Integral of (5/2)cos(x) is

• A) (5/2)tan(x)+C
• B) (5/2)sin(x)+C
• C) None of these
• D) (3/2)csc(x)+C

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

• A) 8
• B) 14
• C) 12
• D) 10

If f(x) = Sin(x) + x, then which of the following is true about it

• A) Its anti – derivative is –Cos(x) + x^2/2 + 10.
• B) Its anti – derivative is Cos(x) + x^2/2 + 10.
• C) None of these.
• D) Its anti – derivative is Cos(x) + 1.

Which of the following is the absolute minima of the function: f(x)=-x in the interval [-1,1]?

• A) 0
• B) 1
• C) 0.5
• D) -1

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

• A) 27
• B) 19
• C) 21
• D) 16

If ‘n’ goes from 1 to 4 and the summation of ‘na’ =Maxima of (e^x) in the interval[-e,0], then the value of ‘a’ is -----------

• A) 1/10
• B) -1/10
• C) -10
• D) 10

If f (x) = x^3 is defined on the interval [1, 3], then which of the following is true about it.

• A) None of these.
• B) Its absolute minimum value exists at the critical point.
• C) Its relative minimum value exists at the critical point.
• D) Its relative minimum value does not exist at the critical point

If x =(3+4+5+...+10)+{(3^3)+(4^3)+(5^3)+...+ (10^3)}, then x = _______.

• A) 3068.
• B) 3080.
• C) None of these.
• D) 55.

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

• A) True
• B) False
• C)
• D)

By applying mean value theorem to the function
f(x)=lnx in the interval [1,e], the corresponding value of ‘c’ is ------------(Hint: lne=1, ln1=0)

• A) 1-e
• B) e-1
• C) -e
• D) e

Subdivide the interval [1, 5] into ‘n’ equally spaced subintervals then the width of each sub-interval is ------

• A) 1/n
• B) 5/n
• C) 5
• D) 4/n

Given a function f(x) = 1 / (x-1) and the interval is (0,2) ,then mean value theorem cannot be applied due to ……….

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

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is ----------

• A) -6
• B) Undetermined
• C) 1
• D) 6

If x = 1 + 2 +3 + 4 + . . . + 20, then
x = ________.

• A) 500.
• B) None of these.
• C) 200.
• D) 210.

If we subdivide the interval [2,4] into n equal parts, then what will be the length ∆x of each part?

• A) 6/n
• B) 8/n
• C) 2/n
• D) 1/n

If a function has an extreme value (either a maximum or a minimum) on an open interval (a,b), then the extreme value occurs at a ........

• A) Any point in the open interval (a,b)
• B) Critical point of f(x)
• C)
• D)

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

• A) 48
• B) 38
• C) 76
• D) 26

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) 3,5,6,8
• C) 4,5,6,7
• D) 5,6,7,8

In Rolle’s theorem, f(x) is continuous in closed interval [a,b] and differentiable in open interval (a,b).Then why we don’t discuss its differentiability in the closed interval [a,b] because ---------

• A) f(a)=f(b)=0
• B) f ‘(a) and f ‘(b) never exist
• C) f(a) and f(b) never exist
• D) f ‘(a)=f ‘(b)=0

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

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