If x =(1+2+3+...+10)+{(1^3)+(2^3)+(3^3)+...+ (10^3)}, then x = _______.

• A) 55.
• B) 3025.
• C) 110.
• D) 3080.

\[{\text{The integral }}\int {\frac{{10x}}{{{{(5{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \frac{1}{{{{(5{x^2} + 1)}^3}}} + c\]
• B) \[\frac{1}{{5{x^2} + 1}} + c\]
• C) \[ - \frac{1}{{5{x^2} + 1}} + c\]
• D) \[ - \frac{1}{{5x + 1}} + c\]

If x=-3 and x=3 are the two critical points of the function: f(x)=81x-3(x^3) then by using the 2nd derivative test, we can conclude that f(x) is relatively maximum at-----

• A) x= 3
• B) x= -9
• C) x=0
• D) x=-3

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

Integral of x^101 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (1/102)x^102+C
• B) None of these
• C) 102x^102+C
• D) 101x^100 +C

‘x.ln(x/e)’ is the anti-derivative of ‘lnx’ if and only if the derivative of ‘x.ln(x/e)’ is euqal to --------

• A) xln(x/e)
• B) lnx
• C) ln(x/e)
• D) x

The estimated area under f(x) = x from
x = 0 to x = 3 with right end points for
n = 3 is ________.

• A) None of these
• B) 7.
• C) 6.
• D) 5.

If f(x) = x^5 + x, then which of the following is true about it.

• A) None of these.
• B) Its anti – derivative is x^5/5 + 1.
• C) Its anti – derivative is 5x^4 + 1.
• D) Its anti – derivative is x^6/6 + x^2/2 + 6.

Integration of 4Cosx with respect to x is………..

• A) 4Sinx
• B) - 4Sinx
• C)
• D)

Integration of (Cosx/Sinx).Cosecx with respect to x…………

• A) Cosecx
• B) -Cosecx
• C) Secx
• D) Cotx

The critical value of the function y=100x – x^2 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) x=50
• C) x=25
• D) x=0

If $f'$ changes from negative to positive at c, then $f$ has a _______________ at c.

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

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

• A) 5
• B) 4
• C) 3
• D) 2

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

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

The vertical asymptotes of a function occur at the points where the denominator of the function becomes

• A) 1
• B) 0
• C) -1
• D) Undefined

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) 20
• B) 0
• C) 10
• D) 30

By applying Roll’s theorem on f(x) = x over the interval [-1,1], the points where the derivative of f(x)=x is not taken are………

• A) x= -1, 1
• B) x=0,0.5,-0.5
• C) x=0,1
• D) x=-1,0

The indefinite integral of 5sinx is ……….

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

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

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of f (xk*) ?

• A) 1
• B) 3
• C) 6
• D) 2