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# JEE(MAIN) Mathematics Mock Test - 4

## 30 Questions MCQ Test JEE Main Mock Test Series 2020 & Previous Year Papers | JEE(MAIN) Mathematics Mock Test - 4

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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. The solved questions answers in this JEE(MAIN) Mathematics Mock Test - 4 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this JEE(MAIN) Mathematics Mock Test - 4 exercise for a better result in the exam. You can find other JEE(MAIN) Mathematics Mock Test - 4 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

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) = x2, 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 [π2] x + cos [− π2] x where [x] is the step function, then

Solution:
QUESTION: 6

The sum of the focal distances from any point on the ellipse 9x2 + 16y2 = 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 x3 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 = x0 , then f ′ (x0) 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 x2+y2=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 x2+y2=338.

Solution:
QUESTION: 12

If z2 = -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 x2+ ba + a = 0 and x2 + 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

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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 x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 - 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 y2 = 2x3 which is perpendicular to the line 4x - 3y + 2 = 0 is drawn at the point

Reason(R): m1.m2 = -1 , if two lines are perpendicular.

Solution: