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.

If nth derivative of y = ( frac{x}{(x+1)(x+2)} ) is yn = a(-1)n+! n! (x+1)-n-1 + b(-1)nn!(x+2)-n-1 then find the value of a and b.

A. -1, -2
B. 2, 1
C. 1, 2
D. -2, -1
Answer» D. -2, -1
Discussion
2.

Find nth derivative of y = Sin(x) Cos3(x)

A. (1/4) 2<sup>n</sup>Sin(2x+n /2) + (1/8) 4<sup>n</sup>Sin(4x+n /2)
B. (1/4) 2<sup>n</sup>Cos(2x+n /2) + (1/8) 4<sup>n</sup>Sin(4x+n /2)
C. (1/4) 2<sup>n</sup>Sin(2x+n /2) + (1/8) 4<sup>n</sup>Cos(4x+n /2)
D. (1/4) 2<sup>n</sup>Cos(2x+n /2) + (1/8) 4<sup>n</sup>Cos(4x+n /2)
Answer» B. (1/4) 2<sup>n</sup>Cos(2x+n /2) + (1/8) 4<sup>n</sup>Sin(4x+n /2)
Discussion
3.

Nth derivative of ( frac{1}{(1+x^2)} )?

A. (-1)<sup>n</sup>n! r<sup>-n-1</sup> Sin(n+1)
B. (-1)<sup>n</sup>(n)! r<sup>-n-1</sup> Sin(-n-1)
C. (-1)<sup>n+1</sup>(n+1)! r<sup>-n-1</sup> Sin(n+1)
D. (-1)<sup>n+1</sup>(n+1)! r<sup>-n-1</sup> Sin(-n-1)
Answer» B. (-1)<sup>n</sup>(n)! r<sup>-n-1</sup> Sin(-n-1)
Discussion
4.

If In=enxTan(x), and ( frac{I_{n+2}-2nI_{n+1}+n^2 I_n}{nI_{n-I}} ) = c (1+x2) ( frac{d^2}{dx^2} ( frac{1}{1+x^2}) ), Then value of c equals to

A. 1
B. 2
C. 3
D. 4
Answer» B. 2
Discussion
5.

nth derivative of y = sin2x cos3x is

A. <sup>1</sup> <sub>8</sub> cos u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 5<sup>n</sup> cos u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 3<sup>n</sup> cos u2061(3x + <sup>n </sup> <sub>2</sub>)
B. <sup>1</sup> <sub>8</sub> sin u2061(x+<sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 5<sup>n</sup> cos u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 3<sup>n</sup> cos u2061(3x + <sup>n </sup> <sub>2</sub>)
C. <sup>1</sup> <sub>8</sub> cos u2061(x+<sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 5<sup>n</sup> sin u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 3<sup>n</sup> sin u2061(3x + <sup>n </sup> <sub>2</sub>)
D. <sup>1</sup> <sub>8</sub> sin u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 5<sup>n</sup> sin u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 3<sup>n</sup> sin u2061(3x + <sup>n </sup> <sub>2</sub>)
Answer» B. <sup>1</sup> <sub>8</sub> sin u2061(x+<sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 5<sup>n</sup> cos u2061(x + <sup>n </sup> <sub>2</sub>) <sup>1</sup> <sub>16</sub> 3<sup>n</sup> cos u2061(3x + <sup>n </sup> <sub>2</sub>)
Discussion
6.

If y=sin(-1) (x) then select the true statement.

A. y<sub>2</sub> = xy<sub>1</sub><sup>3</sup>
B. y<sub>3</sub> = xy<sub>2</sub><sup>3</sup>
C. y<sub>2</sub> = xy<sub>1</sub><sup>2</sup>
D. y<sub>3</sub> = xy<sub>1</sub><sup>2</sup>
Answer» B. y<sub>3</sub> = xy<sub>2</sub><sup>3</sup>
Discussion
7.

If y=x4 x2-1, then?

A. 0.5*(-1)<sup>n</sup> (n-1)! [(x-1)<sup>-n-1</sup> + (x+1)<sup>-n-1</sup>]
B. 0.5*(-1)<sup>n</sup> (n-1)! [x<sup> n-1</sup> + (x-1)<sup>-n-1</sup> + (x+1)<sup>-n-1</sup>]
C. 0.5*(-1)<sup>n</sup> (n-1)! [(x-1)<sup>-n</sup> + (x+1)<sup>-n</sup>)]
D. 0.5*(-1)<sup>n</sup> (n-1)! [x<sup>-n</sup> + (x-1)<sup>-n</sup> + (x+1)<sup>-n</sup>]
Answer» B. 0.5*(-1)<sup>n</sup> (n-1)! [x<sup> n-1</sup> + (x-1)<sup>-n-1</sup> + (x+1)<sup>-n-1</sup>]
Discussion
8.

