If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the MIDDLE point of 8th
sub-interval will be--------.

• A) -0.5
• B) 2.5
• C) 1.5
• D) 0.5

Maximum of the function f(x)=2x+7 occurs at

• A) x=0
• B) x=-2/7
• C) None of these
• D) x=-7/2

Integral of 3sec(x)tan(x) is

NOTE: x^n means ‘x’ to the power ‘n’

• A) 3tan(x)+C
• B) (3/2)sec^2(x)+C
• C) None of these
• D) 3sec(x)+C

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

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

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

NOTE: x^n means ‘x’ to the power ‘n’

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

For the area under the curve f(x) = x+1 from x = 1 to x = 5 with mid points approximations for n = 2, what will be the values of xk* ?

• A) 1 and 3
• B) 2.5 and 3.5
• C) 2 and 4
• D) 3 and 4

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

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

According to the Newton’s method, the equation Cosx=x (where x is in radian) has a solution between ……………

• A) 0 and -1
• B) Solution not exist
• C) 0 and 1
• D) 1 and -1

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

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

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

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

1+2+3+…+339 equals _____.

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

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

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

Subdivide the interval [1, 5] into ‘n’ equally spaced subintervals then the width of each sub-interval is ------

• A) 5/n
• B) 1/n
• C) 4/n
• D) 5

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

• A) -pi/2
• B) 0
• C) pi/4
• D) pi/2

In Rolle’s theorem, f(x) is continuous in closed interval [a,b] and differentiable in open interval (a,b).Then why we don’t discuss its differentiability in the closed interval [a,b] because ---------

• A) f ‘(a)=f ‘(b)=0
• B) f ‘(a) and f ‘(b) never exist
• C) f(a)=f(b)=0
• D) f(a) and f(b) never exist

If f(x) = x^5 + 6, then which of the following is Not true about it.

• A) Its anti – derivative is x^6/6 + 6x.
• B) Its anti – derivative is x^6/6 + 6x + 6.
• C) Its anti – derivative is x^6/6 + 6x + 10.
• D) Its anti – derivative is x^6/6 + 12x

In the indefinite integral of x(y^2) w.r.t ‘y’ , the term ….. serve to identify the independent variable in the function.

• A) x
• B) dy
• C) y^2
• D) y

For the area under the curve f(x) = 2x from x = 0 to x = 12 with right points approximations for n = 3, what will be the values of xk* ?

• A) 2, 7 and 12
• B) 0, 6 and 12
• C) 6, 9 and 12
• D) 4, 8 and 12

Which of the following is the sum of (2k+1) where k goes from 3 to 5?

• A) 27
• B) 16
• C) 19
• D) 21

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

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