A function $f$ has an/a___________ at $c$ if $f(c) \geqslant f(x)\,\forall \,x \in \,D$, where $D$ is the domain of $f$.

• A) absolute maximum
• B) absolute maximum/global maximum
• C) global maximum
• D) local maximum

summation of (n+i);where (i varies from 1 to 1) =………..

• A) n+1
• B) 1
• C) n
• D) 0

If x = 3 + 4 + . . . + 20, then x = ________.

• A) 210.
• B) 250.
• C) None of these.
• D) 207.

Sum the first three terms of the series, whose general term is 5ki
Where first term=k1=10,
Second term= k2=14
Third term=k3= -2
The correct choice is …………
Note: 1, 2, 3 and i with k are in subscript

• A) 111
• B) 011
• C) 101
• D) 110

If ‘n’ goes from 1 to any large ODD number then the summation of ‘(-1)^n’ = ---------

• A) 1
• B) -1
• C) that specific large ODD number
• D) Zero

For the function f(x)=|x|-1, if f(-1)=f(1)=0 then which of the following conclusion can be drawn about the point ‘c’ in the interval [-1,1] such that f ’(c)=0?

• A) c=0.5
• B) Every point in [-1,1] can be taken as ‘c’
• C) No such ‘c’ exists
• D) c=0

12+22+32+…+152 equals _____.

• A) 15(16)(31) / 6
• B) 15(16)(30) / 6
• C) 15(16)(17) / 6
• D) 15(16)(29) / 6

Absolute minimum of the function f(x)=x in the semi open interval (0,2] is-------

• A) 1
• B) Undefined
• C) 2
• D) 0

Which of the following is the sum of 2k+1 where k goes from 0 to 2?

• A) 8
• B) 14
• C) 10
• D) 12

$${\text{The integral }}\int {{{\sec }^2}(5{x^2})\,.10x\,dx\,} {\text{will be equal to ?}}$$

• A) $$\sec (5{x^2}).\tan (5{x^2}) + c$$
• B) $$\tan (5x) + c$$
• C) $$\tan (5{x^2}) + c$$
• D) $${\text{se}}{{\text{c}}^2}(10x) + c$$

If we subdivide the interval [1,6] into n equal parts, then what will be the length ∆x of each part?

• A) 7/n
• B) 1/n
• C) 6/n
• D) 5/n

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 )

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 xk* ?

• A) 1
• B) 2
• C) 1.5
• D) 2.5

While solving the equation, 10x-(e^x)=0 by using Newton method, if x=0 is the initial approximate solution then the next approximation will be-----

• A) 1/9
• B) 1/10
• C) -1/10
• D) -1/9

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=0,1
• C) x=0,0.5,-0.5
• D) x=-1,0

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

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) 2
• B) 3
• C) 1
• D) 6

Summation of 9t where ‘t’ goes from 1 to 30” is same as “summation of 9k where k goes from 1 to 30”.

• A) False
• B) True
• C)
• D)

summation of (6) ;where ( j varies from 1 to 8) indicates to add ‘6’ to itself ……….. times.

• A) 11
• B) 10
• C) 8
• D) 9

If ‘n’ goes from 1 to any large EVEN number then the summation of ‘(-1)^n’ = ---------

• A) -1
• B) zero
• C) 1
• D) that specific large EVEN number