If $f''(x) > 0\,\forall \,x \in I$, then the graph of $f$ is___________ on $I$.

• A) concave upward
• B) None of these
• C) concave downward
• D) constant

13+23+33+…+193 equals _____.

• A) 19(20)/22
• B) 19(20)2/2
• C) [19(20)/2]2
• D) [19(20)]2/2

(1^2)+(2^2)+(3^2)+……………..+(50^2) equals--------
NOTE: x^n means ‘x’ to the power ‘n’

• A) 55227
• B) 42925
• C) None of these
• D) 6373

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

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

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

• A) pi/4
• B) pi/2
• C) pi
• D) 0

$$\text{If we say a function }f\text{ have a relative extremum at a point }{{x}_{0}},\text{ then it means that }f\text{ has }\!\!~\!\!\text{ }\_\_\_\_\_\_\_\_\text{ at }{{x}_{0}}.$$

• A) Relative maximum
• B) Relative minimum
• C) None of these
• D) Either a relative maximum or relative minimum

1+2+3+…+539 equals _____.

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

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)