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/2
• B) pi/3
• C) pi/6
• D) pi/4

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 f(xk*) ?

• A) 3
• B) 5
• C) 4
• D) 6

\[\text{If }{f}'(x)={{x}^{2}}-1.\text{ Then the critical points of the function }f\text{ are}\]

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

Right end point ,left end point, and midpoint evaluation all converges to same result as number of subintervals tends to +ive infinity.

• A) False
• B) True
• C)
• D)

summation of (ai) (i varies from 1 to n) , summation of (aj) (j varies from 1 to n),summation of (ak) (k varies from 1 to n)
All these three represents same summation.

• A) False
• B) True
• C)
• D)

If we subdivide the interval [1,6] into n equal parts, then what will be the length ∆x of each part?

• A) 5/n
• B) 6/n
• C) 1/n
• D) 7/n

$\begin{align} & \text{Let a function }f\text{ is twice differentiable at a stationary point }{{x}_{0}}, \\ & \text{then }f\text{ has relative maximum at }{{x}_{0}}\,\text{if} \\ \end{align}$

• A) $\text{ }{f}''({{x}_{0}})\ge 0$
• B) $\text{ }{f}''({{x}_{0}})=0$
• C) $\text{ }{f}''({{x}_{0}})>0$
• D) $\text{ }{f}''({{x}_{0}})<0$

1+2+3………+t equals

• A) None of these
• B) n(n+1)/2
• C) n(n+1)(2n+1)/6
• D) t(t+1)/2

What is length of each subinterval if the interval [-1,1] is divided into n subintervals of equal length.

• A) None of these
• B) 0
• C) 2/n
• D) 1/n

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

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

If $f$ has a local maximum or minimum at c, and if $f'(c)$ exists, then_________.

• A) $f'(c) = 0$
• B) None of these
• C) $f'(c) < 0$
• D) $f'(c) > 0$

What will be the sigma notation for 32+52+72+92?

• A) summation of (2k-1)2 where (k varies from 1 to 4)
• B) summation of (k2) where (k varies from 3 to 9)
• C) summation of (2k2+1) where (k varies from 3 to 6)
• D) summation of (2k+1)2 where (k varies from 1 to 4)

The area of a rectangle can be found by simply …………its dimensions.

• A) subtracting
• B) multiplying
• C) dividing
• D) adding

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

• A) 4.5
• B) 6.5
• C) 5.0
• D) 3.5

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

• A) There is no such point in the interval (-2, 2) where f(x) has a horizontal tangent.
• B) None of these.
• C) It is discontinuous on the interval [-2, 2].
• D) There is a point in the interval (-2, 2) where f(x) has a horizontal tangent

Let f(x)=x^3 and a=-3 ,b=3 and n = no. of partition of [-3,3]= 4
Let the widths of first, second, third and fourth intervals are 2, 1, 1, 2 respectively. Then “Mesh size” of this partition of [-3,3] is-------

• A) 1
• B) -1
• C) 2
• D) 0

12+22+32+…+152 equals _____.

• A) 15(16)(31) / 6
• B) 15(16)(30) / 6
• C) 15(16)(29) / 6
• D) 15(16)(17) / 6

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

• A) 3, 7 and 11
• B) 2, 6 and10
• C) 1, 5 and 9
• D) 2, 5 and 8

Integral of x^(-10) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) -10x^(-11)+C
• C) 1/(9x^9)+C
• D) - 1/(9x^9)+C

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

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