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This mock test of JEE Main Mathematics Mock - 6 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE JEE Main Mathematics Mock - 6 (mcq) to study with solutions a complete question bank.
The solved questions answers in this JEE Main Mathematics Mock - 6 quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this JEE Main Mathematics Mock - 6 exercise for a better result in the exam. You can find other JEE Main Mathematics Mock - 6 extra questions,
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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.

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 committee of *n* persons is to be formed out of 30 persons.

Assertion(A) : The value of *n* for which the number of committees is maximum is *n* = 15

Reason(R) : In the expansion of (1 + x)^{k} , k ∈ N , the middle term has the greatest binomial coefficient.

Solution:

QUESTION: 3

The general solution of the equation x^{2}(dy/dx)=2 is

Solution:

QUESTION: 4

The area of the region bounded the curve y = 2x - x^{2} and the line y = x is

Solution:

QUESTION: 5

If line y=2x is a chord of the circle x^{2}+y^{2}-10x=0, the equation of the circle drawn on the chord assuming it as a diameter is

Solution:

QUESTION: 6

If (cos θ + i sin θ)(cos 2θ + i sin 2θ).....(cos mθ + i + sin mθ) = 1 then the value of θ ,is (m is an integer)

Solution:

QUESTION: 7

If circles x^{2}+y^{2}+2ax+c=0 and x^{2}+y^{2}+2by+c=0 touch each other, then

Solution:

QUESTION: 8

If the amplitude of z − 2 − 3i is π/4 , then the locus of z = x + iy is

Solution:

QUESTION: 9

then f ′ (1) =

Solution:

QUESTION: 10

The negation of the statement ' he is rich and happy' is given by

Solution:

QUESTION: 11

If N N + denotes the set of all positive integers and if f : N^{N +} → N is defined by f (n) = the sum of positive divisors of n then f (2^{ k} . 3), where *k* is a positive integer is

Solution:

f(2^{k}. 3) = The sum of positive divisors of

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): The function *f(x)=sin x* is symmetric about the line *x* = 0

Reason (R): Every even function is symmetric about y-axis

Solution:

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): If*n* is a positive integer then *3*^{2n} + 7 is divisible by 8

Reason (R): G.C.F. of 16 and 88 is 8

Assertion (A): If

Reason (R): G.C.F. of 16 and 88 is 8

Solution:

QUESTION: 14

If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A are

Solution:

QUESTION: 15

The combined equation to the tangents to the parabola y^{2} = 4ax from an external point A (x_{1}, y_{1}) is

Solution:

QUESTION: 16

In throwing of two dice, the probability of getting a multiple of 4 is

Solution:

QUESTION: 17

If ^{n}P_{r}=840, ^{n}C_{r}=35, then n=

Solution:

QUESTION: 18

Mode is approximately given by

Solution:

QUESTION: 19

The equation of line passing through intersection point of lines x+5y+7=0 and 3x+2y-5=0 and perpendicular to line 7x+2y-5=0 is

Solution:

QUESTION: 20

The subnormal to the curve *xy = c*^{2} at any point varies directly as

Solution:

*Answer can only contain numeric values

QUESTION: 21

The number of solutions of the equation tan^{2}x –sec^{6}x + 1 = 0 in [0, 4π] is :-

Solution:

sec^{6}x = 1 + tan^{2}x ⇒ sec^{6}x = sec^{2}x

if |secx| > 1 then sec^{6}x > sec^{2}x

Hence only possible solution is sec^{2}x = 1 ⇒ x = nπ

Hence in [0, 4π] possible solutions are 0, π, 2π, 3π, 4π

*Answer can only contain numeric values

QUESTION: 22

If solution of equation 3cos^{2}θ – 2√3 sin θ cos θ – 3sin^{2}θ = 0 are nπ + π/r and nπ + π/s then |r – s| is equal to:-

Solution:

Equation can be written as

3tan^{2}θ + 2√3 tanθ – 3 = 0

⇒ tan θ = 1/√3 and tan θ = -√3

⇒ θ = nπ + π/6 or θ = nπ – π/3

⇒ |r – s| = |6 + 3| = 9

*Answer can only contain numeric values

QUESTION: 23

If (x_{1} – x_{2})^{2} + (y_{1} – y_{2})^{2} = a^{2} ;

(x_{2} – x_{3})^{2} + (y_{2} – y_{3})^{2} = b^{2} ;

(x_{3} – x_{1})^{2} + (y_{3} – y_{1})^{2} = c^{2} and

= (a + b + c)(b + c – a)(c + a – b)(a + b – c)

Then the value of k is :-

Solution:

*Answer can only contain numeric values

QUESTION: 24

The interior angles of a convex polygon form an arithmetic progression with a common difference of 4°. Determine the number of sides of the polygon** **if its largest interior angle is 172°:-

Solution:

*Answer can only contain numeric values

QUESTION: 25

equals :-

Solution:

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