JEE Main Practice Test- 6 - JEE MCQ

# JEE Main Practice Test- 6 - JEE MCQ

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## 75 Questions MCQ Test - JEE Main Practice Test- 6

JEE Main Practice Test- 6 for JEE 2024 is part of JEE preparation. The JEE Main Practice Test- 6 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Practice Test- 6 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Practice Test- 6 below.
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JEE Main Practice Test- 6 - Question 1

### Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder? [Assume A << A0  (area of tank)]

Detailed Solution for JEE Main Practice Test- 6 - Question 1

Time required to empty the tank

JEE Main Practice Test- 6 - Question 2

### Which of the following graphs correctly represent the variation of β = −[(dV/dp)/V] with p for an ideal gas at constant temperature?

Detailed Solution for JEE Main Practice Test- 6 - Question 2

PV = constant, according to Boyle’s law
∴ PV = constant
∴ PdV + VdP = 0

The equation between β and P is of the form xy = constant which represents a rectangular hyperbola.
∴ Graph between β and P will be a rectangular hyperbola represented by graph (a)

JEE Main Practice Test- 6 - Question 3

### What is the potential difference between A and B? (where A is the centre of left ring and B is the centre of right ring)

Detailed Solution for JEE Main Practice Test- 6 - Question 3

JEE Main Practice Test- 6 - Question 4

Half-life of a radioactive substance A is 4 days. The probability of a nucleus that,  from the given sample that it will decay in two half-lives is

Detailed Solution for JEE Main Practice Test- 6 - Question 4

After two half-lives 1/4 th fraction of nuclei will remain undecayed. Or, 3/4 th fraction will decay. Hence, the probability that a nucleus decays in two half lives is 3/4

JEE Main Practice Test- 6 - Question 5

Which of the following statement is false for electromagnetic waves ?

Detailed Solution for JEE Main Practice Test- 6 - Question 5

Electromagnetic waves can propagate in material as well as vacuum.

JEE Main Practice Test- 6 - Question 6

The voltage of clouds is 4 × 106 V with respect to ground. In a lightning strike lasting 100 ms, a charge of 4 C is delivered to the ground. The average power of lightning strike is (assume complete discharges)

Detailed Solution for JEE Main Practice Test- 6 - Question 6

Energy stored between cloud and earth, assuming the capacitor model is

The power of lightning strike is

JEE Main Practice Test- 6 - Question 7

A tuning fork vibrates with a frequency of 256 Hz. Taking the speed of sound to be 345.6 m s-1 in the air, find the wavelength and the distance, which the sound travels during the time, fork makes 60 vibrations.

Detailed Solution for JEE Main Practice Test- 6 - Question 7

In one cycle, sound advances by distance λ
Therefore, the required distance travelled by sound,
S = 60. λ = 81 m

JEE Main Practice Test- 6 - Question 8

If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface would

Detailed Solution for JEE Main Practice Test- 6 - Question 8

g = GM/R2
or    g∝1/R2
g will increase if R decreases.

JEE Main Practice Test- 6 - Question 9

Three capacitors each of capacity 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by

Detailed Solution for JEE Main Practice Test- 6 - Question 9

To get equivalent capacitance 6 μF Out of the 4 μF capacitance, two are connected in series and third one is connected in parallel.

JEE Main Practice Test- 6 - Question 10

Six wires of current I1 = 1A, I2 = 2A, I3 = 3A, I4 = 1A, I5 = 5A and I6 = 4A cut the page perpendicularly at the points 1,2,3,4,5 and 6 respectively as shown in the figure. Find the value of integral ∮B→.dℓ around the circular path c.

Detailed Solution for JEE Main Practice Test- 6 - Question 10

JEE Main Practice Test- 6 - Question 11

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the direction of magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s-1. Find the induced emf in the loop when it's radius is 2 cm.

Detailed Solution for JEE Main Practice Test- 6 - Question 11

Here;
Magnetic field. B = 0.025 T
Radius of the loop, r = 2 cm = 2 x 10-2
Constant rate at which radius of the loop shrinks,

Magnetic flux linked with the loop is

From Faraday's law, the magnitude of the induced emf is

JEE Main Practice Test- 6 - Question 12

A body executing S.H.M. has amplitude 5 cm and frequency 5 vibrations per second. Calculate the displacement of particle from mean position after 0.32 s.

