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 may or may not have a critical point.
• B) None of these.
• C) It must have at least one critical point.
• D) It would not have more than one stationary point.

If the graph of $f$ lies below all of its tangents on an interval $I$,then it is called___________ on $I$.

• A) constant function
• B) concave upward
• C) None of these
• D) concave downward

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

• A) 28.
• B) 76.
• C) 50.
• D) 30.

The indefinte integral of ‘cos (x) – sin (x)’ is………………

• A) cos (x) .sin (x) +c
• B) -cos (x) + sin (x) +c
• C) -cos (x) – sin (x)+c
• D) cos (x) +sin (x)+c

Which of the following is the regular partition of the interval [0,2]?

• A) [0,0.5],[0.5,1.25],[1.25,1.50],[1.50,2]
• B) [0,0.50],[0.50,1],[1,1.50],[1.50,2]
• C) [0,0.25],[0.25,1],[1,1.50],[1.50,2]
• D) [0,0.25],[0.25,0.75],[0.75,1.25],[1.25,2]

If f(x) =cos(x) then mean value theorem can be applied on this in the interval (pi/2, 3pi/2)

• A) True
• B) False
• C)
• D)

What will be the value of summation of k3 where k goes from 9 to 10

• A) 1729
• B) 1998
• C) 1081
• D) 1100

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) None of these.
• C) Its absolute maximum value exists at 2.
• D) Its absolute minimum value exists at -2

$${\text{The integral }}\int {\cos (5x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{{\sin (5x)}}{5} + c$$
• B) $${\text{None of these}}$$
• C) $$\frac{{\sin (5x)}}{5} + c$$
• D) $$5\sin (5x) + c$$

If the closed interval [-10,x] is divided into ‘20’ equally spaced subintervals each of which having the width equals to ‘1’ unit then the value of ‘x’ is --------

• A) 30
• B) 20
• C) 0
• D) 10

$$\text{The vertical asymptote of the function }f(x)=\frac{3{{x}^{2}}+1}{2-x}\text{ is}$$

• A) $\infty$
• B) 0
• C) -2
• D) 2

If $f'(c) = 0$ and $f''(c) > 0$, then $f$ has a/an____________ at c.

• A) local maximum
• B) inflection point
• C) None of these
• D) local minimum

The area of a rectangle can be found by simply …………its dimensions.

• A) adding
• B) subtracting
• C) dividing
• D) multiplying

For any continuous function on the interval [0,1], if the area under this curve is divided into ‘5’ equal rectangles ,then the length of each rectangle will be………

• A) 1/5
• B) 1/4
• C) 1/2
• D) 1

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

• A) False
• B) True
• C)
• D)

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

• A) 3,6,8,9
• B) 3,4,5,6
• C) 4,5,6,7
• D) 5,6,7,8

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 relative minimum value exists at the critical point.
• C) Its relative minimum value does not exist at the critical point
• D) Its absolute minimum value exists at the critical point.

For the area under the curve f(x) = x+2 from x = 2 to x = 8 with right end points approximations for n = 3, what will be the values of xk* ?

• A) 0, 4 and 8
• B) 2, 4 and 8
• C) 4, 6 and 8
• D) 2, 5 and 8

If f(x)=1 / (x^2) and the interval is [-1,1] , then Rolle’s theorem can be applied.

• A) False
• B) True
• C)
• D)

Which of the following is the sum of 2t^2 where t goes from 1 to 5?

• A) 2+8+18+32+50
• B) 2+18+32+50+62
• C) 2+8+28+32+50
• D) 2+18+28+32+60