The symbol $\int {}$ was introduced by___________and is called integral sign.

• A) Leibnitz
• B) Lagrange
• C) Cauchy
• D) Newton

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

• A) 10
• B) 8
• C) 18
• D) 16

$\text{A line }y={{y}_{\text{0}}}\text{ is called a horizontal asymptote for the graph of function }f\text{ if}$

• A) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)={{y}_{0}}$
• B) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=0$
• C) $\underset{x\to 0}{\mathop{\lim }}\,f(x)={{y}_{0}}$
• D) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=\infty$

The maximum and minimum values of the function
f(x)=1/x does not lie in the interval [-1,1] because -------

• A) f(x) is discontinuous in [-1,1]
• B) f(x) is not one-to-one
• C) f(x) is differentiable in [-1,1]
• D) f(x) is continuous in [-1,1]

Integration of 3x^2 with respect to x is…………

• A) x^2
• B) x^3
• C) x
• D) x^4

If f(x) = Sec^ (2) x + x^3, then which of the following is NOT true about it.

• A) Its anti – derivative is Tan(x) + x^4/4 + 12.
• B) None of these.
• C) Its anti – derivative is Tan(x) + x^4/4 + 15.
• D) Its anti – derivative is Tan(x) + x^4/4 + 10.

Which of the following is the sum of 3k+1 where k goes from 0 to 2?

• A) 39
• B) 27
• C) 30
• D) 33

Sum of n-terms of a series whose nth term is ‘n’ = ---

• A) (n+1)/2
• B) n(n+1)/2
• C) n(n+1)
• D) n(n-1)/2

The indefinte integral of ‘cos (x) – sin (x)’ is………………

• A) cos (x) +sin (x)+c
• B) cos (x) .sin (x) +c
• C) -cos (x) + sin (x) +c
• D) -cos (x) – sin (x)+c

12+22+32+…+192 equals _____.

• A) 19(20)(21)/6
• B) 19(20)(31)/6
• C) 19(20)(37)/6
• D) 19(20)(39)/6

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

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

summation of (3) ;where ( j varies from 1 to 4) indicates to add ………to itself 4 times.

• A) 2
• B) 3
• C) 4
• D) 1

The estimated area under f(x) = x^2 + 2 from
x = 1 to x = 5 with right end points for
n = 2 is ________.

• A) 28.
• B) 76.
• C) 30.
• D) 50.

Critical point for f(x) = -Cosx on [-pi/2,pi/2] are ------

• A) pi/2
• B) -pi/2
• C) pi/4
• D) 0

summation of (n+i) ; (i varies from 1 to 10 ) , here ‘i’ is known as the …….. of the summation.

• A) Lower limit
• B) Upper limit
• C) None of these
• D) Index

Given f(x)= 1/(x-1) on the interval (0,3) , then ‘f ’ has no relative maxima or relative minima due to………

• A) None of these
• B) Open interval
• C) Discontinuity in the interval
• D) Rational function

$\begin{align} & \text{Let a function }f\text{ is twice differentiable at a stationary point }{{x}_{0}}, \\ & \text{then }f\text{ has relative maximum at }{{x}_{0}}\,\text{if} \\ \end{align}$

• A) $\text{ }{f}''({{x}_{0}})<0$
• B) $\text{ }{f}''({{x}_{0}})>0$
• C) $\text{ }{f}''({{x}_{0}})\ge 0$
• D) $\text{ }{f}''({{x}_{0}})=0$

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

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

$${\text{The integral }}\int {\cot (2x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$\frac{1}{2}\ln \left| {\sec (2x)} \right| + c$$
• B) $$\frac{1}{2}\ln \left| {\sin (2x)} \right| + c$$
• C) $$\ln \left| {{\text{sec}}(2x)} \right| + c$$
• D) $${\text{ln}}\left| {\sin (2x)} \right| + c$$

Subdivision of an interval is also called ………. of the interval.

• A) Partition
• B) Evaluation
• C) Separation
• D) Composition