Explore topic-wise MCQs in Mathematics.

This section includes 11 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

If, y = tan-1(x/a), then what is the value of y ?

A. (2ax/(x<sup>2</sup> a<sup>2</sup>)<sup>2</sup>)
B. -(2ax/(x<sup>2</sup> a<sup>2</sup>)<sup>2</sup>)
C. (2ax/(x<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>)
D. -(2ax/(x<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>)
Answer» E.
Discussion
2.

If, y = (sin-1x)2, then what is the value of (1 x2)y xy + 4?

A. 2
B. 4
C. 6
D. 8
Answer» D. 8
Discussion
3.

What is the value of (x + y)2y if x = et sint and y = et cost?

A. x/2(y + y)
B. x/2(y y)
C. 2(xy + y)
D. 2(xy y)
Answer» E.
Discussion
4.

Given, y = tan-1 (x2 1) then what is the value of (2x2 1)y + x(x2 1)y ?

A. -1
B. 0
C. 1
D. 2
Answer» C. 1
Discussion
5.

What is the value of 4a cos3 (d2y/dx2) if x = a sin2 (1 + cos2 ) and y = a cos2 (1 cos2 )?

A. [1 + (d<sup>2</sup>y/dx<sup>2</sup>)<sup>2</sup>]<sup>3/2</sup>
B. [1 (d<sup>2</sup>y/dx<sup>2</sup>)<sup>2</sup>]<sup>3/2</sup>
C. [1 + (d<sup>2</sup>y/dx<sup>2</sup>)<sup>2</sup>]<sup>1/2</sup>
D. [1 (d<sup>2</sup>y/dx<sup>2</sup>)<sup>2</sup>]<sup>1/2</sup>
Answer» B. [1 (d<sup>2</sup>y/dx<sup>2</sup>)<sup>2</sup>]<sup>3/2</sup>
Discussion
6.

What will be the form of the equation after eliminating a and b from the equation y = a sin-1x + b cos-1x?

A. (1 x<sup>2</sup>)y + xy = 0
B. (1 x<sup>2</sup>)y xy = 0
C. (1 + x<sup>2</sup>)y xy = 0
D. (1 + x<sup>2</sup>)y + xy = 0
Answer» C. (1 + x<sup>2</sup>)y xy = 0
Discussion
7.

If, y = cos(2sin-1x), then what is the value of (1 x2)y xy + 4y?

A. 1
B. 0
C. 1
D. Depends on the value of x
Answer» C. 1
Discussion
8.

What will be the domain of the function, if 3x + 3f(x) = minimum of (t), where (t) = minimum of (2t3 15t2 + 36t 25, 2 + |sint|; 2 t 4} ?

A. (- , 1)
B. (- , log<sub>e</sub>3)
C. (0, log<sub>e</sub>2)
D. (- , log<sub>e</sub>2)
Answer» E.
Discussion
9.

Which of the following is correct for the nature of the roots x5 a0x4 + 3ax3 + bx2 + cx + d = 0 if it is given that 2a02 &lt; 15 and a0, a, b, c, d are real?

A. Can t be real
B. Equal
C. Real
D. Depends on the value of x
Answer» B. Equal
Discussion
10.

The function y = f(x) is represented parametrically by x = t5 5t3 20t + 7 and y = 4t3 3t2 18t + 3 (-2 &lt; t &lt; 2). At which point does y = f(x) has a minimum value?

A. t = -1
B. t = 0
C. t = 1/2
D. t = 3/2
Answer» E.
Discussion
11.

Whichis greater (1/2)e or 1/e2 if there is a given function sinx(sinx), 0 &lt; x &lt; ?

A. 1/e<sup>2</sup>
B. (1/2)<sup>e</sup>
C. Data not sufficient
D. Varies as the value of x changes
Answer» C. Data not sufficient
Discussion