Which of the following is the sum of (2k-1) where k goes from 0 to 2?

• A) -1
• B) 3
• C) 4
• D) -2

The function f(x)= 2x^3-15x^2+36x have the critical points ……………on the interval [1,5]

• A) 2,3
• B) 3,4
• C) 1,5
• D) 2,4

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

• A) 13.
• B) 6.
• C) 5.
• D) None of these.

If the interval [3,7] is divided into ‘4’ equal subintervals ,then right endpoint of each subinterval will be………

• A) 3,4,5,6
• B) 5,6,7,8
• C) 4,5,6,7
• D) 3,5,6,8

For the area under the curve f(x) = 2x from x = 0 to x = 12 with mid points approximations for n = 3, what will be the values of xk* ?

• A) 3, 7 and 11
• B) 2, 5 and 8
• C) 2, 6 and10
• D) 1, 5 and 9

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

• A) 76.
• B) None of these.
• C) 25.
• D) 28.

What will be the value of summation of k2 where k goes from 8 to 8?

• A) 1
• B) 16
• C) 64
• D) 8

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

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

• A) 18
• B) 16
• C) 8
• D) 10

The dimensions of a rectangle are given to be 8ft by 12ft. The perimeter of rectangle will be…………..

• A) 40 feet
• B) 60 feet
• C) 30 feet
• D) 50feet

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

• A) n
• B) -2/n
• C) 1/n
• D) 2/n

summation of (ai) (i varies from 1 to n) , summation of (aj) (j varies from 1 to n),summation of (ak) (k varies from 1 to n)
All these three represents same summation.

• A) False
• B) True
• C)
• D)

$${\text{The integral }}\int {\sec (x).\tan (x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$\cos ec(x) + c$$
• B) $${\text{None of these}}$$
• C) $$\sec (x) + c$$
• D) $$- \ln \left| {\cos (x)} \right| + c$$

A function $f$ has an/a___________ at $c$ if $f(c) \geqslant f(x)\,\forall \,x \in \,D$, where $D$ is the domain of $f$.

• A) absolute maximum
• B) absolute maximum/global maximum
• C) global maximum
• D) local maximum

summation of (n+i);where (i varies from 1 to 1) =………..

• A) n+1
• B) 1
• C) n
• D) 0

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

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

Sum the first three terms of the series, whose general term is 5ki
Where first term=k1=10,
Second term= k2=14
Third term=k3= -2
The correct choice is …………
Note: 1, 2, 3 and i with k are in subscript

• A) 111
• B) 011
• C) 101
• D) 110

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

• A) 1
• B) -1
• C) that specific large ODD number
• D) Zero

For the function f(x)=|x|-1, if f(-1)=f(1)=0 then which of the following conclusion can be drawn about the point ‘c’ in the interval [-1,1] such that f ’(c)=0?

• A) c=0.5
• B) Every point in [-1,1] can be taken as ‘c’
• C) No such ‘c’ exists
• D) c=0

12+22+32+…+152 equals _____.

• A) 15(16)(31) / 6
• B) 15(16)(30) / 6
• C) 15(16)(17) / 6
• D) 15(16)(29) / 6