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

If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the MIDDLE point of 8th
sub-interval will be--------.

• A) -0.5
• B) 2.5
• C) 1.5
• D) 0.5

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

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

Integral of 3sec(x)tan(x) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) 3tan(x)+C
• B) (3/2)sec^2(x)+C
• C) None of these
• D) 3sec(x)+C

$${\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {x^3} - 3x\,{\text{in}}\,{\text{the}}\,{\text{interval}}\,\left[ {0,\sqrt 3 } \right]{\text{.}}$$

• A) $$\frac{1}{3}$$
• B) $$\frac{2}{3}$$
• C) $$1$$
• D) $$- 1$$

(1^3)+(2^3)+(3^3)+….+(20^3) equals ---------

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) 42925
• C) 44100
• D) 34548

For the area under the curve f(x) = x+1 from x = 1 to x = 5 with mid points approximations for n = 2, what will be the values of xk* ?

• A) 1 and 3
• B) 2.5 and 3.5
• C) 2 and 4
• D) 3 and 4

$${\text{The integral }}\int {\frac{x}{{1 + {x^2}}}\,dx\,} {\text{will be equal to ?}}$$

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