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

In the indefinite integral of x(y^2) w.r.t ‘y’ , the independent variable is ……..

• A) none of these
• B) y
• C) xy
• D) x

Subdivide the interval [a, b] into 4 equal subintervals then the width of each subinterval is ------

• A) (b-2a)/4
• B) (2b-a)/4
• C) (b-a)/2
• D) (b-a)/4

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

• A) pi/2
• B) pi
• C) 0
• D) pi/4

$${\text{The integral }}\int {\cos (5x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{{\sin (5x)}}{5} + c$$
• B) $$\frac{{\sin (5x)}}{5} + c$$
• C) $${\text{None of these}}$$
• D) $$5\sin (5x) + c$$

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

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

What will be the value of summation of k2 where k goes from 8 to 8?

• A) 8
• B) 64
• C) 1
• D) 16

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

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