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) $${\text{Area}}\,{\text{under}}\,{\text{the}}\,{\text{curve}}$$

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

• A) 2
• B) -2
• C) $\infty$
• D) 0

$\text{A critical point for a function }f\text{ is any value of }x\text{ in the domain of }f\text{ at which}$

• A) $${f}'\left( x \right)\le 0$$
• B) $${f}'\left( x \right)=0\,\text{or }f\text{ is not differentiable}$$
• C) $$f\text{ is differentiable }$$
• D) $${f}'\left( x \right)>0$$

$${\text{The integral }}\int {{{\left( {{x^3} + 1} \right)}^{10}}\,.3{x^2}\,dx\,} {\text{will be equal to ?}}$$

• A) $$\frac{{{{\left( {{x^3} - 1} \right)}^{11}}}}{{11}} + c$$
• B) $$- \frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$
• C) $$\frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$
• D) $${\text{None of these}}$$

The polynomial function f(x)=6x^2-30x+36 has the critical point over the real line is ………

• A) 2/5
• B) 2
• C) 5/2
• D) 5

While using Newton’s mathod,which of the following will be the best initial approximate solution to solve the equation: x-Sinx=0

• A) x=-pi/2
• B) x=pi/2
• C) x=pi
• D) x=0

3(12)+3(22)+3(32)+…+3(152) equals _____.

• A) 15(16)(31)/2
• B) 15(16)(29)/2
• C) 15(16)(30)/2
• D) 15(16)(17)/2

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

• A) 2, 5 and 8
• B) 2, 4 and 8
• C) 0, 4 and 8
• D) 4, 6 and 8

Absolute minimum of the function f(x)=x in the semi open interval (0,2] is-------

• A) 2
• B) 1
• C) Undefined
• D) 0

If the graph of $f$ lies above all of its tangents on an interval $I$, then it is called___________ on $I$.

• A) None of these
• B) concave downward
• C) concace upward
• D) constant function

$${\text{The integral }}\int {{{\sec }^2}(5{x^2})\,.10x\,dx\,} {\text{will be equal to ?}}$$

• A) $$\sec (5{x^2}).\tan (5{x^2}) + c$$
• B) $$\tan (5{x^2}) + c$$
• C) $$\tan (5x) + c$$
• D) $${\text{se}}{{\text{c}}^2}(10x) + c$$

What is the estimated area under f(x) = 2x from x = 0 to x = 4 with mid points for n = 2?

• A) 8
• B) 18
• C) 16
• D) 10

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

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

$$\begin{align} & \text{A function }f\text{ is said to have a relative minimum at }{{x}_{0}}\text{, if}\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{for all }x\text{ } \\ & \text{in some open interval containing }{{x}_{0}}. \\ \end{align}$$

• A) $$f\left( {{x}_{0}} \right)=f\left( x \right)$$
• B) $$f\left( {{x}_{0}} \right)\le \text{ }f\left( x \right)$$
• C) $$f\left( {{x}_{0}} \right)>\text{ }f\left( x \right)$$
• D) $$f\left( {{x}_{0}} \right)\ge \text{ }f\left( x \right)$$