If $f$ has a local maximum or minimum at c, and if $f'(c)$ exists, then_________.

• A) $f'(c) < 0$
• B) None of these
• C) $f'(c) = 0$
• D) $f'(c) > 0$

1+2+3+…+200 equals _____.

• A) 20012
• B) 21220
• C) 21021
• D) 20100

$${\text{The integral }}\int {\frac{{6x}}{{{{(3{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{1}{{{{(3{x^2} + 1)}^3}}} + c$$
• B) $$- \frac{1}{{6x + 1}} + c$$
• C) $$\frac{1}{{3{x^2} + 1}} + c$$
• D) $$- \frac{1}{{3{x^2} + 1}} + c$$

The vertical asymptotes of a function occur at the points where the denominator of the function becomes

• A) -1
• B) 1
• C) 0
• D) Undefined

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

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

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

• A) It is discontinuous on the interval [-2, 2].
• B) There is a point in the interval (-2, 2) where f(x) has a horizontal tangent
• C) There is no such point in the interval (-2, 2) where f(x) has a horizontal tangent.
• D) None of these.

Critical point of function f(x) =4x^2-4x+1 on closed interval [0,1] is x = ………

• A) 1,2
• B) 0
• C) 1/2
• D) 2

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

• A) $$5\cos 5x + c$$
• B) $${\text{ - }}\frac{{\cos 5x}}{5} + c$$
• C) $$\frac{{\cos 5x}}{5} + c$$
• D) $${\text{ - }}\frac{{\cos 4x}}{5} + c$$

What is length of each subinterval if the interval [-1,1] is divided into n subintervals of equal length.

• A) 1/n
• B) 0
• C) 2/n
• D) None of these

If f(x) = x^5 + 6, then which of the following is Not true about it.

• A) Its anti – derivative is x^6/6 + 6x + 10.
• B) Its anti – derivative is x^6/6 + 12x
• C) Its anti – derivative is x^6/6 + 6x.
• D) Its anti – derivative is x^6/6 + 6x + 6.

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

• A) 5.
• B) 10.
• C) None of these.
• D) 13.

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

• A) Relative minimum
• B) Relative maximum
• C)
• D)

Which of the following is the sum of (2k+1) where k goes from 1 to 4?

• A) 26
• B) 24
• C) 22
• D) 20

summation of (n+i);where (i varies from 1 to 1) =………..

• A) n
• B) 0
• C) n+1
• D) 1

An Inflection Point is a point where a curve changes from

• A) b. Concave down to concave up
• B) d. None of these
• C) a. Concave up to concave down
• D) c. Both a and b

\[{\text{In}}\,{\text{the}}\,{\text{notation:}}\,\int_a^b {f(x)} dx{\text{,}}\;f(x)\,{\text{is}}\,{\text{called___________}}{\text{.}}\]

• A) \[{\text{Differential}}\]
• B) \[{\text{Integrand}}\]
• C) \[{\text{Integration}}\]
• D) \[{\text{None}}\,{\text{of}}\,{\text{these}}\]

In approximation to an area Rn (where n is subscript) when limit is taken as n goes to infinity, approximation becomes actual area.

• A) True
• B) False
• C)
• D)

Integration of “cosecx.cotx” with respect to x is -----

• A) Cosecx
• B) Cotx
• C) -Cosecx
• D) Tanx

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

• A) 10.
• B) 12.
• C) 18
• D) None of these.

\[{\text{For}}\,{\text{Rolle's}}\,{\text{Theorem,}}\,f\,{\text{is}}\,{\text{differentiable}}\,{\text{on}}\,{\text{the}}\,{\text{interval __________}}{\text{.}}\]

• A) \[(a,b)\]
• B) \[[a,b)\]
• C) \[(a,b]\]
• D) \[[a,b]\]