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JEE Main Mathematics Mock - 4

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25 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Main Mathematics Mock - 4

JEE Main Mathematics Mock - 4 for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The JEE Main Mathematics Mock - 4 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Mathematics Mock - 4 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Mathematics Mock - 4 below.
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JEE Main Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 4 - Question 4

If is a purely imaginary number, then is equal to

JEE Main Mathematics Mock - 4 - Question 5

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

JEE Main Mathematics Mock - 4 - Question 6

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

JEE Main Mathematics Mock - 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 Mathematics Mock - 4 - Question 8

Determinant   is not equal to

JEE Main Mathematics Mock - 4 - Question 9

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

JEE Main Mathematics Mock - 4 - Question 10

Solution of the differential equation

JEE Main Mathematics Mock - 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 Mathematics Mock - 4 - Question 12

If z2 = -i, then z is equal o

JEE Main Mathematics Mock - 4 - 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

Detailed Solution for JEE Main Mathematics Mock - 4 - Question 13
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 Mathematics Mock - 4 - Question 14

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

Detailed Solution for JEE Main Mathematics Mock - 4 - Question 14

Here, y = sin θ · sinΦ = sinθ · sin

JEE Main Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 4 - Question 16

JEE Main Mathematics Mock - 4 - Question 17

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

JEE Main Mathematics Mock - 4 - Question 18

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

JEE Main Mathematics Mock - 4 - Question 19

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

JEE Main Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 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 Mathematics Mock - 4 - Question 24

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

Detailed Solution for JEE Main Mathematics Mock - 4 - Question 24

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

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JEE Main & Advanced Mock Test Series

2 videos|324 docs|160 tests