Question # 1

Which of the following is the spring constant k if a spring constant whose natural length is 2m exerts a force of 3N when started 1m beyond its natural legth?

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3 x

3 N/m

2 m

If x>0 then d/dx[lnx]=_______

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1

x

1/x

ln 1/x

d(sec x)/dx=?

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sec x tan x

sec x tan y

cosec x cot x

If 2y-y=-3 then dy/dx ?

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2

-2

0

-3

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

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Convergent

GIve no information

Not Sure

Consider two function f(x)=x³and g(x)=(x+9) then fog(x)=

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(x+9)3

x+3

x+9

Consider a function h(x) and a constant c then d/dx{(c){h(x)}}

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0

d/dx((h(x)))

d/dx((h(cx)))

cd/dx((h(x)))

What is the length of each subinterval,if the interval [1,3]is divided into n sub interval of equal length?

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1/n

2/n

3/n

y=x²/2

Let find the average rate of change of y with respect to x over the interval [3,4]

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25/2

7/2

25/14

7/14

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

If f and g are continuous function on an interval [a,b] f(x)>=g(x) for a<=x<=b and ,then area is bounded by the lines parallel to :

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X-axis

Y axis

Both x and y axis

The tan(x) is discontinuous at the point where

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Cos(x)=0

Sin(x)=0

Tan(x)=0

According to the power rule of differentiation,if f(x)=xⁿwhere n is a real number then d/dx[xⁿ]=

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x^n-1

nx^n-1

nxⁿ⁺¹

Which of the following is true for the sequence {n}∞ n=0?

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Non increasing

non decreasing

increasing

decreasing

Function f is differentiable function if it is differentiable on the interval

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(-∞,∞)

(a,∞) where a is any negative integer

(0,∞)

None of these

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

π is a _____ number

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rational

irrational

natural

integer

h(x)=1/(x-2)(x-4) domain of the function is

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(-∞,2)U (2,4)U (4,+∞)

(-∞,2)U (2,4)U (4,∞)

All are incorrect

The mean value of theorem states that " Let function f can be differentiable on (a,b) and continuous on [a,b] then there is no exist at least one point c in (a,b) where ______

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f'(c)=f(b)-f(a)/b-a

f(c)=f(b)-f(a)/b-a

f(c)=f(a)-f(b)/b-a

Suppose that f and g are differentiable function of f x then d/dx(f)(g)=

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[f'][g]-[f][g']/g²

[f'][g']

[f'][g] + [f][g']

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

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