If Newton’s Method succeeded to get the approximate solution of an equation, then which of the following is NOT true about it.

• A) The slope of the tangent line (at any approximated point) must be non zero.
• B) None of these.
• C) The sequence of approximated points not convergent to the exact solution
• D) The tangent line (at any approximated point) is not parallel to x-axis.

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

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

To get better approximation to actual area under a continuous curve over a closed interval, we have to increase ………

• A) Total area
• B) Size of the interval
• C) Number of subintervals
• D) Width of the subintervals

The critical value of the function y=100x – x^2 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) x=0
• B) x=50
• C) None of these
• D) x=25

Which of the following is the absolute minima of the function: f(x)=-x in the interval [-1,1]?

• A) -1
• B) 0.5
• C) 0
• D) 1

Which of the following will be left end points if the interval [-2,2] is divided into 4 equal subintervals.

• A) -2,-1,1,2
• B) -1,0,1,2
• C) -2,-1,0,1
• D) None of these

Integration of 3x^2 with respect to x is…………

• A) x^4
• B) x
• C) x^3
• D) x^2

Critical point of f(x)=-Sinx in the interval [0,pi] is-----

• A) pi/4
• B) pi
• C) 0
• D) pi/2

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

• A) False
• B) True
• C)
• D)

If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the RIGHT end point of 13th sub-interval will be--------.

• A) 5
• B) 4
• C) 2
• D) 3

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

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

In [0,pi],if the area under the curve f(x)=Sinx is divided into ‘3’ equally spaced rectangles of width ‘pi/3’ then by choosing middle point for height, the area of middle rectangle is ---------.

• A) pi/4
• B) pi/2
• C) pi/3
• D) pi/6

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

• A) 0, 5 and 10
• B) 0, 6 and 12
• C) 0, 3 and 6
• D) 0, 4 and 8

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) 6/5
• B) 6/4
• C) 5/6
• D) 6

$$\begin{align} & \text{A function }f\text{ is said to have a relative minimum at }{{x}_{0}}\text{, if}\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{for all }x\text{ } \\ & \text{in some open interval containing }{{x}_{0}}. \\ \end{align}$$

• A) $$f\left( {{x}_{0}} \right)=f\left( x \right)$$
• B) $$f\left( {{x}_{0}} \right)>\text{ }f\left( x \right)$$
• C) $$f\left( {{x}_{0}} \right)\le \text{ }f\left( x \right)$$
• D) $$f\left( {{x}_{0}} \right)\ge \text{ }f\left( x \right)$$

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

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

What is the estimated area under f(x) = x2+2 from x = 1 to x = 5 with mid points for n = 2

• A) 26
• B) 38
• C) 76
• D) 48

What will be the sigma notation for 32+42+52+62 ?

• A) summation of (k2) where (k varies from 3 to 6)
• B) summation of (k2) where (k varies from 1 to 4)
• C) summation of (k-1)2 where (k varies from 2 to 5)
• D) summation of (k+1)2 where (k varies from 3 to 6)

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

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

Which geometrical figure is used for approximating the area under the curve?

• A) Right angled triangle
• B) None of these
• C) Pentagon
• D) Circle