Detailed Solution for JEE Main Practice Test- 6 - Question 12

Here, A = 5 cm ; f = 5 Hz ; t = 0.32 s
Now,y = A sin ωt = A sin 2π f t = 5 sin (576°) = –2.94 cm

JEE Main Practice Test- 6 - Question 13

For network shown in figure, determine Vand ID. (Where, ID = Current flowing in the diodes)

Detailed Solution for JEE Main Practice Test- 6 - Question 13

Direction of current lD is the same direction as arrow in the diode symbol. Therefore, both the diodes are in forward Bias; hence voltage drops across their terminals are VSi and VGe are 0.7 V and 0.3 V respectively.

JEE Main Practice Test- 6 - Question 14

A particle is projected vertically upwards with a velocity u, from a point O. When it returns to the point of projection, which of the following is incorrect ?

Detailed Solution for JEE Main Practice Test- 6 - Question 14

Total displacement is 0 as the particle returns to the original position, thus the average velocity zero.
Total distance travelled is 2s and total time taken is 2t
02 = u2 - 2gs

Hence option (Its average speed is u) is correct.

Hence only option 3 has incorrect option.

JEE Main Practice Test- 6 - Question 15

Two blocks each of mass m,  lie on a smooth table. They are attached to two other masses as shown in figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces with respect to each other is

Detailed Solution for JEE Main Practice Test- 6 - Question 15

In a plane mirror the image moves twice as faster as mirror thus
acceleration of image in mirror AB = a → AB
acceleration of image in mirror CD= a → cd
acceleration of images w.r.t. each other is

JEE Main Practice Test- 6 - Question 16

An electron is in an excited state in a hydrogen like atom. It has a total energy of  -3.4 eV. The kinetic energy is E and its de Broglie wavelength is λλ. Then

Detailed Solution for JEE Main Practice Test- 6 - Question 16

So, K E = 3.14 ev
Let p = momentum and m = mass of the electron.

de Broglie wavelength,

On substituting the values, we get

JEE Main Practice Test- 6 - Question 17

Two cylindrical rods of uniform cross-sectional area A and 2A, having free electrons per unit volume 2n and n respectively are joined in series. A constant current I flows through them in steady state. The ratio of drift velocity of free electrons in the left rod to that of the right rod is (VL/VR) is:

Detailed Solution for JEE Main Practice Test- 6 - Question 17

Since current I = neAVd through both rods is same
2(n)e AV= ne (2A) VR
or  VL/V=1

JEE Main Practice Test- 6 - Question 18

Uncharged capacitor of capacitance 4 μF4 and a resistance of 2.5 M ΩM Ω are connected in series with 12 V battery at t=0. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given, ln (2) = 0.693]

Detailed Solution for JEE Main Practice Test- 6 - Question 18

Given : VC = 3VR = 3(V - VC)
Here: V is the applied potential.

⇒ t = 2 x 10 x 0.693 = 13.86 sec

JEE Main Practice Test- 6 - Question 19

A refrigerator is to maintain the eatables, kept inside it, at 9oC. The coefficient of performance of the refrigerator, if the room temperature is 36oC, is

Detailed Solution for JEE Main Practice Test- 6 - Question 19

Here, T1 = 36°C = 36 4 - 273 = 309 K
T2 = 9°C = 9 + 273 = 282 K
The coefficient of performance of a refrigerator is given by

JEE Main Practice Test- 6 - Question 20

A ball is projected up an incline of 30o with a velocity of 30 ms−1 at an angle of 30o with reference to the inclined plane from the bottom of the inclined plane. If g = 10 ms−2, then the range on the inclined plane is

Detailed Solution for JEE Main Practice Test- 6 - Question 20

*Answer can only contain numeric values
JEE Main Practice Test- 6 - Question 21

Three balls A, B and C whose masses are m, km and 4m respectively kept at rest on the horizontal smooth surface, as shown in the figure. The ball A is given velocity v0, rightward and it collides with the ball B elastically. Then ball B collides elastically third ball C. For what value of k, does the third ball C receive the maximum speed?

Detailed Solution for JEE Main Practice Test- 6 - Question 21

Solving elastic collisions we get

maximizing vc we get k=2

*Answer can only contain numeric values
JEE Main Practice Test- 6 - Question 22

ABCDECA is a planar body of mass m of uniform thickness and same material. The dimensions are as shown in the figure. The moment of inertia of the body about an axis passing through point A and perpendicular to planar body is 11 and that of about an axis passing through C and perpendicular to planer body is l2. If 11/12 is k. Find the l value of k.

