If f'(r) =0 at some approximation “r” then we cannot proceed on Newton’s method.

• A) False
• B) True
• C)
• D)

1+2+3+…+339 equals _____.

• A) 339(340)/2
• B) 338(340)/2
• C) 338(339)/6
• D) 338(340)/6

$${\text{The integral }}\int {\frac{x}{{1 + {x^2}}}\,dx\,} {\text{will be equal to ?}}$$

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

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

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

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’

$${\text{The integral }}\int {\frac{{6x}}{{{{(3{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{1}{{{{(3{x^2} + 1)}^3}}} + c$$
• B) $$- \frac{1}{{6x + 1}} + c$$
• C) $$- \frac{1}{{3{x^2} + 1}} + c$$
• D) $$\frac{1}{{3{x^2} + 1}} + c$$

(1^3)+(2^3)+(3^3)+….+(20^3) equals ---------

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) 44100
• C) 34548
• D) 42925

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) -1/9
• C) -1/10
• D) 1/10

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

• A) $$\frac{{\cos 5x}}{5} + c$$
• B) $$5\cos 5x + c$$
• C) $${\text{ - }}\frac{{\cos 5x}}{5} + c$$
• D) $${\text{ - }}\frac{{\cos 4x}}{5} + c$$

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

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

A function $f$ has an/a___________ at $c$ if $f(c) \geqslant f(x)\,\forall \,x \in \,D$, where $D$ is the domain of $f$.

• A) absolute maximum
• B) local maximum
• C) absolute maximum/global maximum
• D) global maximum

How many subintervals of length ‘2’ will be formed for the interval [4,16] ?

• A) 6
• B) 5
• C) 4
• D) 7

In approximation to an area Rn (where n is subscript) when limit is taken as n goes to infinity, approximation becomes actual area.

• A) True
• B) False
• C)
• D)

Integration of 5 with respect to x is…………

• A) 5
• B) x
• C) 5x
• D) 5x^2

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

• A) 4
• B) 3
• C) 6
• D) 5

If the interval [3,7] is divided into ‘4’ equal subintervals ,then right endpoint of each subinterval will be………

• A) 4,5,6,7
• B) 3,4,5,6
• C) 3,5,6,8
• D) 5,6,7,8

\[{\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {x^3} - 3x\,{\text{in}}\,{\text{the}}\,{\text{interval}}\,\left[ {0,\sqrt 3 } \right]{\text{.}}\]

• A) \[\frac{2}{3}\]
• B) \[ - 1\]
• C) \[\frac{1}{3}\]
• D) \[1\]

If $f$ is______________ on a closed interval $[a,b]$, then $f$, attains an absolute maximum value $f(c)$ and an absoulte minimum value $f(d)$ at some numbers $c$ and $d$ in $[a,b]$.

• A) constant
• B) differentiable
• C) continuous
• D) None of these

To find the area between continuous curve f(x) and the closed interval [a,b] on x-axis, we take
-------------- of f(x) on the interval [a,b].

• A) right hand limit
• B) derivative
• C) left hand limit
• D) integral

1+2+3+…+200 equals _____.

• A) 20012
• B) 21021
• C) 21220
• D) 20100