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JEE Main Practice Test- 27 - JEE MCQ


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90 Questions MCQ Test Mock Tests for JEE Main and Advanced 2024 - JEE Main Practice Test- 27

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JEE Main Practice Test- 27 - Question 1

The area bounded by the parabola y2 = 8x, the x-axis and the latus rectum is

JEE Main Practice Test- 27 - Question 2

If the coefficients of rth, (r+1)th and (r+2)th terms in the binomial expansion of (1+y)m are in A.P., then m and r satisfy the equation

Detailed Solution for JEE Main Practice Test- 27 - Question 2

Coefficient of the rth term is mCr - 1
According to the given condition mCr - 1 + mCr + 1 = 2(mCr)

⇒ r2 + r + (m - r) (m + 1 - r) = 2(m + 1 - r) (r + 1)
⇒ r2 + r + m2 + (1 - 2r) m - r(1 - r) = 2m (r + 1) + 2(1 - r2)
⇒ m2 - m(4r + 1) + 4r2 - 2 = 0

JEE Main Practice Test- 27 - Question 3

Given that the function f defined by   is continuous . Then the value of k is

JEE Main Practice Test- 27 - Question 4

The equation of the circle passing thro' (1,0) and (0,1) and having smallest possible radius is

JEE Main Practice Test- 27 - Question 5

If |z2 - 1|=|z|2 + 1 ,then z lies on

JEE Main Practice Test- 27 - Question 6

If = a + i b , then a and b are

JEE Main Practice Test- 27 - Question 7

JEE Main Practice Test- 27 - Question 8

The differential equation of the family of curves y2=4a (x+a) is

JEE Main Practice Test- 27 - Question 9

The differential equation obtained by eliminating the arbitrary constants a and b from xy = aex + be−x is

JEE Main Practice Test- 27 - Question 10

If y=sin((1+x2)/(1-x2)), (dy/dx)=

Detailed Solution for JEE Main Practice Test- 27 - Question 10

JEE Main Practice Test- 27 - Question 11

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x2/a2) + (y2/b2) = 1) are given by

JEE Main Practice Test- 27 - Question 12

The value of lim is

JEE Main Practice Test- 27 - Question 13

∼ [ (p ∧ q) → (∼ p ∨ q) ] is

JEE Main Practice Test- 27 - 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 M is a n x n matrix with rank n - 1, then M can be made non-singular by changing one element.
Reason(R): An n x n matrix with rank n - 1 has a non-vanishing minor of order n - 1.

JEE Main Practice Test- 27 - 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): Solution of  
Reason(R): xdx + ydy =

JEE Main Practice Test- 27 - 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):If A and B are two independent events such that
Reason(R):  

JEE Main Practice Test- 27 - 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): If
Reason(R): We know that

JEE Main Practice Test- 27 - Question 18

If I₃ is the identity matrix of order 3, then I₃⁻1 is

JEE Main Practice Test- 27 - Question 19

If α , β are the roots of the quadratic equation x2 − (a − 2) x − (a + 1)   = 0 , where a is a variable, then the least value of α2 + β2 is

JEE Main Practice Test- 27 - Question 20
The mean of first 10 natural numbers is
JEE Main Practice Test- 27 - Question 21

If the parabola y2=4ax passes thro' the point (1,-2), then the tangent at this point is

JEE Main Practice Test- 27 - Question 22

If 20Cn+2 = nC16, then n =

Detailed Solution for JEE Main Practice Test- 27 - Question 22

JEE Main Practice Test- 27 - Question 23
The probability of getting more than 7 when a pair of dice are thrown is
JEE Main Practice Test- 27 - Question 24

If log(a + c), log(c - a), log (a - 2b + c) are in A.P., then

JEE Main Practice Test- 27 - Question 25

If f (x) = {2x - 3, x ≤ 2} {x, x < 2} then f (1) is equal to

JEE Main Practice Test- 27 - Question 26

If the range of a randon variable X is {0, 1, 2, 3, 4 ...} with   , then a =

JEE Main Practice Test- 27 - Question 27
The least value of 3 cosx + 4 sinx + 5 is
Detailed Solution for JEE Main Practice Test- 27 - Question 27
It is in general form as acosx+ bsinx+ c=0 and for this least value is c-√ a²+b² = 5-√3²+4² =0 or you can do like 5(3/5 cosx+ 4/5 sinx)+5 5{ sin(37+ x)}+5 and the range of sin is -1 to 1 so for min.sin(37+ x)= -1, -5+5= 0
JEE Main Practice Test- 27 - Question 28
The direction cosine of a vector a=3i+4j+5k in the direction of positive x-axis is
JEE Main Practice Test- 27 - Question 29

The ratio in which the line joining the points (a,b,c) and (-a,-c,-b) is divided by the xy-plane is

Detailed Solution for JEE Main Practice Test- 27 - Question 29

Let λ:1 be the ratio in which the line joining the points (a,b,c) and (-a, -c, -b) is divided by xy- plane.
So Z = 0

