2(13)+2(23)+2(33)+…+2(153) equals _____.

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

If ‘n’ goes from 1 to any large EVEN number then the summation of ‘(-1)^n’ = ---------

• A) 1
• B) zero
• C) that specific large EVEN number
• D) -1

Summation of 9t where ‘t’ goes from 1 to 30” is same as “summation of 9k where k goes from 1 to 30”.

• A) False
• B) True
• C)
• D)

If f (x) = x^4 is defined on the interval
[-2, 2], then which of the following is true about it.

• A) Its relative maximum value exists at 2.
• B) Its absolute minimum value exists at -2
• C) None of these.
• D) Its absolute maximum value exists at 2.

\[{\text{The integral }}\int {\frac{{4x}}{{{{(2{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}\]

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

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

• A) -1/2
• B) 1
• C) 2
• D) 1/2

$\text{A critical point for a function }f,\text{ where }{f}'(x)=0\text{ is called as}\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{ point}\text{.}$

• A) Corner
• B) Mid
• C) Stationary
• D) Tangent

What are critical points of the function f(x) =x^2-1?
NOTE: x^n means ‘x’ to the power ‘n’

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

1+2+3+…+100 equals _____.

• A) 5055
• B) 5005
• C) 5050
• D) 5500

Subdivide the interval [3, 5] into n equal parts, and then the width of each subinterval is ----

• A) n
• B) -2/n
• C) 2/n
• D) 1/n

By using Newton method, which of the following is the poorest initial approximate solution of equation:x+Cosx=0?

• A) x=0
• B) x=pi/2
• C) x=-pi/3
• D) x=-pi/4

If a function f(x) is defined on an interval
[a, b] satisfying the conditions of the Rolle’s Theorem, then which of the following is true about it.

• A) It must have both absolute maximum and minimum values
• B) It has only absolute maximum value
• C) It has only absolute minimum value.
• D) None of these.

What will be the value of summation of k3 where k goes from 3 to 3?

• A) 1
• B) 27
• C) 9
• D) 3

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

• A) 20
• B) 26
• C) 24
• D) 22

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

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

f(x) = (x^2)+1 is a continuous function on (-infinity ,+infinity ) , and ‘f’ has no absolute maximum on (-infinity ,+infinity ) because………

• A) lim (f(x)) = +infinity as ‘x’ tends to ±infinity
• B) lim (f(x)) = 1 as ‘x’ tends to ±infinity
• C) lim (f(x)) = -infinity as ‘x’ tends to ±infinity
• D) lim (f(x)) = 0 as ‘x’ tends to ±infinity

f(x) = 8x-x^2 on the closed interval [0, 6]
has the critical point at x=………

• A) 5
• B) 4
• C) 0
• D) 1

If x = 3 + 4 + . . . + 20, then x = ________.

• A) 210.
• B) 207.
• C) None of these.
• D) 250.

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 1.5
• B) 1
• C) 2.5
• D) 2

Integral of 5^2 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) 10
• B) (1/3)5^3
• C) 25x
• D) None of these