac{cot^6 u2061(x)}{6}] )
D. ([ frac{cosec^4 u2061(x)}{4}+ frac{cot^6 u2061(x)}{6}] )
Answer» D. ([ frac{cosec^4 u2061(x)}{4}+ frac{cot^6 u2061(x)}{6}] )
Discussion
5.

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

A. 2 ln u2061(t+3)-3 ln u2061(t+2)
B. 2 ln u2061(t+3)+3 ln u2061(t+2)
C. 3 ln u2061(t+3)-2 ln u2061(t+2)
D. 3 ln u2061(t+3)+2ln u2061(t+2)
Answer» D. 3 ln u2061(t+3)+2ln u2061(t+2)
Discussion
6.

Find the value of ln (x) x dx.

A. 3a<sup>2</sup>
B. a<sup>2</sup>
C. a
D. 1
Answer» B. a<sup>2</sup>
Discussion
7.

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

A. Area of f(x) within x1 &lt; x &lt; x<sub>2</sub>
B. Volume of f(x) within x1 &lt; x &lt; x<sub>2</sub>
C. Slope of f(x) within x1 &lt; x &lt; x<sub>2</sub>
D. Maximum value of f(x) within x1 &lt; x &lt; x<sub>2</sub>
Answer» B. Volume of f(x) within x1 &lt; x &lt; x<sub>2</sub>
Discussion
8.

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
9.

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
10.

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
11.

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

A. -e<sup>x</sup> Cos(x)
B. e<sup>x</sup> Cos(x)
C. -e<sup>x</sup> Sin(x)
D. e<sup>x</sup> Sin(x)
Answer» B. e<sup>x</sup> Cos(x)
Discussion
12.

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
13.

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