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

• A) 13.
• B) 6.
• C) None of these.
• D) 5.

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

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

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

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

Which of the following is the sum of 5^ (k+1) where k goes from 1 to 3?

• A) 675
• B) 875
• C) 525
• D) 775

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

• A) 2,4
• B) 1,5
• C) 3,4
• D) 2,3

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

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

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

• A) $${\text{None of these}}$$
• B) $$- \ln \left| {\cos (x)} \right| + c$$
• C) $$\sec (x) + c$$
• D) $$\cos ec(x) + c$$

If f(x)=Tan(x) then mean value theorem can be applied to it on the interval (0,2pi)

• A) True
• B) False
• C)
• D)

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

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

For any continuous function on the interval [0,1], if the area under this curve is divided into ‘5’ equal rectangles ,then the length of each rectangle will be………

• A) 1/2
• B) 1/4
• C) 1/5
• D) 1

Subdivide the interval [3, 5] into n equal parts, and then the width of each subinterval is ----

• A) n
• B) 2/n
• C) -2/n
• D) 1/n

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

$${\text{The integral }}\int {{{\left( {{x^2} + 1} \right)}^{\frac{5}{2}}}.\,x\,dx\,} {\text{will be equal to ?}}$$

• A) $${\left( {{x^2} + 1} \right)^{\frac{7}{2}}} + c$$
• B) $$\frac{{2{{\left( {{x^2} + 1} \right)}^{\frac{7}{2}}}}}{7} + c$$
• C) $${\text{None of these}}$$
• D) $$\frac{{{{\left( {{x^2} + 1} \right)}^{\frac{7}{2}}}}}{7} + c$$

$${\text{The integral }}\int {\sqrt {2x + 3} \,dx} {\text{ will be equal to ?}}$$

• A) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{3}{2}}}}}{3} + c$$
• B) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{3}{2}}}}}{2} + c$$
• C) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{2}{3}}}}}{3} + c$$
• D) $$\frac{{{{\left( {2x + 3} \right)}^{\frac{1}{2}}}}}{3} + c$$

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

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) local maximum
• D) global maximum

(1^3)+(2^3)+(3^3)+….+(20^3) equals ---------

NOTE: x^n means ‘x’ to the power ‘n’

• A) 42925
• B) 34548
• C) None of these
• D) 44100

What is the estimated area under f(x) = 2x from x = 0 to x = 4 with right end points for n = 2?

• A) 8
• B) 24
• C) 18
• D) 10

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

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

If the function f(x)= (x^2)+1 satisfies all the conditions of Rolle’s theorem in the interval [-1,1] , then the value of ‘c’ will be……..

• A) 2
• B) 3
• C) 4
• D) 0