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

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

1+2+3………+t equals

• A) n(n+1)/2
• B) None of these
• C) t(t+1)/2
• D) n(n+1)(2n+1)/6

Which of the following is the sum of (2k+1) where k goes from 1 to 4?

• A) 20
• B) 24
• C) 26
• D) 22

$${\text{In}}\,{\text{the}}\,{\text{notation:}}\,\int_a^b {f(x)} dx{\text{,}}\;f(x)\,{\text{is}}\,{\text{called___________}}{\text{.}}$$

• A) $${\text{Differential}}$$
• B) $${\text{Integration}}$$
• C) $${\text{Integrand}}$$
• D) $${\text{None}}\,{\text{of}}\,{\text{these}}$$

By applying mean value theorem to the function
f(x)=lnx in the interval [1,e], the corresponding value of ‘c’ is ------------(Hint: lne=1, ln1=0)

• A) e-1
• B) -e
• C) 1-e
• D) e

While using Newton’s mathod,which of the following will be the best initial approximate solution to solve the equation: x-Sinx=0

• A) x=pi/2
• B) x=-pi/2
• C) x=pi
• D) x=0

What is length of each subinterval if the interval [-1,1] is divided into n subintervals of equal length.

• A) 0
• B) 2/n
• C) 1/n
• D) None of these

If $f$ has a local maximum or minimum at c, and if $f'(c)$ exists, then $f'(c) = 0$. This is the statement of _________.

• A) None of these
• B) Extreme Value Theorem
• C) Mean Value Theorem
• D) Fermat's Theorem

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

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

The maximum and minimum values of the function
f(x)=1/x does not lie in the interval [-1,1] because -------

• A) f(x) is differentiable in [-1,1]
• B) f(x) is not one-to-one
• C) f(x) is discontinuous in [-1,1]
• D) f(x) is continuous in [-1,1]

Newton’s method uses the …………… to approximate the root.

• A) None of these
• B) Tangent line
• C) Normal line
• D) Secant line

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

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

Let A be the area of a rectangle under a continuous function f(x) over a closed interval
[a, b]. If this area is divided in to ‘n’ sub-rectangles then width of each approximated sub-intervals is ---------

• A) (a-b)/2
• B) (b-a)/2n
• C) (b-a)/n
• D) (a-b)/n

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

• A) None of these.
• B) Its relative minimum value exists at the critical point.
• C) Its absolute minimum value exists at the critical point.
• D) Its relative minimum value does not exist at the critical point.

Increase in number of rectangles under any continuous function gives …………. approximation to area.

• A) better
• B) no change in
• C) None of these
• D) Poor

summation of (3) ;where ( j varies from 1 to 4) indicates to add ………to itself 4 times.

• A) 2
• B) 1
• C) 3
• D) 4

(1^2)+(2^2)+(3^2)+……………..+(50^2) equals--------
NOTE: x^n means ‘x’ to the power ‘n’

• A) 42925
• B) None of these
• C) 6373
• D) 55227

Subdivision of an interval is also called ………. of the interval.

• A) Evaluation
• B) Separation
• C) Partition
• D) Composition

Integration of “cosecx.cotx” with respect to x is -----

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

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

• A) 5x
• B) 5
• C) x
• D) 5x^2