Integration of 5 with respect to x is…………

• A) 5
• B) x
• C) 5x
• D) 5x^2

What is the estimated area under f(x) = x from x = 0 to x = 3 with left end points for n = 3?

• A) 4
• B) 3
• C) 6
• D) 5

If the interval [3,7] is divided into ‘4’ equal subintervals ,then right endpoint of each subinterval will be………

• A) 4,5,6,7
• B) 3,4,5,6
• C) 3,5,6,8
• D) 5,6,7,8

\[{\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {x^3} - 3x\,{\text{in}}\,{\text{the}}\,{\text{interval}}\,\left[ {0,\sqrt 3 } \right]{\text{.}}\]

• A) \[\frac{2}{3}\]
• B) \[ - 1\]
• C) \[\frac{1}{3}\]
• D) \[1\]

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

To find the area between continuous curve f(x) and the closed interval [a,b] on x-axis, we take
-------------- of f(x) on the interval [a,b].

• A) right hand limit
• B) derivative
• C) left hand limit
• D) integral

1+2+3+…+200 equals _____.

• A) 20012
• B) 21021
• C) 21220
• D) 20100

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) 110
• D) 101

For the area under the curve f(x) = x+2 from x = 2 to x = 4 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 2.5
• B) 2
• C) 3.5
• D) 3

\[{\text{For}}\,{\text{Rolle's}}\,{\text{Theorem,}}\,f\,{\text{is}}\,{\text{differentiable}}\,{\text{on}}\,{\text{the}}\,{\text{interval __________}}{\text{.}}\]

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

If the interval [3,7] is divided into ‘4’ equal subintervals ,then left endpoint of each subinterval will be………

• A) 4,5,6,7
• B) 3,4,5,6
• C) 5,6,7,8
• D) 3,6,8,9

Which of the following is the regular partition of the interval [0,2]?

• A) [0,0.25],[0.25,1],[1,1.50],[1.50,2]
• B) [0,0.50],[0.50,1],[1,1.50],[1.50,2]
• C) [0,0.25],[0.25,0.75],[0.75,1.25],[1.25,2]
• D) [0,0.5],[0.5,1.25],[1.25,1.50],[1.50,2]

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

• A) Its anti – derivative is Sin(x) + x^2/2 + 10.
• B) Its anti – derivative is -Sin(x) + x^2/2 + 4.
• C) Its anti – derivative is Sin(x) + x^2/2 + 6.
• D) Its anti – derivative is Sin(x) + x^2/2 + 4.

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = derivative of Cosx at (pi/2), then the value of ‘a’=------

• A) -6
• B) 1/6
• C) 6
• D) -1/6

The function f(x)= 2x^3-15x^2+36x have the critical points ……………on the interval [1,5]

• A) 2,3
• B) 1,5
• C) 2,4
• D) 3,4

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

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

If $f''(x) < 0\,\forall \,x \in I$, then the graph of $f$ is ___________ on $I$.

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

For the area under the curve f(x) = x+2 from x = 2 to x = 8 with left end points approximations for n = 3, what will be the values of xk* ?

• A) 3, 5 and 7
• B) 4, 6 and 8
• C) 2, 6 and 8
• D) 2, 4 and 6

$$\text{If a function }f\text{ has a relative extrema at }{{x}_{0}}\text{, then}$$

• A) $$\text{either}\,{f}'\left( {{x}_{0}} \right)=0\,\text{or }f\text{ is not differentiable at }{{x}_{0}}$$
• B) $${f}'\left( {{x}_{0}} \right)\le 0$$
• C) $${f}'\left( {{x}_{0}} \right)>0$$
• D) $$f\text{ is differentiable at }{{x}_{0}}$$

Critical point of function f(x) =4x^2-4x+1 on closed interval [0,1] is x = ………

• A) 0
• B) 1,2
• C) 1/2
• D) 2