Detailed Solution for JEE Main Practice Test- 6 - Question 22

Form a symmetric structure by completing squares as shown

using superposition and parallel axis theorem we can find l1 = 2ma2  Rotate the parts about to form a square as

*Answer can only contain numeric values
JEE Main Practice Test- 6 - Question 23

A body of mass 6.25 kg is travelling in a horizontal straight line with a velocity of 3 m/sec when a horizontal force P is applied to it at right angle to the initial direction of motion. If P varies according to the accompanying graph, remains constant in direction and is the only force acting on the body in its plane of motion, find the magnitude of the velocity of the body when t = 2 sec.

Detailed Solution for JEE Main Practice Test- 6 - Question 23

Momentum agained in direction of force = Area

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JEE Main Practice Test- 6 - Question 24

If a car is moving rightward with acceleration  rightward as shown in the figure. Find the value of k so that, rod maintains its orientation as shown in the figure. Neglect the friction and mass of the small rollers at A and B.

Detailed Solution for JEE Main Practice Test- 6 - Question 24

The rod will align effective gravity in frame of cart

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JEE Main Practice Test- 6 - Question 25

For identical rods, each of mass m are welded at their ends to form a square, and the corners are then welded to a light metal hoop of radius r. If the rigid assembly of rods and hoop is allowed to roll down the inclined rough surface. If the minimum value of the coefficient of static friction which will prevent slipping is k/10
Find the value of k.

Detailed Solution for JEE Main Practice Test- 6 - Question 25

JEE Main Practice Test- 6 - Question 26

If the nitrogen atom had electronic configuration 1s7, it would have energy lower than that of the normal ground state configuration 1s2 2s2p3, because the electrons would be closer to the nucleus, yet 1s7 is not observed because it violates

Detailed Solution for JEE Main Practice Test- 6 - Question 26

1sviolate Pauli exclusion principle, according to which an orbital cannot have more than two electrons.

JEE Main Practice Test- 6 - Question 27

Amongst the following, the most basic compound is

Detailed Solution for JEE Main Practice Test- 6 - Question 27

Lone pair is not involved in resonance, most basic. In all other cases, lone-pair of nitrogen is involved in resonance, less basic.

JEE Main Practice Test- 6 - Question 28

How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an octahedral complex with a Ca2+

Detailed Solution for JEE Main Practice Test- 6 - Question 28

EDTA, Which has four lone pair donor oxygen atoms and two lone pair donor nitrogen atoms in each molecule forms complex with Ca2+ ion. EDTA is hexa due to need 1 EDTA to form octahedral completes with ca+2

JEE Main Practice Test- 6 - Question 29

The first orbital of H is represented by  where a0 is Bohr's radius The probability of finding the electron at a distance r, from the nucleus in the region dV is

Detailed Solution for JEE Main Practice Test- 6 - Question 29

P(r) = ψ24πr2dr
4πr2dr  = dv = vol of thin spherical shell around nucleus at distance (r)

JEE Main Practice Test- 6 - Question 30

20% of N2O4 molecules are dissociated in a sample of gas at 27C and 760 torr. Mixture has the density at equilibrium equal to:

Detailed Solution for JEE Main Practice Test- 6 - Question 30

Total Moles 1 + α at equilibrium observed Molar Mass at equilibrium

JEE Main Practice Test- 6 - Question 31

Which of the following compounds display geometrical isomerism?

Detailed Solution for JEE Main Practice Test- 6 - Question 31

Apart from this option, the other compounds don’t show geometrical isomerism.

JEE Main Practice Test- 6 - Question 32

Nickel (Z = 28) combines with a uninegative mono dentate ligand X- to form a paramagnetic complex [NiX4]2-.The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively

Detailed Solution for JEE Main Practice Test- 6 - Question 32

Number of unpaired electrons = 2
Geometry = tetrahedral.

JEE Main Practice Test- 6 - Question 33

The correct stability order of the following resonance structures is?

Detailed Solution for JEE Main Practice Test- 6 - Question 33

No. of π π bonds ∝∝ Resonance Energy ∝∝ Stability

+ve charge on electro positive element

-ve charge on electro negative element

unlike charges on adjacent atoms like charges to separate out far.

(i) Two π π bonds unlike charges on adjacent atoms

(iii) Two π π  Bonds unlike charges on adjacent undesired atoms

(ii) One π π bond unlike charges separated but on desired atoms.

