Approximation to an area improves as number of partitions is decreased.

• A) True
• B) False
• C)
• D)

$${\text{The integral }}\int {\frac{{10x}}{{{{(5{x^2} + 1)}^2}}}\,dx\,} {\text{will be equal to ?}}$$

• A) $$- \frac{1}{{5{x^2} + 1}} + c$$
• B) $$- \frac{1}{{5x + 1}} + c$$
• C) $$\frac{1}{{5{x^2} + 1}} + c$$
• D) $$- \frac{1}{{{{(5{x^2} + 1)}^3}}} + c$$

1+2+3……….+1000 equals -------

• A) 3000
• B) None of these
• C) 500500
• D) 1000

If x =(3+4+5+...+10)+{(3^3)+(4^3)+(5^3)+...+ (10^3)}, then x = _______.

• A) None of these.
• B) 55.
• C) 3080.
• D) 3068.

The estimated area under f(x) = x^2 from
x = 1 to x = 3 with left end points for
n = 2 is ________

• A) 5.
• B) None of these.
• C) 13.
• D) 6.

If f(x) = Sin(x) + x, then which of the following is true about it

• A) Its anti – derivative is Cos(x) + x^2/2 + 10.
• B) None of these.
• C) Its anti – derivative is Cos(x) + 1.
• D) Its anti – derivative is –Cos(x) + x^2/2 + 10.

$${\text{The integral }}\int {\sec (x).\tan (x)\,dx\,} {\text{will be equal to ?}}$$

• A) $$\cos ec(x) + c$$
• B) $${\text{None of these}}$$
• C) $$- \ln \left| {\cos (x)} \right| + c$$
• D) $$\sec (x) + c$$

Given a function f(x) = 1 / (x-1) and the interval is (0,2) ,then mean value theorem cannot be applied due to ……….

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

Newton’s method is not applicable when ‘f’ is a …………

• A) Trignometric function
• B) Constant function
• C) Exponential function.
• D) Polynomial

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

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

The indefinite integral of ‘sec(x)tan(x)’ is…………….

• A) Tanx+c
• B) Cotx +c
• C) Sinx+c
• D) Secx+c

\[\text{If a function }f\text{ has a relative extrema at }{{x}_{0}}\text{, then}\]

• A) \[\text{either}\,{f}'\left( {{x}_{0}} \right)=0\,\text{or }f\text{ is not differentiable at }{{x}_{0}}\]
• B) \[f\text{ is differentiable at }{{x}_{0}}\]
• C) \[{f}'\left( {{x}_{0}} \right)\le 0\]
• D) \[{f}'\left( {{x}_{0}} \right)>0\]

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

• A) pi/2
• B) -pi/2
• C) pi/4
• D) 0

x=1 is a critical value of the function.
f(x)=(x-1)^3

NOTE: x^n means ‘x’ to the power ‘n’

• A) False
• B) True
• C)
• D)

12+22+32+…+192 equals _____.

• A) 19(20)(37)/6
• B) 19(20)(39)/6
• C) 19(20)(21)/6
• D) 19(20)(31)/6

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

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

What is the estimated area under f(x) = 12 / x from x = 1 to x = 3 with mid points for n = 2?

• A) 10.5
• B) 12.8
• C) 18.0
• D) 13.1

Sum of n-terms of a series whose nth term is ‘n’ = ---

• A) n(n-1)/2
• B) (n+1)/2
• C) n(n+1)/2
• D) n(n+1)

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

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

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

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