If x = (1^2)+(2^2)+(3^2)+(4^2) + . . . + (30^2), then x = ________.

• A) 900.
• B) None of these.
• C) 465.
• D) 9455.

If f(x)=(x^3)+(x^2)+x+1 , then ‘f’ is continuous and differentiable everywhere because ‘f’ is a ……..

• A) Function
• B) Relation
• C) Equation
• D) Polynomial

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

• A) \[\frac{1}{2}\ln \left| {\sec (2x)} \right| + c\]
• B) \[\ln \left| {{\text{sec}}(2x)} \right| + c\]
• C) \[{\text{ln}}\left| {\sin (2x)} \right| + c\]
• D) \[\frac{1}{2}\ln \left| {\sin (2x)} \right| + c\]

\[{\text{The integral }}\int {\cos e{c^2}(3{x^2})\,.6x\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \cot (3{x^2}) + c\]
• B) \[\sec (3{x^2}) + c\]
• C) \[{\text{None of these}}\]
• D) \[{\text{cot(3}}{{\text{x}}^2}) + c,\]

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = definite integral of ‘1’ on closed interval [0,1], then the value of ‘a’=------------

• A) -1/6
• B) 6
• C) -6
• D) 1/6

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

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

What will be the value of summation of k2 where k goes from 11 to 12

• A) 244
• B) 212
• C) 265
• D) 281

$${\text{The integral }}\int {\frac{{4x}}{{{{(2{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

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

To find out critical values of a function, we put it equal to zero and solve for x.

• A) True
• B) False
• C)
• D)

summation of (6) ;where ( j varies from 1 to 8) indicates to add ‘6’ to itself ……….. times.

• A) 8
• B) 9
• C) 10
• D) 11

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

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

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

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

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

• A) 15
• B) 21
• C) 30
• D) 25

\[{\text{The integral }}\int {\frac{{6x}}{{{{(3{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \frac{1}{{6x + 1}} + c\]
• B) \[ - \frac{1}{{3{x^2} + 1}} + c\]
• C) \[ - \frac{1}{{{{(3{x^2} + 1)}^3}}} + c\]
• D) \[\frac{1}{{3{x^2} + 1}} + c\]

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

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

If x = 5 + 6 + . . . + 40, then x = ________.

• A) None of these.
• B) 820.
• C) 810.
• D) 850.

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

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

Sum of n-terms of a series whose nth term is ‘n’ = 1/n+1.then what is the sum of the first two terms is -----

• A) 5/6
• B) 6
• C) 6/4
• D) 6/5

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

Why the equation: x^2 + 8 = 0 does not have approximate solution while using Newton's method?

• A) x^2 will always be nonnegative
• B) x^2 will always be negative
• C)
• D)