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

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

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

For the area under the curve f(x) = x+2 from x = 2 to x = 4 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 3
• B) 3.5
• C) 2
• D) 2.5

\[{\text{The integral }}\int {\frac{{10x}}{{{{(5{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}\]

• A) \[ - \frac{1}{{{{(5{x^2} + 1)}^3}}} + c\]
• B) \[ - \frac{1}{{5{x^2} + 1}} + c\]
• C) \[ - \frac{1}{{5x + 1}} + c\]
• D) \[\frac{1}{{5{x^2} + 1}} + c\]

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

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

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) -6
• B) 1/6
• C) 6
• D) -1/6

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

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

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

• A) 8
• B) 11
• C) 9
• D) 10

\[\int {\tan x} dx = \_\_\_\_\_\_\_\_\_\_\_\_\_\_.\]

• A) \[{\sec ^2}x + C\]
• B) \[\ln \left| {\sec x} \right| + C\]
• C) \[\ln |\cos x| + C\]
• D) \[\ln \left| {\sin x} \right| + C\]

$$\int {\tan x} dx = \_\_\_\_\_\_\_\_\_\_\_\_\_\_.$$

• A) $$\ln \left| {\sin x} \right| + C$$
• B) $$\ln |\cos x| + C$$
• C) $${\sec ^2}x + C$$
• D) $$\ln \left| {\sec x} \right| + C$$

The approximate solution is possible to generate using Newton’s Method if ___________.

• A) the tangent line(at approximated points) must crosses the x - axis.
• B) the slope of tangent line(at any approximated point) is zero.
• C) None of these.
• D) the tangent line(at any approximated point) is parallel to x- axis.

If f(x) = x^5 + x, then which of the following is true about it.

• A) Its anti – derivative is 5x^4 + 1.
• B) Its anti – derivative is x^5/5 + 1.
• C) Its anti – derivative is x^6/6 + x^2/2 + 6.
• D) None of these.

If $f''(x) > 0\,\forall \,x \in I$, then the graph of $f$ is___________ on $I$.

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

For the area under the curve f(x) = 2x from x = 0 to x = 12 with right points approximations for n = 3, what will be the values of xk* ?

• A) 6, 9 and 12
• B) 0, 6 and 12
• C) 2, 7 and 12
• D) 4, 8 and 12