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This mock test of JEE(MAIN) Mathematics Mock Test - 6 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE JEE(MAIN) Mathematics Mock Test - 6 (mcq) to study with solutions a complete question bank.
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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:

QUESTION: 21

If the direction cosines of a line are < (1/c), (1/c), (1/c) >, then

Solution:

QUESTION: 22

[(cos12°-sin12°)/(cos12°+sin12°]+[(sin147°)/(cos147°)]=

Solution:

QUESTION: 23

Three forces i+2j-3k, 2i+3j+4k and i-j+k are acting at a point (0,1,2). The modulus of moment of forces about the point (1,-2,0) is

Solution:

QUESTION: 24

The projection of the vector on the vector

Solution:

QUESTION: 25

Solution:

QUESTION: 26

If f : ℝ → ℝ is defined by

Solution:

QUESTION: 27

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-

Let f(x) = 2 + cos x for all real x.

Assertion(A): For each real t , there exists a point c in [ t,t + π ] such that f'(c) = 0.

Reason(R):f(t) = f(t + 2π) for each real t.

Solution:

QUESTION: 28

If x ∈ [-1, 1] then the minimum value of f(x) = x^{2} + x + 1 is

Solution:

QUESTION: 29

If -1, 0 and 1 are the elements of two matrices *A* and *B* of order 1 x 3 and of order 3 x 1 respectively, then A B equals -

Solution:

QUESTION: 30

If the sum to infinity of the series 1 + 4 x + 7x^{2} + 10x^{3} + … is 35/16 , then the value of x is

Solution:

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