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This mock test of Mathematics Test 6 - Application Of Derivatives, Relation And Function for JEE helps you for every JEE entrance exam.
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QUESTION: 1

Let A ={1,2,3,......,45} and R be the relation ‘is

square of’ in A.Which of the following is false?

Solution:

QUESTION: 2

If number of elements in sets A and B are m and n respectively, then number of relations from A to B is

Solution:

QUESTION: 3

The relation R is

Solution:

QUESTION: 4

Given the relation R = {(1, 2),(2,3)} in the set

{1,2,3}, the minimum number of ordered pairs which

when added to R make it an equivalence relation is

{1,2,3}, the minimum number of ordered pairs which

when added to R make it an equivalence relation is

Solution:

QUESTION: 5

Let R and S be two equivalence relations in a set

A.Then

A.Then

Solution:

QUESTION: 6

Let R be an equivalence relation in a finite set A having

n elements. The number of ordered pairs in R is

n elements. The number of ordered pairs in R is

Solution:

QUESTION: 7

The domain of the function f(x) = is

Solution:

QUESTION: 8

Let A and B be two finite sets having m and n elements

respectively.If the total number of injective

functions from A to B is

respectively.If the total number of injective

functions from A to B is

Solution:

QUESTION: 9

Let f(x) = x, 1/x and h(x) = f(x) g(x). Then h(x) = 1 if

and only if

and only if

Solution:

QUESTION: 10

The inverse of the function f(x) = is

Solution:

QUESTION: 11

If a function defined by is a bijection, then B is equal to

Solution:

QUESTION: 12

If and x is a positive integer, then is equal to

Solution:

QUESTION: 13

if then =

Solution:

QUESTION: 14

If f(x) = then f`(x)at x = e is

Solution:

QUESTION: 15

If then dy/dx =

Solution:

QUESTION: 16

If f ` (x) = sin (logx) & y= then dy/dx is

Solution:

QUESTION: 17

If then

Solution:

QUESTION: 18

Differential coefficient of w.r.t

is equal to

is equal to

Solution:

QUESTION: 19

The sequence 1/2,2/3,3/4,…*n/**n*+1 is

Solution:

QUESTION: 20

Equation of the tangent at the point P(t), where t is

any parameter, to the parabola is

any parameter, to the parabola is

Solution:

QUESTION: 21

The angle of intersection of the curves

Solution:

QUESTION: 22

If the function f(x) satisfies conditions of Rolle’s theorem in [1,3] &

= 0, then values of a and b are respectively

Solution:

QUESTION: 23

If from mean value theorem then

Solution:

QUESTION: 24

If a+ b+ c = 0, then the equation has

Solution:

QUESTION: 25

The maximum value of the function sinx (1 + cosx) is

Solution:

QUESTION: 26

For the parabola the ratio of the subtangent to the abscissa is

Solution:

QUESTION: 27

has point of maxima at

Solution:

QUESTION: 28

The function assumes minimum

value for x given by

value for x given by

Solution:

QUESTION: 29

Divide 64 into two parts such that the sum of cubes

of two parts is minimum. The two parts as

of two parts is minimum. The two parts as

Solution:

QUESTION: 30

The functions decreases on the interval

Solution:

### Increasing, decreasing function - Application of Derivatives

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