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This mock test of JEE(MAIN) Mathematics Mock Test - 7 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE JEE(MAIN) Mathematics Mock Test - 7 (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) :A relation *R* on the set of complex number defined by Z_{1} R Z_{2} ⇔ Z_{1} − Z_{2} is real, is an equivalence relation.

Reason(R) :Reflexive and symmetric properties may not imply transitivity.

Solution:

QUESTION: 2

Straight line px+qy+r=0 touches the circle x^{2}+y^{2}=a^{2} if

Solution:

QUESTION: 3

The area contained between the curve x y = a^{2} , the vertical line *x = a, x = 4a (a > 0) *and *x* -axis is

Solution:

QUESTION: 4

A circle passes through (0,0) and its centre lies on y=x. If it cuts the circle x^{2}+y^{2}-4x-6y+10=0 orthogonally, then its equation is

Solution:

QUESTION: 5

Solution:

QUESTION: 6

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 n ≥ 3 and let the complex numbers α_{1} , α_{2} , . . . , α_{n} be the roots of x^{n} − 1 = 0 with α_{1} = 1 .

Assertion(A) :For any positive integer is again a positive integer.

Reason(R) :For any positive integer

Solution:

QUESTION: 7

The solution of the equation |z| - z = 1 + 2i is

Solution:

QUESTION: 8

For solving dy/dx=4x+y+1 suitable substitution is

Solution:

QUESTION: 9

If y=x^{2}(x-2)^{2}, then the values of x for which y is increasing, are

Solution:

QUESTION: 10

When y = 3, which of the following is FALSE?

Solution:

Remember what is TRUE: 3 is prime, odd and 2(3) is even.

Choice 1: T and T is TRUE

Choice 2: T or F is TRUE

Choice 3: F and T is FALSE

Choice 4: T and T is TRUE

QUESTION: 11

Let the function f be defined by f(x) = 2x + 1/1- 3x. Then f⁻^{1}(x) is

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): If f : R → R defined by f (x) = x^{3} then *f* is one one onto

Reason(R) : Function *f* is strictly decreasing on *R*.

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): y = sin (ax + b) is a general solution of y" + a^{2} y = 0 .

Reason(R) : y = sin (ax + b) is a trigonometric function.

Solution:

QUESTION: 14

If A is a square matrix such that A^{2} = I, then A⁻^{1} is equal to

Solution:

QUESTION: 15

If x+y+1=0 tocuhes the parabola y^{2}=λx,then λ is equal to

Solution:

QUESTION: 16

If P(B)=(3/4), P(A∩B∩C̅) = (1/3) and P(A̅∩B∩C̅) = 1/3, then P(B∩C) is

Solution:

QUESTION: 17

A polygon has 44 diagonals. The number of its sides is

Solution:

QUESTION: 18

Given n = 10, ∑x = 4, ∑y = 3, ∑x^{2} = 8, ∑y^{2} = 9 and ∑xy = 3, then coefficient of correlation is

Solution:

QUESTION: 19

The equation of sides of a quadrilateral AB, BC, CD and DA are x+2y=3, x=1, x-3y=4, 5x+y+12=0, the angle between diagonals AC and AD is

Solution:

QUESTION: 20

The straight line x + y = a will be a tangent to the ellipse x^{2}/9 + y^{2}/16 = 1 if a =

Solution:

QUESTION: 21

The shortest distance from the point (1, 2, -1) to the surface of the sphere x^{2} + y^{2} + z^{2} = 24 is

Solution:

QUESTION: 22

If cos (A - B)=3/5 tan A tan B=2, then

Solution:

QUESTION: 23

The angle between the vectors 3i+j+2k and 2i-2j+4k is

Solution:

QUESTION: 24

If the dot product of vector i+j+k and the unit vector along the sum of vectors 2i+4j-5k and λi+2j+3k is 1, then λ=

Solution:

QUESTION: 25

Solution:

QUESTION: 26

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-

Assertion(A):If A and B are two independent events such that

Reason(R):

Solution:

QUESTION: 28

If are two matrices such that the prouduct *PQ* is null matrix, then θ − φ is

Solution:

QUESTION: 29

Consider an infinite geometric series with first term a and common ratio r. if its sum is 4 and the second term is 3/4 ,then

Solution:

QUESTION: 30

The largest value of 2x^{3} - 3x^{2} - 12x + 5 for - 2 ≤ x ≤ 4 occurs at x =

Solution:

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