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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:

*Answer can only contain numeric values

QUESTION: 21

If the slope of tangent to the curve y = ax^{2} – bx atx = 1 is equal to 3 where a ∈ [5, 10], then number of possible integral value of b is -

Solution:

*Answer can only contain numeric values

QUESTION: 22

Number of integral values of parameter λ for which ƒ(x) = 2x^{3} – 3(2 + λ)x^{2} + 12λx + log(16 – λ^{2}) has exactly one local maxima & one local minima is

Solution:

ƒ'(x) = 6x^{2} – 6(2 + λ)x + 12λx & 16 – λ^{2} > 0

ƒ'(x) = 6(x^{2} + (2 + λ)x + 2λ) & λ ∈ (–4, 4)

= 6(x – λ)(x – 2)

for different max & minima λ ≠ 2

⇒ λ = ±3, –2, ±1, 0

has exactly one local max & one local minima

*Answer can only contain numeric values

QUESTION: 23

If y = 3[x] + 1 = 4[x – 1] – 10, then [x + 2y] is equal to (where [.] is G.I.F.)

Solution:

*Answer can only contain numeric values

QUESTION: 24

If g(x) = ℓn(1 + x) – then is -

Solution:

*Answer can only contain numeric values

QUESTION: 25

Number of ordered pairs (p, q) from the set S = {1, 2, 3, 4, 5} so that the real function ƒ (x) = is one-one, is -

Solution:

ƒ '(x) = x^{2} + px + q

for the function to be one-one D ≤ 0

p^{2} – 4q ≤ 0

p q No. of (p, q)

1 1, 2, 3, 4, 5 5

2 1, 2, 3, 4, 5 5

3 3, 4, 5 3

4 4, 5 2

5 x 15

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