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This mock test of JEE(MAIN) Mathematics Mock Test - 4 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE JEE(MAIN) Mathematics Mock Test - 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Points A(2,2), B(-4,-4), C(5,-8) are vertices of ∆ ABC the length of the median through C is

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Let *f(x)* be a function satisfying f ′(x) = f (x) with *f(0)* = 1 and *g(x)* be a function that satisfies *f(x) + g(x) = x*^{2}, then value of integral

is equal to

Solution:

QUESTION: 4

If is a purely imaginary number, then is equal to

Solution:

QUESTION: 5

If f (x) = cos [π^{2}] x + cos [− π^{2}] x where [x] is the step function, then

Solution:

QUESTION: 6

The sum of the focal distances from any point on the ellipse 9x^{2} + 16y^{2} = 144 is

Solution:

QUESTION: 7

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): f (x) = log x^{3} and g (x) = 3 log x are equal.

Reason(R) : Two functions f and g are said to be equal if their domains, ranges are equal and f (x) = g (x)∀ x in the domain .

Solution:

QUESTION: 8

Determinant is not equal to

Solution:

QUESTION: 9

If is continuous at x = x_{0} , then f ′ (x_{0}) is equal to

Solution:

QUESTION: 10

Solution of the differential equation

Solution:

QUESTION: 11

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-

Tangents are drawn from the point (17,7) to the circle x^{2}+y^{2}=169.

Statement-1:

The tangents are mutually perpendicular.

Statement-2:

The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^{2}+y^{2}=338.

Solution:

QUESTION: 12

If z^{2} = -i, then z is equal o

Solution:

QUESTION: 13

The sum of the digits in the unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is

Solution:

If the unit place is â€˜3â€™ then remaining three places can be filled in 3! ways.

Thus â€˜3â€™ appears in unit place in 3! times.

Similarly each digit appear in unit place 3! times.

So, sum of digits in unit place = 3!(3 + 4 + 5 + 6) = 18 * 6 = 108

QUESTION: 14

If θ + Φ = π/3 then sin θ . sinΦ has a maximum value at θ =

Solution:

Here, y = sin θ · sinΦ = sinθ · sin

QUESTION: 15

An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of odd number of points is

Solution:

QUESTION: 16

The probability of A = probability of B = probability of C = 1/4, P(Aâˆ©B) = P(Câˆ©B) = 0 and P(Aâˆ©C) = 1/8, then P(AâˆªBâˆªC) is equal to:

Solution:

QUESTION: 17

If the equations x^{2}+ ba + a = 0 and x^{2} + ax + b = 0 have a common root, then a + b =

Solution:

QUESTION: 18

If a, b, c, d, e, f are in A.P., then e - c is equal to

Solution:

QUESTION: 19

If a line passes through points (4,3) and (2,λ) and perpendicular to y=2x+3, then λ=

Solution:

QUESTION: 20

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

Solution:

QUESTION: 21

The equation of the plane which bisects the line joining (2,3,4) and (6,7,8) is

Solution:

QUESTION: 22

The intersection of the spheres x^{2} + y^{2} + z^{2} + 7x - 2y - z = 13 and x^{2} + y^{2} + z^{2} - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane

Solution:

QUESTION: 23

If A=130° and x=sinA+cosA, then

Solution:

QUESTION: 24

The unit vector perpendicular to each of the vector

Solution:

QUESTION: 25

The smallest positive integral value of *P* for which the equation cos (*P* sin *x*) = sin (*P* cos *x*) in *x* has a solution in [0, 2π] is

Solution:

QUESTION: 26

Let A, B, C be three angles such that A = π/4 and tan B tan C = p. Then all possible values of p such that A, B, C are the angles of a triangle is:

Solution:

QUESTION: 27

If are non-coplanar unit vectors such that , then the angle between is

Solution:

QUESTION: 28

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 term independent of x in

Reason(R): The number of terms in the expansion of (x+y+z)^{n}, where n is a +ve integer, is 1/2 (n + 1) (n + 2).

Solution:

QUESTION: 29

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 number of diagonals that can be drawn in a plane figure of 16 sides is 120 .

Reason(R): Number of circular arrangements of n different things = (n + 1)!.

Solution:

QUESTION: 30

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): Tangent to the curve y^{2} = 2x^{3} which is perpendicular to the line 4x - 3y + 2 = 0 is drawn at the point

Reason(R): m_{1}.m_{2} = -1 , if two lines are perpendicular.

Solution:

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