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JEE Main Practice Test- 24 - JEE MCQ


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30 Questions MCQ Test - JEE Main Practice Test- 24

JEE Main Practice Test- 24 for JEE 2024 is part of JEE preparation. The JEE Main Practice Test- 24 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Practice Test- 24 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Practice Test- 24 below.
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JEE Main Practice Test- 24 - Question 1

49n2+16n-1 divisible by

JEE Main Practice Test- 24 - Question 2

Which of the following statements are true?
1. The amplitude of the product of complex numbers is equals to the product of their amplitudes
2.For any polynomial f (x)=0 with real coefficients ,imaginary roots occur in conjugate pairs
3. Order relation exists in complex number whereas it does not exist in real numbers
4.The values of ω used as a cube roots of unity and as a fourth root of unity are different

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JEE Main Practice Test- 24 - Question 3

The area of the triangle formed by joining the origin of the points of intersection of the line x √5 + 2y = 3√5 and the circle x2 + y2 = 10 is

JEE Main Practice Test- 24 - Question 4

[(-1 + √(-3))/2]3n +[(-1 - √(-3))/2]3n is equal to

JEE Main Practice Test- 24 - Question 5

The area bounded by the x-axis and the curve y = 4x − x2 − 3 is

Detailed Solution for JEE Main Practice Test- 24 - Question 5


y = 0, y = 4x - x2 - 3
⇒ 4x - x2 - 3 = 0
⇒ x2 - 4x + 3 = 0
⇒ (x - 1) (x - 3) = 0
⇒ x = 1, 3

JEE Main Practice Test- 24 - Question 6

If f: R → R defined by f x is continuous function, then

JEE Main Practice Test- 24 - Question 7

If , then what is the value of k ?

JEE Main Practice Test- 24 - Question 8
If x=a[(cost)+(log tan(t/2))], y=a sint, (dy/dx)=
JEE Main Practice Test- 24 - Question 9

The radius of the circle passing through the foci of the ellipse ((x2/16) + (y2/9) = 1), and having its centre (0,3) is

JEE Main Practice Test- 24 - Question 10

The solution of is

JEE Main Practice Test- 24 - Question 11

If c is parameter then the differential equation whose solution is is

Detailed Solution for JEE Main Practice Test- 24 - Question 11

JEE Main Practice Test- 24 - Question 12

JEE Main Practice Test- 24 - Question 13

Sneha says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Sneha is thinking of is

Detailed Solution for JEE Main Practice Test- 24 - Question 13

This sentence contains the word "or" (disjunction). A disjunction is only false if BOTH conditions are false. The only number that is not divisble by 2 and is not divisible by 3 is 11.

JEE Main Practice Test- 24 - Question 14

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 n and r are positive integers such that 1 ≤ r ≤ n, then
Reason(R):

JEE Main Practice Test- 24 - Question 15

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): Two dice are thrown simultaneously . The probability of obtaining a total score of 5 is 0.11 .
Reason(R): A subset of the sample space S which contains more than one elements is called mixed events.

JEE Main Practice Test- 24 - Question 16

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 slope of the line whose equation is 5x + 6y = 7 is − 5/6 and the y-intercept is 7/6
Reason(R): The equation of straight line which makes an angle θ with x-axis and intercept c on the y-axis is y = mx - c, where m = tan θ

JEE Main Practice Test- 24 - Question 17
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):ABC is a triangle, where A ≡(2,3,5), B ≡ (-1,3,2) and c ≡ (λ,5,μ). If the median through A is equally inclined towards the axes, then the values of λ and μ are respectively 7 and 10.
Reason(R): If median through A is equally inclined to the axis, then its direction ratios will be equal (say k), where k is a constant.
JEE Main Practice Test- 24 - Question 18

If A is a non-zero column matrix of order m x 1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal to

JEE Main Practice Test- 24 - Question 19

Minimum area of the triangle formed by any tangent to the ellipse with the coordinate axes is

Detailed Solution for JEE Main Practice Test- 24 - Question 19

JEE Main Practice Test- 24 - Question 20

Which of the following relations among the locations parameters does not hold?

JEE Main Practice Test- 24 - Question 21

Two tangents are drawn from the point (-2,-1) to the parabola y2=4x. If α is the angle between them, then tan α =

Detailed Solution for JEE Main Practice Test- 24 - Question 21
The eqn of any tangent to a parabola y^2 = 4ax is y = mx+a/m
So the equation of any tangent to this parabola, would be y=mx+1/m (as a=1, for y^2=4x)

Now these tangents pass through (-2,-1)... so -1=-2m+1/m

Or 2m2-m-1=0.

Where m1,m2 are the slopes of the two tangents that satisfy this equation (m1,m2 are the roots of the quad)....

So tan(angle between the tangents) = |(m1-m2)/(1+m1m2)|

Now m1m2 = -1/2

And m1-m2 = root { (m1+m2)2-4m1m2 } = root [ (1/2)2 - 4(-1/2) ] = root[9/4].

So |m1-m2| = 3/2.

Hence tan(Angle) = (3/2) / (1/2) = 3
JEE Main Practice Test- 24 - Question 22
The number of ways in which 5 boys and 3 girls be seated in a row so that each girl is between two boys is
Detailed Solution for JEE Main Practice Test- 24 - Question 22
First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways.
So number of ways = 5! 4! = 2880
JEE Main Practice Test- 24 - Question 23

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is

JEE Main Practice Test- 24 - Question 24
If the 7th term of an H.P. is 1/10 and 12th term is 1/25, then the 20th term is
JEE Main Practice Test- 24 - Question 25

Sin⁻1(3/5) + tan⁻1(1/7) is equal to

JEE Main Practice Test- 24 - Question 26

In a Poisson distribution the variance is m. The sum of the terms is odd places in this distribution is

JEE Main Practice Test- 24 - Question 27
The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is
Detailed Solution for JEE Main Practice Test- 24 - Question 27
The equation of required plane is
(x + 2y + 3z + 4) + λ (4x + 3y + 2z + 1) = 0
It passes through (0, 0, 0) So
4 + λ = 0
λ = - 4
So the equation of plane is
(x + 2y + 3z + 4) -4 (4x + 3y + 2z + 1) = 0
or x + 2y + 32 + 4 - 16x - 12y - 82 - 4 = 0
or 15x + 10y + 5z = 0
or 3x + 2y + z = 0
JEE Main Practice Test- 24 - Question 28
In ∆ABC cosecA(sinB cosC+cosB sinC)=
JEE Main Practice Test- 24 - Question 29
The position vectors of A and B are i-j+2k and 3i-j+3k, then the position vector of mid point of AB is
JEE Main Practice Test- 24 - Question 30

is equal to

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