The dimensions of a rectangle are given to be 8ft by 12ft. The perimeter of rectangle will be…………..

• A) 40 feet
• B) 30 feet
• C) 50feet
• D) 60 feet

The indefinite integral of 5sinx is ……….

• A) 5cosx +c
• B) -5cosx+c
• C) cosx/5+c
• D) -cosx/5+c

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

NOTE: x^n means ‘x’ to the power ‘n’

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

To find out critical values of a function, we put it equal to zero and solve for x.

• A) True
• B) False
• C)
• D)

13+23+33+…+193 equals _____.

• A) [19(20)]2/2
• B) 19(20)2/2
• C) [19(20)/2]2
• D) 19(20)/22

Which of the following is the sum of (2k-1) where k goes from 0 to 2?

• A) -2
• B) 3
• C) 4
• D) -1

For the area under the curve f(x) = 2x from x = 0 to x = 12 with left points approximations for n = 3, what will be the values of xk* ?

• A) 0, 5 and 10
• B) 0, 4 and 8
• C) 0, 6 and 12
• D) 0, 3 and 6

1+2+3………+t equals

• A) n(n+1)(2n+1)/6
• B) None of these
• C) n(n+1)/2
• D) t(t+1)/2

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

• A) False
• B) True
• C)
• D)

What will be the sigma notation for 43+63+83+103?

• A) summation of (2k)3 where (k varies from 1 to 4)
• B) summation of (2k)3 where (k varies from 2 to 5)
• C) summation of (2k3) where (k varies from 2 to 5)
• D) summation of (2k+1)3 where (k varies from 2 to 5)

$$\text{If }{f}'(x)={{x}^{2}}-x\text{. Then the critical points of the function }f\text{ are}$$

• A) 1, -1
• B) 1, 2
• C) 0, 1
• D) 0, 2

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

If x = (1^2)+(2^2)+(3^2)+(4^2) + . . . + (30^2), then x = ________.

• A) 465.
• B) 9455.
• C) 900.
• D) None of these.

If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the LEFT end point of 13th sub-interval will be--------.

• A) 4
• B) 5
• C) 2
• D) 3

For the area under the curve f(x) = 2x from x = 0 to x = 8 with mid points approximations for n = 2, what will be the values of xk* ?

• A) 3 and 7
• B) 2 and 6
• C) 4 and 6
• D) 1 and 5

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

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

If $f$ is______________ on a closed interval $[a,b]$, then $f$, attains an absolute maximum value $f(c)$ and an absoulte minimum value $f(d)$ at some numbers $c$ and $d$ in $[a,b]$.

• A) differentiable
• B) constant
• C) None of these
• D) continuous

$\text{A critical point for a function }f,\text{ where }{f}'(x)=0\text{ is called as}\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{ point}\text{.}$

• A) Stationary
• B) Tangent
• C) Mid
• D) Corner

Integral of x^(-10) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) - 1/(9x^9)+C
• B) -10x^(-11)+C
• C) 1/(9x^9)+C
• D) None of these

\[{\text{The integral }}\int {\frac{{4x}}{{{{(2{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \frac{1}{{2{x^2} + 1}} + c\]
• B) \[ - \frac{1}{{{{(2{x^2} + 1)}^3}}} + c\]
• C) \[\frac{1}{{2{x^2} + 1}} + c\]
• D) \[ - \frac{1}{{2x + 1}} + c\]