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

• 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) \[[a,b]\]

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

• A) -2
• B) 0
• C) $\infty$
• D) 2

By applying Roll’s theorem on f(x) = x over the interval [-1,1], the points where the derivative of f(x)=x is not taken are………

• A) x= -1, 1
• B) x=0,1
• C) x=-1,0
• D) x=0,0.5,-0.5

$${\text{For}}\,{\text{Rolle's}}\,{\text{Theorem,}}\,f\,{\text{is}}\,{\text{continuous}}\,{\text{on}}\,{\text{the}}\,{\text{interval __________}}{\text{.}}$$

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

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) 1
• D) 0

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

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

\[\text{If we say a function }f\text{ have a relative extremum at a point }{{x}_{0}},\text{ then it means that }f\text{ has }\!\!~\!\!\text{ }\_\_\_\_\_\_\_\_\text{ at }{{x}_{0}}.\]

• A) Relative minimum
• B) None of these
• C) Either a relative maximum or relative minimum
• D) Relative maximum

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.