Area of a rectangle whose width is 5 units and length is 6 units will be ….

• A) 22 units
• B) 30 square units
• C) 11 units
• D) None of these

\[{\text{The integral }}\int {\sin (5x)dx} {\text{ will be equal to ?}}\]

• A) \[{\text{ - }}\frac{{\cos 5x}}{5} + c\]
• B) \[\frac{{\cos 5x}}{5} + c\]
• C) \[5\cos 5x + c\]
• D) \[{\text{ - }}\frac{{\cos 4x}}{5} + c\]

Mean value theorem states that between any two points A and B on a curve y=f(x) , there must be at least one point where the Tangent line to the curve is……………joining A and B

• A) Parallel to the tangent line
• B) Perpendicular to the secant line
• C) Perpendicular to the tangent line
• D) Parallel to the secant line

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) e-1
• B) -e
• C) e
• D) 1-e

$${\text{The integral }}\int {\sqrt {2x + 3} \,dx} {\text{ will be equal to ?}}$$

• A) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{3}{2}}}}}{3} + c$$
• B) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{1}{2}}}}}{3} + c$$
• C) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{2}{3}}}}}{3} + c$$
• D) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{3}{2}}}}}{2} + c$$

Summation of 2 where sum ranges from 0 to 10 equals 20.

• A) False
• B) True
• C)
• D)

If $f$ has a local maximum or minimum at c, and if $f'(c)$ exists, then $f'(c) = 0$. This is the statement of _________.

• A) Extreme Value Theorem
• B) Fermat's Theorem
• C) Mean Value Theorem
• D) None of these

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