JEE Main Practice Test- 27 - Question 30

ix(axi)+jx(axj)+kx(axk)=

JEE Main Practice Test- 27 - Question 31

If 'S' is stress and 'Y' is Young's modulus of material of a wire, then the energy stored in the wire per unit volume is

JEE Main Practice Test- 27 - Question 32
The objective of an astronomical telescope has a large aperture to
JEE Main Practice Test- 27 - Question 33

Alcohols of low molecular weight are

JEE Main Practice Test- 27 - Question 34

Three separate samples of a solution of a single salt gave these results. One formed a white ppt. with excess ammonia solution, one formed a white ppt. with dil. NaCl solution and one formed a black ppt. with H₂S. The salt could be

JEE Main Practice Test- 27 - Question 35

The atoms of different elements, having same number of neutrons, but different mass numbers and atomic numbers, are called

JEE Main Practice Test- 27 - Question 36

Which one of the following compounds in most acidic

JEE Main Practice Test- 27 - Question 37

Sweetest sugar is

JEE Main Practice Test- 27 - Question 38

Homolytic fission of C - C bond in ethane (CH₃ - CH₃) gives an intermediate in which carbon atom is

JEE Main Practice Test- 27 - Question 39

The compound in which C uses sp3 hybrid orbitals for bond formation is

JEE Main Practice Test- 27 - Question 40

If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then

JEE Main Practice Test- 27 - Question 41

A gas bulb is filled with NO₂ gas and imersed in an ice bath at 0ºC which becomes colourless after sometime. This colourless gas will be

JEE Main Practice Test- 27 - Question 42

For the reaction A→B, the rate law expression is rate = k[A]. Which of the following statements is incorrect?

JEE Main Practice Test- 27 - Question 43

The calorific value of fat is

JEE Main Practice Test- 27 - Question 44

Which of the following gas molecule has the maximum specific heat at constant pressure?

JEE Main Practice Test- 27 - Question 45

For a reaction to occur spontaneously

JEE Main Practice Test- 27 - Question 46

Increasing order of stability among the three main conformations(i.e.,Eclipse,Anti,Gauche) of 2-fluorethanol is

JEE Main Practice Test- 27 - Question 47

Eka-aluminium and eka-silicon are known as

Detailed Solution for JEE Main Practice Test- 27 - Question 47

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- 27 - Question 48

The I.P. of sodium is 5.14eV. The I.P. of potassium could be

Detailed Solution for JEE Main Practice Test- 27 - Question 48

The ionisation potential keep on decreasing regularly as we move down a group from one element to the other. Because on moving down the group the atomic size increases gradually due to the addition of one new principal energy shell at each succeeding element. As a result, the force of attraction by the nucleus for the valence electrons decreases and the shielding effect increases. Consequently, ionisation potential also decreases.

JEE Main Practice Test- 27 - Question 49


then the formation constant of [Ag(NH3)2]+ is :

JEE Main Practice Test- 27 - Question 50

Which of the following oxide of vanadium is most basic?

JEE Main Practice Test- 27 - Question 51

The electrode potentials of half-cell reactions are: Zn → Zn2⁺ + 2e⁻ ; E = -0.76 V and Fe → Fe2⁺ + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe2⁺ + Zn → Zn2⁺ + Fe is

JEE Main Practice Test- 27 - Question 52

The unit of specific conductivity is

JEE Main Practice Test- 27 - Question 53

A helium molecule is two times heavier than a hydrogen molecule at 298 K. The kinetic energy of the helium molecule is

JEE Main Practice Test- 27 - Question 54

The electronic configuration of an element is 1s₂2s₂2p₆3s₂3p₆3d₁₀4s₂4p₃. Its properties would be similar to which of the following elements?

JEE Main Practice Test- 27 - Question 55

Water can be tested by

JEE Main Practice Test- 27 - Question 56

Replacement of Cl of chlorobenzene to give phenol requires drastic conditions but chlorine of 2,4-dinitrochlorobenzene is readily replaced. This is because

Detailed Solution for JEE Main Practice Test- 27 - Question 56

NO2 is an electron withdrawing group and it withdraws e - from ortho/para positions. That's why it facilitate nucleophilic substitution reactions.

JEE Main Practice Test- 27 - Question 57

Which of the following will not be soluble in sodium bicarbonate?

JEE Main Practice Test- 27 - Question 58

Increasing order of p k a values (pKa = - log ka) pka of H2O,CH3OH and C6H5OH is :

Detailed Solution for JEE Main Practice Test- 27 - Question 58

p k a

value of H2O is 15.7, C6H5OH is 9.95 and CH3OH is 16 so C6H5OH< H2O <CH3OH

JEE Main Practice Test- 27 - Question 59

In order to get Bakelite from phenol which of the following reagent is required?

JEE Main Practice Test- 27 - Question 60

Which is maximum acidic?

JEE Main Practice Test- 27 - Question 61



Relation between (X) and (Y) is :

Detailed Solution for JEE Main Practice Test- 27 - Question 61

If a carbon is bonded to two hydrogens and replacing each of them in turn with deuterium (or another group) creates a pair of diastereomers, the hydrogens are called diastereotopic hydrogens.

