JEE Main Mathematics Mock

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-
Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.

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-

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 area, in square unit, of the region bounded by the curve x² = 4y , the line x = 2 and the x-axis is

A.
1
B.
2/3
C.
4/3
D.
8/3

Solution:

QUESTION: 4

The radical axis of the circles, belongs to the coaxial system of circles whose limiting points are (1,3) and (2,6) is

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

Solution:

QUESTION: 5

If y=sin((1+x²)/(1-x²)), (dy/dx)=

A.
[(4)/(1-x²)²]. cos[(1+x²)/(1-x²)]
B.
[(x)/(1-x²)²]. cos[(1+x²)/(1-x²)]
C.
[(x)/(1-x²)]. cos[(1+x²)/(1-x²)]
D.
[(4x)/(1-x²)]. cos[(1+x²)/(1-x²)]

Solution:

QUESTION: 6

If z₁ and z₂ are any two complex numbers then |z₁ + z₂|² + |z₁ - z₂|² =

A.
2 |z₁|²|z₂|²
B.
2 |z₁|² + 2 |z₂|²
C.
|z₁|²+ |z₂|²
D.
2 |z₁||z₂|

Solution:

QUESTION: 7

If the line 2x - y + k = 0 is a diameter of the circle x² + y² + 6x -6y + 5 =0, then k is equal to

A.
3
B.
6
C.
9
D.
12

Solution:

QUESTION: 8

The solution of the differential equation cos x sin y dx + sin x cos y dy =0 is

A.
sin x/sin y = C
B.
cos x + cos y =C
C.
sin x + sin y = C
D.
sin x sin y = C

Solution:

QUESTION: 9

The complex equation |z + 1 − i| = |z + i − 1| represents a

A.
Straight line
B.
Circle
C.
Parabola
D.
Hyperbola

Solution:

QUESTION: 10

The minimum value of sinx + cosx is

A.
- √2
B.
√2
C.
- 2√2
D.
0

Solution:

QUESTION: 11

Which of the following is a Contradiction ?

A.
(p ∧ q) ∧ ∼ (p ∨ q)
B.
p ∨ (∼ p ∧ q)
C.
(p ⇒ q) ⇒ p
D.
None of these

Solution:

QUESTION: 12

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): Three vectors
Reason (R): The coplanar vectors are linearly independent

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: 13

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Consider the system of equations
x - 2y + 3z = -1
- x + y - 2z = k
x - 3y + 4z = 1
Statement-1:
The system of equations has no solution for k ≠3.
Statement-2:
The determinant

A.
Statement-1 is True, Statement-2 is True ; Statement-2 is a correct explanation for Statement-1
B.
Statement-1 is True, Statement-2 is True ; Statement-2 is not a correct explanation for Statement-1
C.
Statement-1 is True, Statement-2 is False
D.
Statement-1 is False, Statement-2 is True

Solution:

QUESTION: 14

If the traces of the matrices A and B are 20 and -8, then the trace of (A + B)=

A.
- 160
B.
6
C.
12
D.
28

Solution:

QUESTION: 15

Twelve students compete for a race. The number of ways in which first three prizes can be taken is

A.
(12)! - 3
B.
(12)! / 3!
C.
3!
D.
12.11.10

Solution:

QUESTION: 16

The tangents at the points a on the parabola are at right angles if

A.
t₁ t₂ = − 1
B.
t₁ t₂ = 1
C.
t₁ t₂ = 2
D.
t₁ t₂ = − 2

Solution:

QUESTION: 17

If the coefficient of correlation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the standard deviation of the y series is

A.
9.8
B.
10.1
C.
9.05
D.
10.05

Solution:

QUESTION: 18

Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =

A.
(11/290)
B.
(√11/290)
C.
(-11/290)
D.
-(√11/290)

Solution:

QUESTION: 19

8 coins are tossed simultaneously. The probability of getting at least 6 heads is

A.
57/64
B.
229/256
C.
7/64
D.
37/256

Solution:

QUESTION: 20

The angle between the lines (x - 1)/1 = (y - 1)/1 = (z - 1)/2 and (x - 1)/(- √3 - 1) = (y - 1)/(√3 - 1) = (z - 1)/4 is

A.
cos⁻¹ (1/65)
B.
π/6
C.
π/3
D.
π/4

Solution: