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# Mathematics Test 6 - Application Of Derivatives, Relation And Function

## 25 Questions MCQ Test Mock Test Series for JEE Main & Advanced 2021 | Mathematics Test 6 - Application Of Derivatives, Relation And Function

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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. This contains 25 Multiple Choice Questions for JEE Mathematics Test 6 - Application Of Derivatives, Relation And Function (mcq) to study with solutions a complete question bank. The solved questions answers in this Mathematics Test 6 - Application Of Derivatives, Relation And Function quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Mathematics Test 6 - Application Of Derivatives, Relation And Function exercise for a better result in the exam. You can find other Mathematics Test 6 - Application Of Derivatives, Relation And Function extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

Solution:
QUESTION: 2

Solution:
QUESTION: 3

### Let be a relation in RThe 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
Solution:
QUESTION: 5
Let R and S be two equivalence relations in a set
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
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
Solution:
QUESTION: 9
Let f(x) = x, 1/x and h(x) = f(x) g(x). Then h(x) = 1 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
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
Solution:
*Answer can only contain numeric values
QUESTION: 21

If the slope of tangent to the curve y = ax2 – 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) = 2x3 – 3(2 + λ)x2 + 12λx + log(16 – λ2) has exactly one local maxima & one local minima is

Solution:

ƒ'(x) = 6x2 – 6(2 + λ)x + 12λx  &  16 – λ2 > 0
ƒ'(x) = 6(x2 + (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) = x2 + px + q
for the function to be one-one D ≤ 0
p2 – 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