(iv) One π π bond unlike charges separated but on undesired atoms

(i) > (iii) > (ii) > (iv)

JEE Main Practice Test- 6 - Question 34

Identify Z in the sequence,

Detailed Solution for JEE Main Practice Test- 6 - Question 34

In presence of H2O2, HBr adds in anti-Markownikoffs way (peroxide effect).

JEE Main Practice Test- 6 - Question 35

The shape of XeF4 is :

Detailed Solution for JEE Main Practice Test- 6 - Question 35

Due to presence of two lone pairs of electrons, it is square planar in shape. Lone pairs are arranged at pyramidal position as per Bent's Rule.

JEE Main Practice Test- 6 - Question 36

(i)  Tensile strength of vulcanised rubber is almost ten times more than raw rubber.
(ii)  Elasticity of raw rubber is very high.
Choose the correct option.

Detailed Solution for JEE Main Practice Test- 6 - Question 36

Natural rubber is soft and sticky and after vulcanisation its strength increases due to cross linked formed between different

JEE Main Practice Test- 6 - Question 37

The correct order of reducing ability for the four successive elements Cr, Mn, Fe and Co is: Their Eored values are given below.

Detailed Solution for JEE Main Practice Test- 6 - Question 37

The values of Eored gives us an idea of the ease with which metals get reduced. A higher negative value implies that it has greater tendency to get oxidised.

For a metal to act as a reducing agent, it should itself get oxidised. Hence, the order of reducing ability is proportional to ease of oxidation which is inversly proportional to Eored
Mn > Cr > Fe > Co

JEE Main Practice Test- 6 - Question 38

An unknown alkyl halide (A) reacts with alcoholic KOH to produce a hydrocarbon (C4H8) as the major product. Ozonolysis of the hydrocarbon affords one mole of propanaldehyde and one mole of formaldehyde. Suggest which organic compound among the following has the correct structure of the above alkyl halide (A)?

Detailed Solution for JEE Main Practice Test- 6 - Question 38

Since the product on ozonolysis is propanaldehyde and formaldehyde, it implies that the the double bond is shared between C1 and C2.

If the compound were option 1, the result of such elimination would have been 2 butene whose ozonolysis would give ethanals

1- butene on ozonolysis gives propanaldehyde and formaldehyde thus the hydrocarbon is
CH3CH2CH = CH2
(C4H8) 1-butene
1 butene can be obtained by

JEE Main Practice Test- 6 - Question 39

Which one of the following reactions of Xenon compounds is not feasible?

Detailed Solution for JEE Main Practice Test- 6 - Question 39

The reaction XeO3+6HF⟶XeF6+3H2O is not feasible because XeFformed will further produce XeO3 by getting hydrolysed.
XeF6 + H2O → XeOF4 + 2HF
XeOF4 + H2O → XeO2F2 + 2HF
XeO2F+ H2O → XeO3 + 2HF

JEE Main Practice Test- 6 - Question 40

One mole of a non-ideal gas undergoes a change of state(2.0 atm, 3.0 L, 95 K) ⟶ (4.0 atm, 5.0 L, 245 K) with a change in internal energy, ΔE = 30.0 L-atm. The change in enthalpy (ΔH) of the process in L-atm

Detailed Solution for JEE Main Practice Test- 6 - Question 40

H = E+PVH
ΔH = ΔE+Δ(PV)
= ΔE+(P2V2−P1V1)
= 30.0+(4×5−2×3)
= 30.0+14.0
= 44 L atm.

JEE Main Practice Test- 6 - Question 41

How many moles of KMnO4 are needed to oxidise a mixture of 1 mole each of FeSO4, FeC2O4 and Fe2(C2O4)3 completely in acidic medium :

Detailed Solution for JEE Main Practice Test- 6 - Question 41

Equialents of {FeSO4 + Fe(C2O4) + Fe2 (C2O4)3}
= {1 x1 + 1 x 3 + 1 x 6} = 10 Equialents

Equialents of KMnO4 = 10 Equialents
Moles of KMnO4 = 10/5 = 2 Moles

JEE Main Practice Test- 6 - Question 42

The catalyst used in the manufacture of polyethylene by Ziegler method is

Detailed Solution for JEE Main Practice Test- 6 - Question 42

Ziegler - Natta catalyst is used in polymerisation of ethene : (C2H5)3 Al + TiCl4.

