Question # 1

Which of the following are first two terms for the taylor series of f(x)=e^-xat x=0?

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1+(1)(x-0)

1+(-1)(x-0)

1+(-1)(x+0)

Tan(x) is continuous every where except at points

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+- kπ/2 where k=(1,3,5.....)

+- kπ/2 where k=(2,4,6.....)

+- kπ/2 where k=(1,2,3,4,5,6.....)

Let x_obe the critical point of the function f,those critical point for which f'(x_o)=0 are called _______ of

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Local points

End points

Stationary points

set{...-4,-3 ,-2,-1,0,1,2,3,4} is known as the set of

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natural number

Integer

whole number

The set {x:a<=x<=b} can be written in the form of interval ?

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(a,b)

(a.b)

[a,b]

Average velocity of a body is V_ave

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d₁-d_o/ t₁- t_o

t₁- t_o/f(t₁₎- f(t_o)

_f(t₁₎- f(t_o)/t₁- t_o

None of these

If a slope m of a nonvertical line is m=1 then the angle of inclination of the line is

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π /4

π /2

π /5

Which of the following option is true for the sequence a_n={1/n}_n=1which of the following option is true for the sequence

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Increasing

Decreasing

Non increasing

Non Decreasing

What is the base of natural logarithm ?

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2.71

10

5

______ is the special case for the Taylor's theorem

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Roll's Theorem

Picard's Method

Integration

Maclaurin Theorem

lim x→0 sin2x/x____

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2

4

1

8

A line is called a tangent line to the circle if it meets the circle at precisely.....

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one point

two point

infinite points

Lim _x→₀sinx/x

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1

-1

0

2

Sigma notation which is represent which of the following greek letter?

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χ

η

Σ

ψ

If the partial sum of series is finite then the series will be:

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Convergent

GIve no information

Not Sure

If there is some function F such that d/dx[F(x)]=f(x) then antiderivatives of f(x) are F(x)+C .What does C represent?

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Polynomial

Constant

Dependent variable

Independent variable

An object is displaced 1m by a force of 1N then the work done

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2

1

0

Let a function be defined on an interval and let x₁ and x₂denotes two distinct points in that interval ,If f(x₁)= f(x₂) for all points x_{1 and}x₂then which of the following statement is correct ?

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f is decreasing function

f is increasing function

f is constant function

What is the sum of the following series?

1+2+3+----+n

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n+1/2

(n+1)(n+2)/2

n(n+2)/2

n(n+1)/2

For a sequence {a_n} if the ration of successive terms a_n+1/ a_n<1 then the sequence is known as :

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increasing

decreasing

Non increasing

non decreasing

no of x and y are intercept for the equation y=1/x

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Two x intercepts

Two y intercepts

No x and y intercept correct

None of these

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