In the indefinite integral of x(y^2) w.r.t ‘y’ , the independent variable is ……..

• A) none of these
• B) x
• C) y
• D) xy

Which of the following is the sum of 3k+1 where k goes from 0 to 2?

• A) 39
• B) 27
• C) 33
• D) 30

If x = (4^2) + (5^2) + (6^ 2) + . . . + (30^2), then x = ________.

• A) 400.
• B) 9441.
• C) 465.
• D) 9455.

Let A be the area of a rectangle under a continuous function f(x) over a closed interval
[a, b]. If this area is divided in to ‘n’ sub-rectangles then width of each approximated sub-intervals is ---------

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

If Newton’s Method succeeded to get the approximate solution of an equation, then which of the following is NOT true about it.

• A) The slope of the tangent line (at any approximated point) must be non zero.
• B) The tangent line (at any approximated point) is not parallel to x-axis.
• C) None of these.
• D) The sequence of approximated points not convergent to the exact solution

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

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

In the indefinite integral of x(y^2) w.r.t ‘y’ , the term ….. serve to identify the independent variable in the function.

• A) y
• B) y^2
• C) x
• D) dy

Maximum of the function f(x)=2x+7 occurs at

• A) x=-2/7
• B) None of these
• C) x=0
• D) x=-7/2

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

• A) 1/n
• B) 4/n
• C) 5
• D) 5/n

If f (x) = x^3 is defined on the interval
[-1, 2], then which of the following is true about it

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

If f(x)=Cot(x) then mean value theorem can be applied to it on the interval (0,2pi)

• A) False
• B) True
• C)
• D)

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

• A) -1
• B) 0.5
• C) 0
• D) 1

What is the summation of ‘kx’ where k goes from 1 to 30?

• A) 465x
• B) 414x
• C) 523x
• D) 419x

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