Explore topic-wise MCQs in Engineering Mathematics.

This section includes 14 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}{16x^2+16x+10}dx ).

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

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
3.

Find the value of (x4 5x2 6x)4 4x3 10x 6 dx.

A. ( frac{(x^4-5x^2-6x)^4}{4} )
B. ( frac{(x^4-5x^2-6x)^5}{5} )
C. ( frac{(4x^3-10x-6)^5}{5} )
D. ( frac{(4x^3-10x-6)^4}{4} )
Answer» C. ( frac{(4x^3-10x-6)^5}{5} )
Discussion
4.

Find the area inside function ( frac{(2x^3+5x^2-4)}{x^2} ) from x = 1 to a.

A. <sup>a<sup>2</sup></sup> <sub>2</sub> + 5a 4ln(a)
B. <sup>a<sup>2</sup></sup> <sub>2</sub> + 5a 4ln(a) <sup>11</sup> <sub>2</sub>
C. <sup>a<sup>2</sup></sup> <sub>2</sub> + 4ln(a) <sup>11</sup> <sub>2</sub>
D. <sup>a<sup>2</sup></sup> <sub>2</sub> + 5a <sup>11</sup> <sub>2</sub>
Answer» C. <sup>a<sup>2</sup></sup> <sub>2</sub> + 4ln(a) <sup>11</sup> <sub>2</sub>
Discussion
5.

Find the area inside integral f(x)= ( frac{sec^4 (x)}{ sqrt{tan (x)}} ) from x = 0 to .

A.
B. 0
C. 1
D. 2
Answer» C. 1
Discussion
6.

Find the area inside a function f(t) = ( frac{t}{(t+3)(t+2)} dt ) from t = -1 to 0.

A. 4 ln u2061(3) 5ln u2061(2)
B. 3 ln u2061(3)
C. 3 ln u2061(3) 4ln u2061(2)
D. 3 ln u2061(3) 5 ln u2061(2)
Answer» E.
Discussion
7.

Find the area ln(x) x from x = x = aeb to a.

A. <sup>b<sup>2</sup></sup> <sub>2</sub>
B. <sup>b</sup> <sub>2</sub>
C. b
D. 1
Answer» B. <sup>b</sup> <sub>2</sub>
Discussion
8.

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> <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> <sub>3</sub> + Cos(a) + Sin(a) 1
Discussion
9.

Find the value of x3 ex e2x e3x .enx dx.

A. ( frac{2}{n(n+1)} e^{ frac{n(n+1)}{2}x} left [x^3+3x^2 [ frac{2}{n(n+1)}]^1+6x[ frac{2}{n(n+1)}]^2 +6[ frac{2}{n(n+1)}]^3 right ] )
B. ( frac{2}{n(n+1)} e^{ frac{n(n+1)}{2}x} left [x^3+3x^2 [ frac{2}{n(n+1)}]^1+6x[ frac{2}{n(n+1)}]^2 +6[ frac{2}{n(n+1)}]^3 right ] )
C. ( frac{2}{n(n+1)} e^{ frac{n(n+1)}{2}x} left [x^3+3x^2 [ frac{2}{n(n+1)}]^1+6x[ frac{2}{n(n+1)}]^2 +6[ frac{2}{n(n+1)}]^3 right ] )
D. ( frac{2}{n(n+1)} e^{ frac{n(n+1)}{2}x} left [x^3+3x^2 [ frac{2}{n(n+1)}]^1+6x[ frac{2}{n(n+1)}]^2 +6[ frac{2}{n(n+1)}]^3 right ] )
Answer» B. ( frac{2}{n(n+1)} e^{ frac{n(n+1)}{2}x} left [x^3+3x^2 [ frac{2}{n(n+1)}]^1+6x[ frac{2}{n(n+1)}]^2 +6[ frac{2}{n(n+1)}]^3 right ] )
Discussion
10.

Find the value of x7 Cos(x) dx.

A. x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x)
B. x<sup>7</sup> Sin(x) 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) 2520x<sup>2</sup> Cos(x) + 5040xSin(x) 5040Cos(x)
C. x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x)
D. x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 10080Cos(x)
Answer» B. x<sup>7</sup> Sin(x) 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) 2520x<sup>2</sup> Cos(x) + 5040xSin(x) 5040Cos(x)
Discussion
11.

Value of uv dx,where u and v are function of x.

A. ( sum_{i=1}^n(-1)^i u_i v^{i+1} )
B. ( sum_{i=0}^nu_i v^{i+1} )
C. ( sum_{i=0}^n(-1)^i u_i v^{i+1} )
D. ( sum_{i=0}^n(-1)^i u_i v^{n-i} )
Answer» D. ( sum_{i=0}^n(-1)^i u_i v^{n-i} )
Discussion
12.

Find the value of 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
13.

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
14.

Find the value of tan-1 (x)dx.

A. sec<sup>-1</sup> (x) <sup>1</sup> <sub>2</sub> ln u2061(1 + x<sup>2</sup>)
B. xtan<sup>-1</sup> (x) <sup>1</sup> <sub>2</sub> ln u2061(1 + x<sup>2</sup>)
C. xsec<sup>-1</sup> (x) <sup>1</sup> <sub>2</sub> ln u2061(1 + x<sup>2</sup>)
D. tan<sup>-1</sup> (x) <sup>1</sup> <sub>2</sub> ln u2061(1 + x<sup>2</sup>)
Answer» C. xsec<sup>-1</sup> (x) <sup>1</sup> <sub>2</sub> ln u2061(1 + x<sup>2</sup>)
Discussion