Sum of n-terms of a series whose nth term is ‘n’ = 1/n+1.then what is the sum of the first two terms is -----

• A) 6/5
• B) 6/4
• C) 5/6
• D) 6

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

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

$${\text{The integral }}\int {\sqrt {2x + 3} \,dx} {\text{ will be equal to ?}}$$

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

What is the estimated area under f(x) = x2+2 from x = 1 to x = 5 with mid points for n = 2

• A) 26
• B) 38
• C) 76
• D) 48

What will be the sigma notation for 32+42+52+62 ?

• A) summation of (k2) where (k varies from 3 to 6)
• B) summation of (k2) where (k varies from 1 to 4)
• C) summation of (k-1)2 where (k varies from 2 to 5)
• D) summation of (k+1)2 where (k varies from 3 to 6)

Area of a rectangle whose width is 5 units and length is 6 units will be ….

• A) None of these
• B) 22 units
• C) 30 square units
• D) 11 units

Which geometrical figure is used for approximating the area under the curve?

• A) Right angled triangle
• B) None of these
• C) Pentagon
• D) Circle

The Area $A$ of the region $S$ that lies under the graph of the continuous function $f$ is the limit of the sum of the areas of approximating rectangles:

• A) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \left[ {f\left( {{x_1}} \right)\Delta x + f\left( {{x_2}} \right)\Delta x + \ldots + f\left( {{x_{n - 1}}} \right)\Delta x} \right]$
• B) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \frac{1}{{\Delta x}}\;\left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$
• C) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$
• D) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \Delta x\left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$

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

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

• A) 8
• B) 24
• C) 18
• D) 10

The area between f(x)=-x and the closed interval
[-1,0] on x-axis is ----------

• A) 1
• B) 1/2
• C) -1/2
• D) 2

The estimated area under f(x) = x from
x = 0 to x = 3 with right end points for
n = 3 is ________.

• A) 6.
• B) 7.
• C) None of these
• D) 5.

$${\text{The integral }}\int {\frac{{10x}}{{{{(5{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{1}{{5x + 1}} + c$$
• B) $$- \frac{1}{{{{(5{x^2} + 1)}^3}}} + c$$
• C) $$- \frac{1}{{5{x^2} + 1}} + c$$
• D) $$\frac{1}{{5{x^2} + 1}} + c$$

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

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

Let f(x)=x^3 and a= -5 ,b=5 and n= no. of partition of [-3,3]=4
Let the widths of first, second, third and fourth intervals are 3,0,1,2 respectively. Then the “Mesh size” of partition is……………

• A) 3
• B) 0
• C) 1
• D) 2

1+2+3……….+1000 equals -------

• A) 500500
• B) 1000
• C) None of these
• D) 3000

Approximation to an area improves as number of partitions is decreased.

• A) True
• B) False
• C)
• D)

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

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

13+23+33+…+153 equals _____.

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

If the function f(x)= (x^2)+1 satisfies all the conditions of Rolle’s theorem in the interval [-1,1] , then the value of ‘c’ will be……..

• A) 2
• B) 0
• C) 4
• D) 3