Critical point for f(x) = -Cosx on [-pi/2,pi/2] are ------

• A) pi/2
• B) -pi/2
• C) pi/4
• D) 0

summation of (n+i) ; (i varies from 1 to 10 ) , here ‘i’ is known as the …….. of the summation.

• A) Lower limit
• B) Upper limit
• C) None of these
• D) Index

Given f(x)= 1/(x-1) on the interval (0,3) , then ‘f ’ has no relative maxima or relative minima due to………

• A) None of these
• B) Open interval
• C) Discontinuity in the interval
• D) Rational function

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

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

What are critical points of the function f(x) =x-1?

• A) None of these
• B) x=0
• C) No critical point
• D) x=1

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

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

Subdivision of an interval is also called ………. of the interval.

• A) Partition
• B) Evaluation
• C) Separation
• D) Composition

If the closed interval [-2,2] is divided into ‘50’ equally spaced sub-intervals then the width of each sub-interval is ------------

• A) 4/25
• B) 1/25
• C) -4/25
• D) 2/25

If a function f(x) is defined on an interval
[a, b] satisfying the conditions of the Rolle’s Theorem, then which of the following is true about it.

• A) It must have at least one critical point.
• B) It would not have more than one stationary point.
• C) It may or may not have a critical point.
• D) None of these.

What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 2?

• A) 21
• B) 12
• C) 25
• D) 16

The estimated area under f(x) = x^2 + 2 from
x = 1 to x = 5 with left end points for
n = 2 is ________.

• A) 28.
• B) None of these.
• C) 76.
• D) 25.

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) 0
• C) -1
• D) 2

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

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) 6
• B) 3
• C) 5
• D) 4

1+2+3+…+539 equals _____.

• A) 538(540)/2
• B) 538(539)/6
• C) 539(540)/2
• D) 538(540)/6

‘x.ln(x/e)’ is the anti-derivative of ‘lnx’ if and only if the derivative of ‘x.ln(x/e)’ is euqal to --------

• A) ln(x/e)
• B) xln(x/e)
• C) lnx
• D) x

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of f (xk*) ?

• A) 6
• B) 1
• C) 2
• D) 3

1+2+3+…+100 equals _____.

• A) 5050
• B) 5055
• C) 5005
• D) 5500

The area between f(x)=-x and the closed interval
[-1,0] on x-axis is ----------

• A) -1/2
• B) 1/2
• C) 2
• D) 1

f(x) = 8x-x^2 on the closed interval [0, 6]
has the critical point at x=………

• A) 4
• B) 5
• C) 1
• D) 0