How many subintervals of length ‘2’ will be formed for the interval [4,16] ?

• A) 4
• B) 6
• C) 5
• D) 7

Integral of x^2+x^3 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) (1/3)x^4+(1/4)x^3 +C
• B) (1/4)x^4+(1/3)x^3 +C
• C) None of these
• D) x^3+x^4+C

What is the estimated area under f(x) = x from x = 0 to x = 3 with mid points for n = 3?

• A) 3.5
• B) 5.0
• C) 6.5
• D) 4.5

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) (b-a)/n
• B) (a-b)/2
• C) (b-a)/2n
• D) (a-b)/n

Newton’s Method fails to find the approximate solution of an equation if _____________.

• A) the tangent line (at any approximated point) is not parallel to x-axis.
• B) None of these
• C) the tangent line(at any approximated point) is parallel to x-axis.
• D) the slope of the tangent line(at any approximated point) is non-zero

If x=-3 and x=3 are the two critical points of the function: f(x)=81x-3(x^3) then by using the 2nd derivative test, we can conclude that f(x) is relatively maximum at-----

• A) x= -9
• B) x=0
• C) x= 3
• D) x=-3

If the interval [3,7] is divided into ‘4’ equal subintervals ,then left endpoint of each subinterval will be………

• A) 4,5,6,7
• B) 5,6,7,8
• C) 3,4,5,6
• D) 3,6,8,9

For the area under the curve f(x) = x+2 from x = 2 to x = 8 with right end points approximations for n = 3, what will be the values of xk* ?

• A) 2, 5 and 8
• B) 2, 4 and 8
• C) 0, 4 and 8
• D) 4, 6 and 8

What is the summation of ‘kx’ where k goes from 1 to 30?

• A) 523x
• B) 419x
• C) 465x
• D) 414x

Which of the following is the sum of 2t^2 where t goes from 1 to 5?

• A) 2+8+28+32+50
• B) 2+18+32+50+62
• C) 2+18+28+32+60
• D) 2+8+18+32+50

By using Newton method, which of the following is the poorest initial approximate solution of equation:x+Cosx=0?

• A) x=0
• B) x=-pi/4
• C) x=pi/2
• D) x=-pi/3

Mean value theorem states that between any two points A and B on a curve y=f(x) , there must be at least one point where the Tangent line to the curve is……………joining A and B

• A) Perpendicular to the secant line
• B) Perpendicular to the tangent line
• C) Parallel to the tangent line
• D) Parallel to the secant line

If f(x)=1 / (x^2) and the interval is [-1,1] , then Rolle’s theorem can be applied.

• A) True
• B) False
• C)
• D)

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

• 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) \[\frac{{{{\left( {{x^3} - 1} \right)}^{11}}}}{{11}} + c\]

For the given function f(x)= 2(x^2)+1 in the interval [-1,2] , which condition of Rolle’s theorem is not satisfied.

• A) The function is differentiable in the interval
• B) The function is continuous in the interval
• C) None of these.
• D) f (-1) = f (2)

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = derivative of Cosx at (pi/2), then the value of ‘a’=------

• A) -6
• B) 6
• C) 1/6
• D) -1/6

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

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

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

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

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

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

\[{\text{The integral }}\int {\sin (5x)dx} {\text{ will be equal to ?}}\]

• A) \[5\cos 5x + c\]
• B) \[{\text{ - }}\frac{{\cos 5x}}{5} + c\]
• C) \[\frac{{\cos 5x}}{5} + c\]
• D) \[{\text{ - }}\frac{{\cos 4x}}{5} + c\]