What are critical points of the function f(x) =x-1?

• A) x=0
• B) x=1
• C) None of these
• D) No critical point

According to the Newton’s method, the equation Cosx=x (where x is in radian) has a solution between ……………

• A) 0 and -1
• B) Solution not exist
• C) 0 and 1
• D) 1 and -1

$${\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{Theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {e^x}\sin x,\,\,x \in [0,\pi ]\,{\text{is}}\_\_\_\_\_\_\_\_\_\_.$$

• A) $$\frac{{3\pi }}{4}$$
• B) $$\frac{\pi }{6}$$
• C) $$\frac{\pi }{4}$$
• D) $$\frac{{3\pi }}{2}$$

The approximate solution is possible to generate using Newton’s Method if ___________.

• A) the tangent line(at approximated points) must crosses the x - axis.
• B) the slope of tangent line(at any approximated point) is zero.
• C) the tangent line(at any approximated point) is parallel to x- axis.
• D) None of these.

Let y = f(x) be a discontinuous function on a finite closed interval, then which of the following is true about it.

• A) It must have absolute extreme values.
• B) It may or may not have absolute extreme values.
• C) None of these.
• D) It has only absolute minimum value.

13+23+33+…+153 equals _____.

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

\[\text{The vertical asymptote of the function }f(x)=\frac{3{{x}^{2}}+1}{2-x}\text{ is}\]

• A) $\infty $
• B) -2
• C) 2
• D) 0

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

• A) 16
• B) 8
• C) 1
• D) 64

If f(x) = x^4, then which of the following is Not true about it.

• A) Its anti – derivative is x^5/5.
• B) Its anti – derivative is x^5/5 + 10.
• C) Its anti – derivative is x^5/5 + 2.
• D) Its anti – derivative is x^5 + 5.

If f (x) = x^3 is defined on the interval [1, 3], then which of the following is true about it.

• A) Its absolute minimum value exists at the critical point.
• B) Its relative minimum value does not exist at the critical point
• C) None of these.
• D) Its relative minimum value exists at the critical point.

$${\text{The integral }}\int {\sqrt {4x - 3} \,dx\,} {\text{will be equal to ?}}$$

• A) $$\frac{{{{(4x + 3)}^{\frac{3}{2}}}}}{6} + c$$
• B) $${\text{None of these}}$$
• C) $$\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{6} + c$$
• D) $$\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{3} + c$$

What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 1?

• A) 20
• B) 24
• C) 28
• D) 21

Subdivide the interval [0, 1] into 2 equal parts, and then the width of each sub-interval will have length ………

• A) -1/2
• B) 1/2
• C) 0
• D) 1

If f(x)=Tan(x) then mean value theorem can be applied to it on the interval (0,2pi)

• A) True
• B) False
• C)
• D)

For the given function f(x)= 2(x^2)+1 in the interval [-1,2] , which condition of Rolle’s theorem is not satisfied.

• A) f (-1) = f (2)
• B) The function is differentiable in the interval
• C) None of these.
• D) The function is continuous in the interval

Sigma notation is used to write lengthy……….in compact form.

• A) products
• B) difference
• C) sums
• D) quotient

$$\int {\tan x} dx = \_\_\_\_\_\_\_\_\_\_\_\_\_\_.$$

• A) $$\ln |\cos x| + C$$
• B) $$\ln \left| {\sec x} \right| + C$$
• C) $$\ln \left| {\sin x} \right| + C$$
• D) $${\sec ^2}x + C$$

\[{\text{The integral }}\int {\sqrt {4x - 3} \,dx\,} {\text{will be equal to ?}}\]

• A) \[\frac{{{{(4x + 3)}^{\frac{3}{2}}}}}{6} + c\]
• B) \[{\text{None of these}}\]
• C) \[\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{6} + c\]
• D) \[\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{3} + c\]

For the function f(x)=|x|-1, if f(-1)=f(1)=0 then which of the following conclusion can be drawn about the point ‘c’ in the interval [-1,1] such that f ’(c)=0?

• A) c=0.5
• B) No such ‘c’ exists
• C) Every point in [-1,1] can be taken as ‘c’
• D) c=0

$${\text{What}}\,{\text{does}}\,{\text{the}}\,{\text{indefinite}}\,{\text{integral }}\int_{}^{} {f(x)} dx\,{\text{represent?}}$$

• A) $${\text{Families}}\,{\text{of}}\,{\text{antiderivative}}\,{\text{of}}\,{\text{the}}\,{\text{function }}f(x)$$
• B) $${\text{Curvature}}\,{\text{of}}\,{\text{the}}\,{\text{curve}}$$
• C) $${\text{None}}\,{\text{of}}\,{\text{these}}$$
• D) $${\text{Area}}\,{\text{under}}\,{\text{the}}\,{\text{curve}}$$