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Mathematics Test 6 - Application Of Derivatives, Relation And Function


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

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Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 1

Let A ={1,2,3,......,45} and R be the relation ‘is
square of’ in A.Which of the following is false?

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

Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 3

Let be a relation in R
The relation R is

Mathematics Test 6 - Application Of Derivatives, Relation And Function - 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
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 5
Let R and S be two equivalence relations in a set
A.Then
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 6
Let R be an equivalence relation in a finite set A having
n elements. The number of ordered pairs in R is
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 7
The domain of the function f(x) = is
Mathematics Test 6 - Application Of Derivatives, Relation And Function - 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
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 9
Let f(x) = x, 1/x and h(x) = f(x) g(x). Then h(x) = 1 if
and only if
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 10
The inverse of the function f(x) = is
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 11
If a function defined by  is a bijection, then B is equal to
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 12
If and x is a positive integer, then  is equal to
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 13
if then   =
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 14

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

Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 15

If then dy/dx =

Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 16
If f ` (x) = sin (logx) & y= then dy/dx is
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 17
If then
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 18
Differential coefficient of w.r.t 
is equal to
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 19

The sequence 1/2,2/3,3/4,…n/n+1 is

Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 20
Equation of the tangent at the point P(t), where t is
any parameter, to the parabola is
*Answer can only contain numeric values
Mathematics Test 6 - Application Of Derivatives, Relation And Function - 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 -


Detailed Solution for Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 21

*Answer can only contain numeric values
Mathematics Test 6 - Application Of Derivatives, Relation And Function - 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


Detailed Solution for Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 22

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
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 23

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


*Answer can only contain numeric values
Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 24

If g(x) = ℓn(1 + x) – then is -


Detailed Solution for Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 24

*Answer can only contain numeric values
Mathematics Test 6 - Application Of Derivatives, Relation And Function - 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 -


Detailed Solution for Mathematics Test 6 - Application Of Derivatives, Relation And Function - Question 25

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

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