If nth derivative of eax sin (bx+c) cos (bx+c) is, eax rn sin (bx+c+n 2) cos (bx+c+n 2) then,

A. r = ( sqrt{a^2+b^2}, alpha=tan^{-1} frac{ u2061b}{a} )
B. r = ( sqrt{a^2+4b^2}, alpha=tan^{-1} u2061 frac{2b}{a} )
C. r = ( sqrt{a^2+8b^2}, alpha=tan^{-1} u2061 frac{4b}{a} )
D. r = ( sqrt{a^2+16b^2}, alpha=tan^{-1} frac{ u20614b}{a} )
Answer» C. r = ( sqrt{a^2+8b^2}, alpha=tan^{-1} u2061 frac{4b}{a} )
Discussion
9.

What is the value of ( frac{d^n (x^m)}{dx^n} ) for m<n, m=n, m>n?

A. 0, n!, m<sub>P<sub>n</sub></sub> x<sup>(m-n)</sup>
B. m<sub>P<sub>n</sub></sub> x<sup>(m-n)</sup>, n!, 0
C. 0, n!, m<sub>C<sub>n</sub></sub> x<sup>(m-n)</sup>
D. m<sub>C<sub>n</sub></sub> x<sup>(m-n)</sup>, n!, 0
Answer» B. m<sub>P<sub>n</sub></sub> x<sup>(m-n)</sup>, n!, 0
Discussion
10.

If y=tan(-1) (x) , then which one is correct ?

A. y<sub>3</sub> + y<sub>1</sub><sup>2</sup> + 4xy<sub>2</sub> y<sub>1</sub>=0
B. y<sub>3</sub> + y<sub>1</sub><sup>2</sup> + xy<sub>2</sub> y<sub>1</sub>=0
C. y<sub>3</sub> + 2y<sub>1</sub><sup>2</sup> + xy<sub>2</sub> y<sub>1</sub>=0
D. y<sub>2</sub> + 2y<sub>1</sub><sup>2</sup> + 4xy<sub>2</sub> y<sub>1</sub>=0
Answer» E.
Discussion
11.

If x = a(Cos(t) + t2) and y = a(Sin(t) + t2 + t3) then dy/dx equals to

A. (Cos(t) + 3t<sup>2</sup> + 2t) / (-Sin(t) + 2t)
B. (Sin(t) + 3t<sup>2</sup> + 2t) / (-Cos(t) + 2t)
C. (Sin(t) + 3t<sup>2</sup> + 2t) / (Cos(t) + 2t)
D. (Cos(t) + 3t<sup>2</sup> + 2t) / (Sin(t) + 2t)
Answer» B. (Sin(t) + 3t<sup>2</sup> + 2t) / (-Cos(t) + 2t)
Discussion
12.

If y=log (x (x2 1)), then nth derivative of y is ?

A. (-1)<sup>(n-1)</sup> (n-1)!(x<sup>(-n)</sup> + (x-1)<sup>(-n)</sup> + (x+1)<sup>(-n)</sup>)
B. (-1)<sup>n</sup> (n)! (x<sup>(-n-1)</sup> + (x-1)<sup>(-n-1)</sup> + (x+1)<sup>(-n-1)</sup>)
C. (-1)<sup>(n+1)</sup> (n+1)!(x<sup>(-n)</sup> + (x-1)<sup>(-n)</sup> + (x+1)<sup>(-n)</sup>)
D. (-1)<sup>n</sup>(n)! (x<sup>(-n-1)</sup> + (x-1)<sup>(-n+1)</sup> + (x+1)<sup>(-n+1)</sup>)
Answer» B. (-1)<sup>n</sup> (n)! (x<sup>(-n-1)</sup> + (x-1)<sup>(-n-1)</sup> + (x+1)<sup>(-n-1)</sup>)
Discussion
13.

nth derivative of Sinh(x) is

A. 0.5(e<sup>x</sup> e<sup>-x</sup>)
B. 0.5(e<sup>-x</sup> e<sup>x</sup>)
C. 0.5(e<sup>x</sup> (-1)<sup>n</sup> e<sup>-x</sup>)
D. 0.5((-1)<sup>-n</sup> e<sup>-x</sup> -e<sup>x</sup>)
Answer» D. 0.5((-1)<sup>-n</sup> e<sup>-x</sup> -e<sup>x</sup>)
Discussion