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JEE Main Mathematics Mock

25 Questions MCQ Test Mock Test Series for JEE Main & Advanced 2022 | JEE Main Mathematics Mock

Description

Attempt JEE Main Mathematics Mock | 25 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mock Test Series for JEE Main & Advanced 2022 for JEE Exam | Download free PDF with solutions

QUESTION: 1

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 2

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A) :A relation R on the set of complex number defined by Z₁ RZ₂ ⇔ Z₁ − Z₂ is real, is an equivalence relation.
Reason(R) :Reflexive and symmetric properties may not imply transitivity.

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 3

The limiting point of the system of co-axial circles x²+y²-6x-6y+4=0, x²+y²-2x-4y+3=0 is

A.
(-1,2)
B.
(-1,1)
C.
(-1,-2)
D.
(1,1)

Solution:

QUESTION: 4

The are (in square units) of the region bounded by x² = 8 y , x = 4 and x-axis is

A.
2/3
B.
4/3
C.
8/3
D.
10/3

Solution:

QUESTION: 5

The number of tangents drawn from the point (-1,2) to x²y²+2x-4y+4=0 is

A.
1
B.
2
C.
3
D.
0

Solution:

The correct option is Option D.

It is found that the centre of the circle is (-1,2)

Hence, no tangents would pass through it.

QUESTION: 6

The conjugate of complex number [(2+5i)/(4-3i)] is

A.
[(7-26i)/(25)]
B.
[(-7-26i)/(25)]
C.
[(-7+26i)/(25)]
D.
[(7+26i)/(25)]

Solution:

QUESTION: 7

[(1-i)/(1+i)] =

A.
[cos(π/2) + i sin(π/2)]
B.
[cos(π/2) - i sin(π/2)]
C.
[sin(π/2) + i cos(π/2)]
D.
[sin(π/2) - i cos(π/2)]

Solution:

QUESTION: 8

The solution of differential equation

Solution:

QUESTION: 9

The maximum value of the function f(x)=[(x)/(4+x+x²)] at the interval [-1,1] will be

A.
-(1/4)
B.
-(1/3)
C.
1/6
D.
1/5

Solution:

QUESTION: 10

sin⁻¹ (cos(sin⁻¹ x) + cos⁻¹ (sin(cos⁻¹ x) is equal to

A.
0
B.
π/4
C.
π/2
D.
3π/4

Solution:

QUESTION: 11

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): y = sin (ax + b) is a general solution of y" + a^2y = 0 .
Reason(R) : y = sin (ax + b) is a trigonometric function.

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 12

The inverse of the converse of a conditional statement is the _______________.

A.
converse
B.
inverse
C.
contrapositive
D.
none of the above

Solution:

The inverse will insert NOT into the statement.
The converse will switch the IF and THEN.
The contrapositive does both.
The contrapositive is the inverse of the converse of the conditional statement.

QUESTION: 13

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The domain of the function
Reason (R): The domain of the function

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 14

If A is a square matrix such that A² = I, then A⁻¹ is equal to

A.
2 A
B.
0
C.
A
D.
A + I

Solution:

QUESTION: 15

Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second. The value of m and n are respectively

A.
7, 6
B.
6, 3
C.
5, 1
D.
8, 7

Solution:

Let A denote the first set and B denote the second set
We have, n(A) = 2^m and n(B) = 2ⁿ
As per the question, we have
n(A) = 56 + n(B)
⇒ n(A) - n(B) = 56
⇒ 2^m - 2ⁿ = 56
⇒ 2ⁿ (2^{m - n} - 1)
⇒ 2ⁿ (2^{m - n} - 1) = 8 x 7
⇒ 2ⁿ = 8 = 2³ or (2^{m - n} - 1) = 7
⇒ n = 3 or 2^{m - n} = 8 = 2³ = 2^{6 - 3}
⇒ n = 3 or m - n = 3
⇒ n = 3 or m = 6
Hence, the required values of m and n are 6 and 3 respectively

QUESTION: 16

The equation of the directrix to the parabola y² − 2x − 6y − 5 = 0 is

A.
2 x + 15 = 0
B.
x + 5 = 0
C.
2 x + 3 = 0
D.
x + 2 = 0

Solution:

QUESTION: 17

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

A.
50
B.
25
C.
10
D.
100

Solution:

QUESTION: 18

If in a moderately asymmetrical distribution mode and mean of the data are 6λ and 9λ respectively, then median is

A.
8λ
B.
7λ
C.
6λ
D.
5λ

Solution:

QUESTION: 19

The sides of a parallelogram are lx + ny + n = 0, lx + my + n' = 0, mx + ly + n = 0, mx + ly + n' = 0, the angle between its diagonals is

A.
π/2
B.
π/3
C.
π/4
D.
π

Solution:

QUESTION: 20

Equation of normal to the curve y = x(2 - x) at the point (2, 0) is

A.
x - 2y = 2
B.
2x + y = 4
C.
x - 2y + 2 = 0
D.
None of these

Solution: