$${\text{The integral }}\int {\cos e{c^2}(3{x^2})\,.6x\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \cot (3{x^2}) + c$$
• B) $$\sec (3{x^2}) + c$$
• C) $${\text{None of these}}$$
• D) $${\text{cot(3}}{{\text{x}}^2}) + c,$$

The derivative of the area under the continuous function f(x)= 2+3Sinx in the interval[-pi,pi] is---------

• A) 2-3Cosx
• B) 2-3Sinx
• C) 2+3Cosx
• D) 2+3Sinx

Integration of 3x^2 with respect to x is…………

• A) x^2
• B) x
• C) x^4
• D) x^3

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

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

If a function f has a relative extrema at a point c, then c is a critical point for f .

• A) False
• B) True
• C)
• D)

The anitderivative of the function f(x)=2-7Cosx, is -------

• A) 2x-7Sinx+100
• B) 2x-7Sinx+C
• C) 2x-7Sinx-100
• D) All choices are true

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
• C) 1/2
• D) 1/4

$$\begin{align} & \text{A function }f\text{ is said to have a }\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{at }{{x}_{0}}\text{, if }f({{x}_{0}})\ge f(x)\text{ for all }x\text{ } \\ & \text{in some open interval containing }{{x}_{0}}. \\ \end{align}$$

• A) Relative minimum
• B) Relative maximum
• C)
• D)

summation of (3) ;where ( j varies from 1 to 4) indicates to add ………to itself 4 times.

• A) 3
• B) 4
• C) 2
• D) 1

In sigma notation 12+14+16+18+20 can be written as……….

• A) summation of (k^2) where (k varies from 6 to10)
• B) summation of (2k) where (k varies from 1 to5)
• C) summation of (k) where (k varies from 6 to10)
• D) summation of (2k) where (k varies from 6 to10)

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

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)

Which of the following is the sum of 5^ (k+1) where k goes from 1 to 3?

• A) 875
• B) 775
• C) 525
• D) 675

$${\text{In}}\,{\text{the}}\,{\text{notation:}}\,\int_a^b {f(x)} dx{\text{,}}\;f(x)\,{\text{is}}\,{\text{called___________}}{\text{.}}$$

• A) $${\text{None}}\,{\text{of}}\,{\text{these}}$$
• B) $${\text{Integrand}}$$
• C) $${\text{Integration}}$$
• D) $${\text{Differential}}$$

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) 30.
• C) 50.
• D) 76.

If ‘n’ goes from 1 to 4 and the summation of ‘na’ =Maxima of (e^x) in the interval[-e,0], then the value of ‘a’ is -----------

• A) -10
• B) 1/10
• C) 10
• D) -1/10

If f (x) = 2 x + 7 is defined on the interval
[2, 4), then which of the following is true about it.

• A) None of these.
• B) It has both absolute maximum and minimum values.
• C) It has only absolute maximum value.
• D) It has only absolute minimum value.

Sum of cubes of n-terms of a series whose nth term is ‘n’ = ---

• A) Square of n(n+1)(2n+1)/6
• B) Square of (n+1)/2
• C) Square of n(n+1)/6
• D) Square of n(n+1)/2

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

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

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

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