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/6
• C) pi/3
• D) pi/2

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

If $f'$ changes from negative to positive at c, then $f$ has a _______________ at c.

• A) constant
• B) local maximum
• C) local minimum
• D) None of these

While solving the equation, 10x-(e^x)=0 by using Newton method, if x=0 is the initial approximate solution then the next approximation will be-----

• A) -1/9
• B) -1/10
• C) 1/9
• D) 1/10

Newton’s method uses the …………… to approximate the root.

• A) Tangent line
• B) Normal line
• C) Secant line
• D) None of these

What is the estimated area under f(x) = 2x from x = 0 to x = 4 with left end points for n = 2?

• A) 24
• B) 10
• C) 8
• D) 18

2(13)+2(23)+2(33)+…+2(153) equals _____.

• A) 15(16)2/2
• B) [15(16)]2 / 2
• C) [15(16)/2]2
• D) 15(16)/22

The Area $A$ of the region $S$ that lies under the graph of the continuous function $f$ is the limit of the sum of the areas of approximating rectangles:

• A) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \Delta x\left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$
• B) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \frac{1}{{\Delta x}}\;\left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$
• C) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \left[ {f\left( {{x_1}} \right) + f\left( {{x_2}} \right) + \ldots + f\left( {{x_n}} \right)} \right]$
• D) $A = \mathop {\lim }\limits_{n \to \infty } {R_n} = \mathop {\lim }\limits_{n \to \infty } \left[ {f\left( {{x_1}} \right)\Delta x + f\left( {{x_2}} \right)\Delta x + \ldots + f\left( {{x_{n - 1}}} \right)\Delta x} \right]$

If ‘k’ goes from zero to ‘n’ in the summation of ‘Sink’ then which of the following will be other expression for this given summation such that its lower limit changes to ‘5’?

• A) Summation ‘Sin(k-5)’ while ‘k’ goes from ‘5’ to ‘n-5’
• B) Summation ‘Sin(k+5)’ while ‘k’ goes from ‘5’ to ‘n+5’
• C) Summation ‘Sin(k-5)’ while ‘k’ goes from ‘5’ to ‘n+5’
• D) Summation ‘Sin(k+5)’ while ‘k’ goes from ‘5’ to ‘n-5'

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

• A) True
• B) False
• C)
• D)

If f(x) = Cos(x) + Sin(x) + x, then which of the following is NOT true about it.

• A) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 4.
• B) None of these.
• C) Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 5.
• D) Its anti – derivative is -Sin(x) – Cos(x) + x^2/2 + 4.

3(12)+3(22)+3(32)+…+3(152) equals _____.

• A) 15(16)(31)/2
• B) 15(16)(30)/2
• C) 15(16)(29)/2
• D) 15(16)(17)/2

Summation of 2 where sum ranges from 0 to 10 equals 20.

• A) False
• B) True
• C)
• D)

Integral of 5^2 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) 25x
• C) (1/3)5^3
• D) 10

Let f(x)=x^3 and a= -5 ,b=5 and n= no. of partition of [-3,3]=4
Let the widths of first, second, third and fourth intervals are 3,0,1,2 respectively. Then the “Mesh size” of partition is……………

• A) 3
• B) 1
• C) 0
• D) 2

If ‘n’ goes from 1 to any large ODD number then the summation of ‘(-1)^n’ = ---------

• A) -1
• B) that specific large ODD number
• C) 1
• D) Zero

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

• A) 3
• B) 6
• C) 5
• D) 4

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

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

What will be the value of summation of k2 where k goes from 11 to 12

• A) 281
• B) 212
• C) 265
• D) 244

If x =(1+2+3+...+10)+{(1^3)+(2^3)+(3^3)+...+ (10^3)}, then x = _______.

• A) 55.
• B) 3025.
• C) 3080.
• D) 110.