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

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

• A) Its relative maximum value is 9.
• B) None of these.
• C) Its absolute maximum value is 9.
• D) Its absolute maximum value is 0.

\[{\text{The integral }}\int {{{\sec }^2}(5{x^2})\,.10x\,dx\,} {\text{will be equal to ?}}\]

• A) \[\sec (5{x^2}).\tan (5{x^2}) + c\]
• B) \[\tan (5x) + c\]
• C) \[{\text{se}}{{\text{c}}^2}(10x) + c\]
• D) \[\tan (5{x^2}) + c\]

Sum of cubes of n-terms of a series whose nth term is ‘n’ = ---

• A) Square of n(n+1)/2
• B) Square of n(n+1)(2n+1)/6
• C) Square of (n+1)/2
• D) Square of n(n+1)/6

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

If x = (4^2) + (5^2) + (6^ 2) + . . . + (30^2), then x = ________.

• A) 465.
• B) 9455.
• C) 9441.
• D) 400.

Area of a rectangle whose width is 5 units and length is 6 units will be ….

• A) None of these
• B) 11 units
• C) 22 units
• D) 30 square units

What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 1?

• A) 20
• B) 21
• C) 24
• D) 28