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JEE Main Practice Test- 24 - JEE MCQ


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90 Questions MCQ Test Mock Tests for JEE Main and Advanced 2024 - JEE Main Practice Test- 24

JEE Main Practice Test- 24 for JEE 2024 is part of Mock Tests for JEE Main and Advanced 2024 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

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

JEE Main Practice Test- 24 - Question 31

2R ― OH + 2Na → 2RONa + H₂. In the above reaction the reactivity of different alcohols is

JEE Main Practice Test- 24 - Question 32

A chloride dissolves appreciably in cold water. When placed on a platinum wire in Bunsen flame no distinctive colour is noticed, the cation would be

JEE Main Practice Test- 24 - Question 33

The configuration of X is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3. Its properties are similar to

JEE Main Practice Test- 24 - Question 34

The effect of atoms or groups loosing electrons towads a carbon atom is called

JEE Main Practice Test- 24 - Question 35

Reference proteins are those obtained from

JEE Main Practice Test- 24 - Question 36

If we know the bond of NO and NO+, then which of the following statement is true for these two species?

Detailed Solution for JEE Main Practice Test- 24 - Question 36

Bond order of NO is 2.5 while that of NO+ is 3. Bond length is inversely proportional to the bond order.

JEE Main Practice Test- 24 - Question 37

The correct order of the O―O bond length in O2, H2O2 and O3 is___

Detailed Solution for JEE Main Practice Test- 24 - Question 37

The bond length of O―O bond in O3 (1.278Å) is intermediate that for a single bond in H2O2 (1.48 Å) and for a double bond in O2 (1.121 Å).

JEE Main Practice Test- 24 - Question 38

Which of the following compound has a linear structure?

JEE Main Practice Test- 24 - Question 39

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 KJ mol⁻1 respectively .The enthalpy of formation of carbon monoxide per mol is

JEE Main Practice Test- 24 - Question 40

A chemical reaction is catalyzed by a catalyst X. Hence X

JEE Main Practice Test- 24 - Question 41

The activation energy of a reaction can be determined by

JEE Main Practice Test- 24 - Question 42

Heat of combustion ΔH for C(s), H2(g) and CH4(g) are -94, -68 and -213 cal/mol. Then ΔH for C(s) + 2H2(g) → CH4(g) is

Detailed Solution for JEE Main Practice Test- 24 - Question 42

CH4 + 2O2 = CO2 + 2H2O
ΔH = -213 cal/mol .....(1)
C + O2 = CO2
ΔH = - 94 cal/mol .....(2)
H2 + (1/2) O2 = H2O
ΔH = - 68 cal/mol .....(3)
ΔH for C(s) + 2H2(g) → CH4(g)
= 2(eq 3) + (eq 2) - (eq 1)
= (- 68 x 2) + (- 94) - (- 213) = -17Kcal

JEE Main Practice Test- 24 - Question 43

In the reaction CH2COOHaq + OH(aq) → CH3COO- + H2O(l) ; ΔH = -55.2kJ mol-1 What is the heat of dissociation (in kJ mol-1) of acetic acid?

Detailed Solution for JEE Main Practice Test- 24 - Question 43

ΔH = -55.2 KJ.mol-1
-[H+ (aq) + OH- (aq) → H2O(l) ΔH = -57.3 KJ .mol-1]]

CH2COOHaq → CH3COO- (aq) + H+ (aq) ΔH = ?
CH2COOH(aq) + OH- (aq) → CH3COO- (aq) + H2O(l) ΔH = -55.2 KJ .mol-1
-H+ + OH- (aq) → - H2O(l) ΔH = + 57.3KJ .mol-1
CH3COOH(aq) → CH3COO- (aq) + H+(aq) ΔH = 2.1 KJmol-1

JEE Main Practice Test- 24 - Question 44

Which of the following is an example of intensive property?

JEE Main Practice Test- 24 - Question 45

Which of the following is an isomers of propanal ?

JEE Main Practice Test- 24 - Question 46

Eka-aluminium and eka-silicon are known as

Detailed Solution for JEE Main Practice Test- 24 - Question 46

Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them eka-aluminium and eka-silicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.

JEE Main Practice Test- 24 - Question 47

Which of the following is the correct order of ionic radii?

Detailed Solution for JEE Main Practice Test- 24 - Question 47

Na+, Mg2+, Al3+ and Si4+ are isoelectronic cations with 10 electrons, but when we go from Na+ to Si4+, one unit nuclear charge increases. Thus, the ionic size of isoelectronic species is compared on the basis of their atomic number/number of electrons, i.e. Z/e ratio. Smaller the value of Z/e, larger the size of the species. For example,

JEE Main Practice Test- 24 - Question 48

Among the following complexes, optical activity is possible in__

Detailed Solution for JEE Main Practice Test- 24 - Question 48

Optical isomers of [Co(NH3)2(H2O)2Cl2] are

JEE Main Practice Test- 24 - Question 49

Which of the following belongs to the actinide series?

JEE Main Practice Test- 24 - Question 50

The charge required to liberate 112 ml of hydrogen from acidified water is

JEE Main Practice Test- 24 - Question 51

In electrorefining of copper a minor percentage of gold accumulates in

JEE Main Practice Test- 24 - Question 52

A gaseous mixture of three gases A, B and C has a pressure of 10 atm. The total number of moles of all the gases is 10. If the partial pressures of A and B are 3.0 and 1.0 atm respectively and if C has a mol. wt. 2.0. What is the weight of C in gms present in the mixture?

JEE Main Practice Test- 24 - Question 53

Which of the following compounds does not exist ?

JEE Main Practice Test- 24 - Question 54

In which of the following reactions, H₂O₂ acts as a reducing agent?

