What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 2?

• A) 25
• B) 21
• C) 16
• D) 12

Subdivide the interval [a, b] into 4 equal subintervals then the width of each subinterval is ------

• A) (b-a)/4
• B) (b-2a)/4
• C) (2b-a)/4
• D) (b-a)/2

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

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) 1
• B) 2
• C) 0
• D) 3

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

• A) 14
• B) 12
• C) 10
• D) 8

Which of the following is the sum of (2k+1) where k goes from 3 to 5?

• A) 21
• B) 16
• C) 19
• D) 27

Integral of x^2+x^3 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (1/4)x^4+(1/3)x^3 +C
• B) (1/3)x^4+(1/4)x^3 +C
• C) x^3+x^4+C
• D) None of these

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