In the indefinite integral of x(y^2) w.r.t ‘y’ , the independent variable is ……..

• A) none of these
• B) y
• C) xy
• D) x

Subdivide the interval [a, b] into 4 equal subintervals then the width of each subinterval is ------

• A) (b-2a)/4
• B) (2b-a)/4
• C) (b-a)/2
• D) (b-a)/4

Critical point of f(x)=-Sinx in the interval [0,pi] is-----

• A) pi/2
• B) pi
• C) 0
• D) pi/4

$${\text{The integral }}\int {\cos (5x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{{\sin (5x)}}{5} + c$$
• B) $$\frac{{\sin (5x)}}{5} + c$$
• C) $${\text{None of these}}$$
• D) $$5\sin (5x) + c$$

$$\text{If }{f}'(x)={{x}^{2}}-1.\text{ Then the critical points of the function }f\text{ are}$$

• A) 0, 2
• B) 1, 2
• C) 0, 1
• D) 1, -1

What will be the value of summation of k2 where k goes from 8 to 8?

• A) 8
• B) 64
• C) 1
• D) 16

What will be the sigma notation for 32+42+52+62 ?

• A) summation of (k-1)2 where (k varies from 2 to 5)
• B) summation of (k2) where (k varies from 1 to 4)
• C) summation of (k+1)2 where (k varies from 3 to 6)
• D) summation of (k2) where (k varies from 3 to 6)

\[{\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {x^3} - 3x\,{\text{in}}\,{\text{the}}\,{\text{interval}}\,\left[ {0,\sqrt 3 } \right]{\text{.}}\]

• A) \[\frac{2}{3}\]
• B) \[ - 1\]
• C) \[\frac{1}{3}\]
• D) \[1\]

The estimated area under f(x) = 12 / x from
x = 1 to x = 3 with right end points for
n = 2 is ________.

• A) 10
• B) 18.
• C) None of these.
• D) 20.

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 2.5
• B) 2
• C) 1.5
• D) 1

12+22+32+…+152 equals _____.

• A) 15(16)(30) / 6
• B) 15(16)(29) / 6
• C) 15(16)(17) / 6
• D) 15(16)(31) / 6

13+23+33+…+153 equals _____.

• A) 15(16)2/2
• B) [15(16)/2]2
• C) [15(16)]2/2
• D) 15(16)/22

If f (x) = x^4 is defined on the interval
[-2, 2], then which of the following is true about it.

• A) Its relative maximum value exists at 2.
• B) None of these.
• C) Its absolute minimum value exists at -2
• D) Its absolute maximum value exists at 2.

The anitderivative of the function f(x)=2-7Cosx, is -------

• A) 2x-7Sinx+100
• B) 2x-7Sinx-100
• C) All choices are true
• D) 2x-7Sinx+C

For the area under the curve f(x) = x+2 from x = 2 to x = 8 with left end points approximations for n = 3, what will be the values of xk* ?

• A) 2, 6 and 8
• B) 3, 5 and 7
• C) 2, 4 and 6
• D) 4, 6 and 8

If the closed interval [-10,x] is divided into ‘20’ equally spaced subintervals each of which having the width equals to ‘1’ unit then the value of ‘x’ is --------

• A) 20
• B) 0
• C) 10
• D) 30

Summation of ‘kx’ where k goes from 1 to 5 equals

• A) 15k
• B) 15x
• C) None of these
• D) 55

$\begin{align} & \text{If a function }f\text{ is twice differentiable at a stationary point }{{x}_{0}}\text{ and }{f}''({{x}_{0}})>0, \\ & \text{then }f\text{ has relative }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ at }{{x}_{0}}. \\ \end{align}$

• A) b. Minimum
• B) d. None of these
• C) a. Maximum
• D) c. Both a and b

If f (x) = 2 x + 7 is defined on the interval
[2, 4), then which of the following is true about it.

• A) It has only absolute minimum value.
• B) It has both absolute maximum and minimum values.
• C) It has only absolute maximum value.
• D) None of these.

What will be the value of summation of k3 where k goes from 3 to 3?

• A) 9
• B) 3
• C) 1
• D) 27