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JEE Main Maths Mock Test- 4 - JEE MCQ


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25 Questions MCQ Test - JEE Main Maths Mock Test- 4

JEE Main Maths Mock Test- 4 for JEE 2024 is part of JEE preparation. The JEE Main Maths Mock Test- 4 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Maths Mock Test- 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Maths Mock Test- 4 below.
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JEE Main Maths Mock Test- 4 - Question 1

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

JEE Main Maths Mock Test- 4 - Question 2

The slope m of a tangent through the point (7, 1) to the circle x2 + y2 = 25 satisfies the equation

JEE Main Maths Mock Test- 4 - 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

JEE Main Maths Mock Test- 4 - Question 4

If is a purely imaginary number, then is equal to

JEE Main Maths Mock Test- 4 - Question 5

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

JEE Main Maths Mock Test- 4 - Question 6

The sum of the focal distances from any point on the ellipse 9x2 + 16y2 = 144 is

JEE Main Maths Mock Test- 4 - 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 .

JEE Main Maths Mock Test- 4 - Question 8

Determinant   is not equal to

JEE Main Maths Mock Test- 4 - Question 9

Solution of the differential equation 

JEE Main Maths Mock Test- 4 - Question 10

If is continuous at x = x0 , then f ′ (x0) is equal to

JEE Main Maths Mock Test- 4 - 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.

JEE Main Maths Mock Test- 4 - Question 12

If z2 = -i, then z is equal o

JEE Main Maths Mock Test- 4 - Question 13

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

Detailed Solution for JEE Main Maths Mock Test- 4 - Question 13

 

Here, y = sin θ · sinΦ = sinθ · sin

JEE Main Maths Mock Test- 4 - Question 14

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

Detailed Solution for JEE Main Maths Mock Test- 4 - Question 14
If the unit place is ‘3’ then remaining three places can be filled in 3! ways.
Thus ‘3’ 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
JEE Main Maths Mock Test- 4 - 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

JEE Main Maths Mock Test- 4 - Question 16

The probability of A = probability of B = probability of C = 1/4, P(A∩B) = P(C∩B) = 0 and P(A∩C) = 1/8, then P(A∪B∪C) is equal to:

Detailed Solution for JEE Main Maths Mock Test- 4 - Question 16

JEE Main Maths Mock Test- 4 - Question 17

If the equations x2+ ba + a = 0 and x2 + ax + b = 0 have a common root, then a + b =

JEE Main Maths Mock Test- 4 - Question 18

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

JEE Main Maths Mock Test- 4 - Question 19

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

JEE Main Maths Mock Test- 4 - 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

*Answer can only contain numeric values
JEE Main Maths Mock Test- 4 - Question 21

If a, b are odd integers then number of integral root, of equation x10 + ax9 + b = 0 is equal to :


Detailed Solution for JEE Main Maths Mock Test- 4 - Question 21

Let P is a root (∈I)
Case-I : p is odd
p10 + ap9 + b ≠ 0
Because LHS odd
Case-II : p is even
p10 + ap9 + b ≠ 0
because, LHs is odd

*Answer can only contain numeric values
JEE Main Maths Mock Test- 4 - Question 22

If the number of distinct positive rational numbers p/q smaller than 1, where  p, q ∈ {1, 2, 3 ....., 6} is k then k is :


Detailed Solution for JEE Main Maths Mock Test- 4 - Question 22

Out of numbers   will result only 3 distinct rational numbers. 
⇒ Total numbers = 6C2 – 7 + 3 = 11

*Answer can only contain numeric values
JEE Main Maths Mock Test- 4 - Question 23

If two distinct chords of a parabola y2 = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to :


Detailed Solution for JEE Main Maths Mock Test- 4 - Question 23

Any point on x + y = 1 can be taken as (t, 1–t)
The equation of chord with this as mid-point is y(1–t) –2a (x + t) = (1 – t)2 – 4at
It passes through (a, 2a)
So, t2 – 2t + 2a2 – 2a + 1 = 0
This should have two distinct real roots. So D > 0
⇒ a2 – a < 0
⇒ 0 < a < 1
So, length of latus rectum < 4 and 0 < a < 1
⇒ LR = 1, 2, 3

*Answer can only contain numeric values
JEE Main Maths Mock Test- 4 - Question 24

If  the value of  is e–A then ‘A’ is :


Detailed Solution for JEE Main Maths Mock Test- 4 - Question 24

*Answer can only contain numeric values
JEE Main Maths Mock Test- 4 - Question 25

If  be three vectors of magnitude √3, 1, 2, such that   is the angle between  is equal  to:-


Detailed Solution for JEE Main Maths Mock Test- 4 - Question 25

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