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

$${\text{The integral }}\int {{{\left( {{x^3} + 1} \right)}^{10}}\,.3{x^2}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$
• B) $$\frac{{{{\left( {{x^3} + 1} \right)}^{11}}}}{{11}} + c$$
• C) $$\frac{{{{\left( {{x^3} - 1} \right)}^{11}}}}{{11}} + c$$
• D) $${\text{None of these}}$$

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

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

If x = 1 + 2 +3 + 4 + . . . + 20, then
x = ________.

• A) None of these.
• B) 500.
• C) 200.
• D) 210.

Which of the following is the sum of 3k+1 where k goes from 0 to 2?

• A) 30
• B) 27
• C) 33
• D) 39

What will be the sigma notation for 32+52+72+92?

• A) summation of (2k2+1) where (k varies from 3 to 6)
• B) summation of (2k+1)2 where (k varies from 1 to 4)
• C) summation of (k2) where (k varies from 3 to 9)
• D) summation of (2k-1)2 where (k varies from 1 to 4)

f(x) = (x^2)+1 is a continuous function on (-infinity ,+infinity ) , and ‘f’ has no absolute maximum on (-infinity ,+infinity ) because………

• A) lim (f(x)) = +infinity as ‘x’ tends to ±infinity
• B) lim (f(x)) = -infinity as ‘x’ tends to ±infinity
• C) lim (f(x)) = 0 as ‘x’ tends to ±infinity
• D) lim (f(x)) = 1 as ‘x’ tends to ±infinity

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)