JEE Main Practice Test- 27 - Question 62

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- 27 - Question 62

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- 27 - Question 63

The ratio of th efrequencies of the long wavelength limits of the Lyman and Balmer series of hydrogen is

JEE Main Practice Test- 27 - Question 64

What was the fissionable material used in bomb dropped at Nagasaki in the year 1945 ?

JEE Main Practice Test- 27 - Question 65

When a resistance of 2 ohm is connected across the terminals of a cell, the current is 0.5 A;but when the resistance across the cell is 5 ohm, the current is 0.25 A. The e.m.f. of the cell is

JEE Main Practice Test- 27 - Question 66

The potential difference between two electrodes of a galvanic cell, in an open circuit, is known as

JEE Main Practice Test- 27 - Question 67

If we consider electrons and photons of the same wavelength, then they will have the same

JEE Main Practice Test- 27 - Question 68

The work function of sodium is 2.3eV. The threshold wavelength of sodium will be

JEE Main Practice Test- 27 - Question 69

Which one of the following electromagnetic radiations have the smallest wavelength?

JEE Main Practice Test- 27 - Question 70

The capacitor of a parallel plate capacitor with no dielectric substance and a separation of 0.4 cm is 2 μF. The separation is reduced to half and it is filled with a substance of dielectric value 2.8. The new capacity of the capacitor is

JEE Main Practice Test- 27 - Question 71

Two similar point charges at a certain distance experience a force of 80 N. Each charge is halved in magnitude and distance between them is doubled. The new electrostatic force between them would be

JEE Main Practice Test- 27 - Question 72

Orbit of a planet around a star is

JEE Main Practice Test- 27 - Question 73

Which of the following statements is correct in respect of a geostationary satellite ?

JEE Main Practice Test- 27 - Question 74

We consider the radiation emitted by the human body. Which of the following statements is true

JEE Main Practice Test- 27 - Question 75

A calorimeter of mass 0.2 kg and specific heat 900 J/kg-K. Containing 0.5 kg of a liquid of specific heat 2400J/kg-K. Its temperature falls from 60ºC to 55ºC in one minute. The rate of cooling is

JEE Main Practice Test- 27 - Question 76

A mass m falls freely from rest. The linear momentum, after it has fallen through height h, is

Detailed Solution for JEE Main Practice Test- 27 - Question 76

u = 0; since it falls freely from rest

JEE Main Practice Test- 27 - Question 77

To convert a 800mV range millivoltmeter of resistance 40 Ω into a milliammeter of 100mA range, the resistance to be connected as shunt is

JEE Main Practice Test- 27 - Question 78

A stone is thrown up with a velocity of 4.9 m−s−1 from a bridge. It falls down in water after 2 s. The height of the bridge is

JEE Main Practice Test- 27 - Question 79

Which one of the following is ture for a small iron ball when placed just at the centre of the horizontal pole pieces of a strong electromagnet and then released ?

JEE Main Practice Test- 27 - 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): Orbiting satellite or body has K.E. of always less than that of Potential energy.
Reason(R): For any bound state, the magnitude of potential energy is always twice that of kinetic energy (K.E.)

JEE Main Practice Test- 27 - Question 81

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 Lorentzian force acts like a torque on the charge moving with a velocity.
Reason(R) : As any torque is I α , the Lorentzian force produces acceleration.

JEE Main Practice Test- 27 - Question 82

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): Pure rolling may be produced when there is sufficient friction to prevent slipping.
Reason(R) : Friction opposes the translatory motion of the rolling body.

JEE Main Practice Test- 27 - Question 83

The substance which shows practically no elastic after effect is

JEE Main Practice Test- 27 - Question 84

A flywheel has a moment of inertia 0.5 kg-m2. What torque is required to increase its velocity from 2π rad-s⁻2 to 15 π rad-s⁻2 in 8 s?

JEE Main Practice Test- 27 - Question 85

The time period of a simple pendulum is T. When the length is increased by 10cm, its period is T1. When the length is decreased by 10cm, its period is T2. Then relation between T, T1 and T2 is

JEE Main Practice Test- 27 - Question 86

Let Vs be the speed of the source emitting sound waves, 'n' the actual frequency of the source of sound, 'V' the speed of sound, and ' n1 ' the frequency of sound waves as perceived by a stationary observer to whom the source is approaching. The formula for calculating n 1 is

JEE Main Practice Test- 27 - Question 87

With respect to the figures of above question, no heat exchange between the gas and the surroundings will take place, if the gas is taken along curve

JEE Main Practice Test- 27 - Question 88

How many times is diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half?

JEE Main Practice Test- 27 - Question 89

If C and R denote the capacitance and resistance respectively, then the dimensional formula for CR is same as that fore

Detailed Solution for JEE Main Practice Test- 27 - Question 89

CR is time constant of CR circuit

JEE Main Practice Test- 27 - Question 90

If Young's double slit experiment of light, interference is performed in water, which one of the following is correct?

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