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

If f(x) = Cos(x) + Sin(x) + x, then which of the following is NOT true about it.

• A) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 4.
• B) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 5.
• C) None of these.
• D) Its anti – derivative is -Sin(x) – Cos(x) + x^2/2 + 4.

If a function has an extreme value (either a maximum or a minimum) on an open interval (a,b), then the extreme value occurs at a ........

• A) Any point in the open interval (a,b)
• B) Critical point of f(x)
• C)
• D)

f(x)=x^3-3x, is increasing on the interval (0 ,infinity)

• A) True
• B) False
• C)
• D)

If f (x) = x^2 is defined on the interval [-1, 3], then which of the following is true about it.

• A) Its absolute maximum value is 0.
• B) None of these.
• C) Its absolute maximum value is 9.
• D) Its relative maximum value is 9.

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

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

$${\text{For}}\,{\text{Rolle's}}\,{\text{Theorem,}}\,f\,{\text{is}}\,{\text{continuous}}\,{\text{on}}\,{\text{the}}\,{\text{interval __________}}{\text{.}}$$

• A) $$[a,b)$$
• B) $$(a,b)$$
• C) $$(a,b]$$
• D) $$[a,b]$$

If the function f(x)= (x^2)+1 satisfies all the conditions of Rolle’s theorem in the interval [-1,1] , then the value of ‘c’ will be……..

• A) 2
• B) 3
• C) 4
• D) 0

What will be the sigma notation for 32+42+52+62 ?

• A) summation of (k+1)2 where (k varies from 3 to 6)
• B) summation of (k2) where (k varies from 3 to 6)
• C) summation of (k-1)2 where (k varies from 2 to 5)
• D) summation of (k2) where (k varies from 1 to 4)

For the application of mean value theorem on f( x ) =x^3-3x^2-2x ; [0,2], which of the following is true?

• A) f( x ) is continuous over [ 0, 2) and f(x) is differentiable over ( 0,2 )
• B) f( x ) is continuous over [ 0, 2] and f(x) is differentiable over ( 0,2 )
• C) f( x ) is continuous over [ 0, 2] and f(x) is not differentiable over ( 0,2 )
• D) f( x ) is continuous over [ 0, 2] and f(x) is differentiable over [ 0,2 )

The estimated area under f(x) = x^2 from
x = 1 to x = 3 with right end points for
n = 2 is ________.

• A) 10.
• B) 5.
• C) 13.
• D) None of these.

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

• A) 0, 6 and 12
• B) 4, 8 and 12
• C) 2, 7 and 12
• D) 6, 9 and 12

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

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

If f(x) = Sec^ (2) x + x^3, then which of the following is NOT true about it.

• A) None of these.
• B) Its anti – derivative is Tan(x) + x^4/4 + 15.
• C) Its anti – derivative is Tan(x) + x^4/4 + 12.
• D) Its anti – derivative is Tan(x) + x^4/4 + 10.