$$\text{The vertical asymptote of the function }f(x)=\frac{3{{x}^{2}}+1}{2-x}\text{ is}$$

• A) -2
• B) 0
• C) $\infty$
• D) 2

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=-1,0
• D) x=0,0.5,-0.5

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

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

Subdivide the interval [0, 1] into 2 equal parts, and then the width of each sub-interval will have length ………

• A) -1/2
• B) 1/2
• C) 1
• D) 0

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

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

\[\text{If we say a function }f\text{ have a relative extremum at a point }{{x}_{0}},\text{ then it means that }f\text{ has }\!\!~\!\!\text{ }\_\_\_\_\_\_\_\_\text{ at }{{x}_{0}}.\]

• A) Relative minimum
• B) None of these
• C) Either a relative maximum or relative minimum
• D) Relative maximum

Let y = f(x) be a discontinuous function on a finite closed interval, then which of the following is true about it.

• A) It must have absolute extreme values.
• B) It may or may not have absolute extreme values.
• C) None of these.
• D) It has only absolute minimum value.

$${\text{The integral }}\int {{{\sec }^2}(2{x^2})\,.4x\,dx\,} {\text{will be equal to ?}}$$

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

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) 101
• B) 011
• C) 110
• D) 111

The polynomial function f(x)=6x^2-30x+36 has the critical point over the real line is ………

• A) 5/2
• B) 5
• C) 2/5
• D) 2

What is the estimated area under f(x) = 10-x2 from x = 0 to x = 3 with left end points for n = 3?

• A) 25
• B) 15
• C) 30
• D) 21

\[{\text{The integral }}\int {\sqrt {4x - 3} \,dx\,} {\text{will be equal to ?}}\]

• A) \[\frac{{{{(4x + 3)}^{\frac{3}{2}}}}}{6} + c\]
• B) \[{\text{None of these}}\]
• C) \[\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{3} + c\]
• D) \[\frac{{{{(4x - 3)}^{\frac{3}{2}}}}}{6} + c\]

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

• A) $$f\left( {{x}_{0}} \right)\ge \text{ }f\left( x \right)$$
• B) $$f\left( {{x}_{0}} \right)=f\left( x \right)$$
• C) $$f\left( {{x}_{0}} \right)>\text{ }f\left( x \right)$$
• D) $$f\left( {{x}_{0}} \right)\le \text{ }f\left( x \right)$$

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

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

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

• A) 1.5
• B) 2.5
• C) 0.5
• D) -0.5

\[{\text{The integral }}\int {{{\sec }^2}(2{x^2})\,.4x\,dx\,} {\text{will be equal to ?}}\]

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

\[\text{If }{f}'(x)={{x}^{2}}-1.\text{ Then the critical points of the function }f\text{ are}\]

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

$$\text{If we say a function }f\text{ have a relative extremum at a point }{{x}_{0}},\text{ then it means that }f\text{ has }\!\!~\!\!\text{ }\_\_\_\_\_\_\_\_\text{ at }{{x}_{0}}.$$

• A) Either a relative maximum or relative minimum
• B) Relative minimum
• C) None of these
• D) Relative maximum

To get better approximation to actual area under a continuous curve over a closed interval, we have to increase ………

• A) Size of the interval
• B) Number of subintervals
• C) Total area
• D) Width of the subintervals

Right end point ,left end point, and midpoint evaluation all converges to same result as number of subintervals tends to +ive infinity.

• A) False
• B) True
• C)
• D)