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.

$$\begin{align} & \text{A function }f\text{ is said to have a }\,\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\,\text{at }{{x}_{0}}\text{, if }f({{x}_{0}})\ge f(x)\text{ for all }x\text{ } \\ & \text{in some open interval containing }{{x}_{0}}. \\ \end{align}$$

• A) Relative maximum
• B) Relative minimum
• C)
• D)

1+2+3………+t equals

• A) n(n+1)/2
• B) None of these
• C) t(t+1)/2
• D) n(n+1)(2n+1)/6

Which of the following is the sum of (2k+1) where k goes from 1 to 4?

• A) 20
• B) 24
• C) 26
• D) 22

$${\text{In}}\,{\text{the}}\,{\text{notation:}}\,\int_a^b {f(x)} dx{\text{,}}\;f(x)\,{\text{is}}\,{\text{called___________}}{\text{.}}$$

• A) $${\text{Differential}}$$
• B) $${\text{Integration}}$$
• C) $${\text{Integrand}}$$
• D) $${\text{None}}\,{\text{of}}\,{\text{these}}$$

By applying mean value theorem to the function
f(x)=lnx in the interval [1,e], the corresponding value of ‘c’ is ------------(Hint: lne=1, ln1=0)

• A) e-1
• B) -e
• C) 1-e
• D) e

While using Newton’s mathod,which of the following will be the best initial approximate solution to solve the equation: x-Sinx=0

• A) x=pi/2
• B) x=-pi/2
• C) x=pi
• D) x=0

What is length of each subinterval if the interval [-1,1] is divided into n subintervals of equal length.

• A) 0
• B) 2/n
• C) 1/n
• D) None of these