JEE Main Practice Test- 24 - Question 55

Which of the following possesses highest melting point?

JEE Main Practice Test- 24 - Question 56

When ethylene glycol is heated with acidified potassium permanganate, the main organic compound obtained is:

JEE Main Practice Test- 24 - Question 57

Relatives stabilites of the following carbocation will be in order :




JEE Main Practice Test- 24 - Question 58

In the addition of HBr to propene in presence of peroxide, most stable free radical formed is :

JEE Main Practice Test- 24 - Question 59

Increasing order of acid strength among p-methoxyphenol, p-methylphenol and p-nitrophenol is

Detailed Solution for JEE Main Practice Test- 24 - Question 59

Electron withdrawing groups increase the acid strength while electron releasing groups decrease the acid strength of the phenol.
-NO2 group is strongly withdrawing group while -CH3 is mildly releasing and -OCH3 is strongly releasing group. Thus, p-methoxyphenol is the weakest acid while p-nitrophenol is the strongest acid among the given compounds.

JEE Main Practice Test- 24 - Question 60

The molecule which shows optical isomerism is

JEE Main Practice Test- 24 - Question 61

The decay constant λ of the radioactive sample is the probability of decay of an atom in unit time, then

JEE Main Practice Test- 24 - Question 62

A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance is

JEE Main Practice Test- 24 - Question 63

By increasing the temperature, the specific resistance of a conductor and a semiconductor

JEE Main Practice Test- 24 - Question 64

On increasing the temperature of a conductor, its resistance increases because

JEE Main Practice Test- 24 - Question 65

An electron and a proton have same de-Broglie's wavelength. The kinetic energy of an electron is

JEE Main Practice Test- 24 - Question 66

During X-ray formation if voltage is increased

JEE Main Practice Test- 24 - Question 67

An electromagnetic wave of frequency 3 MHz passes from vacuum into a medium with dielectric constant k = 4. Then

JEE Main Practice Test- 24 - Question 68

Minimum no. of 8 μF and 250 V capacitors, used to make a combination of 16 μF and 1000 V, is

JEE Main Practice Test- 24 - Question 69

If 1000 droplets each of charge q and radius r are mixed to form a big drop, then the potential of big drop, as compared to small droplet will be

Detailed Solution for JEE Main Practice Test- 24 - Question 69

If the value of potential on each small drop be V and potential on each small drop be V '
V ' = n 2/3 V
⇒ V ' = 1000 2/3 V

JEE Main Practice Test- 24 - Question 70

The gravitational potential energy of a body (in earth's field) is minimum

JEE Main Practice Test- 24 - Question 71

If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is

JEE Main Practice Test- 24 - Question 72

A black body, at a temperature of 227ºC, radiates heat at a rate of 84 J-m⁻2-s⁻1. When its temperature is raised to 727ºC, the heat radiated by it in J-m⁻2-s⁻1 will be

JEE Main Practice Test- 24 - Question 73

The energy spectrum of a black body exhibits a maximum around a wavelength λ₀. The temperature of the black body is now changed such that the energy is maximum around a wavelength 3λ₀/4. The power radiated by the black body will increase by a factor of

JEE Main Practice Test- 24 - Question 74

Momentum is closely related to

JEE Main Practice Test- 24 - Question 75

If 10% of the current passes through a moving coil galvanometer of resistance 99 ohm, then the shunt resistance will be

JEE Main Practice Test- 24 - Question 76

A particle under the action of a constant force moves from rest upto 20 seconds. If distance covered in first 10 seconds is s₁ and that covered in next 10 seconds is s₂, then

JEE Main Practice Test- 24 - Question 77

Two simple pendulums of length 0.5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed... oscillations

JEE Main Practice Test- 24 - Question 78

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 principle of homogeneity of dimensions state that dimensions on both sides of equation must be same
Reason (R) : An equation which is dimensionally correct is also practically correct

JEE Main Practice Test- 24 - Question 79

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-
Statement-1:
If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.
Statement-2:
The linear momentum of an isolated system remains constant

JEE Main Practice Test- 24 - Question 80

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 spherical conductors A and B having different potentials are separated by a long distance so that they can be considered as isolated. Then charge flown through the wire, to equilize the potentials of A and B as a result some current flows through connecting wire for some-time. During this time over Ampere's loop is zero.
Reason(R) : According to Ampere's circuital law, over any closed path is equal to the number of times the net current enclosed by the loop provided the electric field over the region of ampere's loop is remains constant.

JEE Main Practice Test- 24 - Question 81

The upper end of wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle an angle of 30º. Then angle of shear is

JEE Main Practice Test- 24 - Question 82

Motion of a liquid in a tube is described by

JEE Main Practice Test- 24 - Question 83

The distance between eye lens and cross wire in Ramsden eye piece which has a field lens of focal length 1.2 cm is .......cm.

JEE Main Practice Test- 24 - Question 84

A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of body of mass 27 kg moving with a speed of

JEE Main Practice Test- 24 - Question 85

When the potential energy of a particle executing simple harmonic motion is one-fourth of the maximum value during the oscillation, its displacement from the equilibrium position in terms of its amplitude a is

JEE Main Practice Test- 24 - Question 86

The internal energy of a gas, during isothermal expansion

JEE Main Practice Test- 24 - Question 87

If the ratio of the densities of two monoatomic gases is 16 : 9, the ratio of the velocities of sound in them is

JEE Main Practice Test- 24 - Question 88

An ideal gas A and a real gas B have their volumes increased from V to 2V under isothermal conditions. The increase in internal energy

JEE Main Practice Test- 24 - Question 89

Who gave the universal law of gravitation?

JEE Main Practice Test- 24 - Question 90

In Huygen's wave theory, the locus of all points oscillating in the same phase is called a

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