Absolute minimum of the function f(x)=x in the semi open interval (0,2] is-------

• A) 1
• B) Undefined
• C) 2
• D) 0

Which of the following is the sum of 2k+1 where k goes from 0 to 2?

• A) 8
• B) 14
• C) 10
• D) 12

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

• A) $$\sec (5{x^2}).\tan (5{x^2}) + c$$
• B) $$\tan (5x) + c$$
• C) $$\tan (5{x^2}) + c$$
• D) $${\text{se}}{{\text{c}}^2}(10x) + c$$

If we subdivide the interval [1,6] into n equal parts, then what will be the length ∆x of each part?

• A) 7/n
• B) 1/n
• C) 6/n
• D) 5/n

For the application of mean value theorem on f( x ) =x^3-3x^2-2x ; [0,2], which of the following is true?

• A) f( x ) is continuous over [ 0, 2) and f(x) is differentiable over ( 0,2 )
• B) f( x ) is continuous over [ 0, 2] and f(x) is differentiable over ( 0,2 )
• C) f( x ) is continuous over [ 0, 2] and f(x) is not differentiable over ( 0,2 )
• D) f( x ) is continuous over [ 0, 2] and f(x) is differentiable over [ 0,2 )

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of xk* ?

• A) 1
• B) 2
• C) 1.5
• D) 2.5

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) 1/10
• C) -1/10
• D) -1/9

By applying Roll’s theorem on f(x) = x over the interval [-1,1], the points where the derivative of f(x)=x is not taken are………

• A) x= -1, 1
• B) x=0,1
• C) x=0,0.5,-0.5
• D) x=-1,0

The vertical asymptotes of a function occur at the points where the denominator of the function becomes

• A) -1
• B) 0
• C) 1
• D) Undefined

For the area under the curve f(x) = x+1 from x = 1 to x = 3 with mid points approximations for n = 1, what will be the value of f (xk*) ?

• A) 2
• B) 3
• C) 1
• D) 6

Summation of 9t where ‘t’ goes from 1 to 30” is same as “summation of 9k where k goes from 1 to 30”.

• A) False
• B) True
• C)
• D)

summation of (6) ;where ( j varies from 1 to 8) indicates to add ‘6’ to itself ……….. times.

• A) 11
• B) 10
• C) 8
• D) 9

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

• A) -1
• B) zero
• C) 1
• D) that specific large EVEN number

Integral of x^2+x^3 is

NOTE: x^n means ‘x’ to the power ‘n’

• A) None of these
• B) (1/3)x^4+(1/4)x^3 +C
• C) (1/4)x^4+(1/3)x^3 +C
• D) x^3+x^4+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) Rational function
• B) None of these
• C) Discontinuity of the function in the given interval
• D) Open interval

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

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

$$\text{The vertical asymptotes of the function }f(x)=\frac{{{x}^{2}}-2x+1}{x(x-2)}\text{ are}$$

• A) 0, 1
• B) 1, -1
• C) 0, 2
• D) 1, 2

3(12)+3(22)+3(32)+…+3(152) equals _____.

• A) 15(16)(17)/2
• B) 15(16)(30)/2
• C) 15(16)(31)/2
• D) 15(16)(29)/2

Mean value theorem states that between any two points A and B on a curve y=f(x) , there must be at least one point where the Tangent line to the curve is……………joining A and B

• A) Perpendicular to the secant line
• B) Parallel to the tangent line
• C) Perpendicular to the tangent line
• D) Parallel to the secant line

Why the equation: x^2 + 8 = 0 does not have approximate solution while using Newton's method?

• A) x^2 will always be nonnegative
• B) x^2 will always be negative
• C)
• D)