JEE Main Practice Test- 6 - Question 43

The reagent with which both acetaldehyde and acetone react easily is

Detailed Solution for JEE Main Practice Test- 6 - Question 43

Grignard’s reagent reacts with both aldehydes and ketones while other three reagents reacts only with aldehydes, not with ketones.

JEE Main Practice Test- 6 - Question 44

Which of the following facts about the complex [Cr(NH3)6]Cl3 is wrong?

Detailed Solution for JEE Main Practice Test- 6 - Question 44

The complex [Cr(NH3)6]Cl3 involves d2sp3 hybridization as it involves (n - 1)d orbitals for hybridization. It is an inner orbital complex.

JEE Main Practice Test- 6 - Question 45

Consider the reaction 2NO(g)+O2(g) ⟶ 2NO2(g) Predict whether the reaction is spontaneous at 298 K. ΔfG(NO) = 86.69kJ/mol,ΔfG(NO2) = 51.84kJ/mol

Detailed Solution for JEE Main Practice Test- 6 - Question 45

2NO(g)+O2(g) ⟶ 2NO2(g)
ΔG = 2ΔfG(NO2)−[2ΔfG(NO)+ΔfG(O2)]
= (2×51.84)−(2×86.69+0)
= 103.68−173.38
= −69.7kJ/mol ; Δ G is negative
So the reaction is spontaneous

*Answer can only contain numeric values
JEE Main Practice Test- 6 - Question 46

The pH range of a basic indicator (InOH, pKln.= 4) is 3.4 to 4.6. For what minimum ratio of  does the solution appear in the colour of In+

Detailed Solution for JEE Main Practice Test- 6 - Question 46

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JEE Main Practice Test- 6 - Question 47

x moles of phosgene gas is allowed to attain equilibrium with its gaseous decomposition products in a 1 litre vessel. For what value of x; half the chlorine atoms in the equilibrium mixture remain with phosgene. (KC for phosgene decomposition = 3)

Detailed Solution for JEE Main Practice Test- 6 - Question 47

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JEE Main Practice Test- 6 - Question 48

If the number of 109°28' angles in the structure of TMS (tetra methyl silane) is x, find x/6.

Detailed Solution for JEE Main Practice Test- 6 - Question 48

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JEE Main Practice Test- 6 - Question 49

How many moles of water vapour is evolved when 1 mole of hydrated aluminium chloride dimer (Al2Cl6.12H2O) is strongly heated.

Detailed Solution for JEE Main Practice Test- 6 - Question 49

*Answer can only contain numeric values
JEE Main Practice Test- 6 - Question 50

Calculate the energy required (in Joules) to convert all atoms of Mg to Mg2+ ions present in 48 mg of Mg vapours. IE1 and IE2 of Mg are 740 and 1450 kJ mol–1 respectively.

Detailed Solution for JEE Main Practice Test- 6 - Question 50

Mg(g) ➔ Mg+(g) + e–; IE1 = 740 kJ mol–1
Mg+(g) ➔ Mg2+(g) + e; IE2 = 1450 kJ mol–1
∴ Total energy required to convert 1 mol of Mg(g) into
Mg2+(g) ion = IE1 + IE2
= (740 + 1450) kJ mol–1
= 2190 kJ mol–1

= 2 × 10-3 mol
∴ Energy required to ionize 2 × 10-3 mol of Mg(g)
= 2190 × 2 × 10-3
= 4.380 kJ
= 4380 J

JEE Main Practice Test- 6 - Question 51

Detailed Solution for JEE Main Practice Test- 6 - Question 51

[Cancelling x as x ≠ 0]

Alternate Solution
Use L’Hospital Rule,

JEE Main Practice Test- 6 - Question 52

The equation of a circle C1 is x+ y− 4x − 2y − 11 = 0. A circle C2 of radius 1 unit rolls on the outside of the circle C1 touching it externally. The locus of the centre of C2 has the equation

Detailed Solution for JEE Main Practice Test- 6 - Question 52

The centre of C1 = (2,1) and the radius

JEE Main Practice Test- 6 - Question 53

Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (- 6, 1). The coordinates of its third vertex are-

Detailed Solution for JEE Main Practice Test- 6 - Question 53

Solving Eqs. (i) and (ii), we get
α = - 1 , β = 6
∴ Third vertex is (-1,6).

JEE Main Practice Test- 6 - Question 54

The equation of the common tangent to the equal parabolas y2 = 4ax and x2 = 4ay is

Detailed Solution for JEE Main Practice Test- 6 - Question 54

Any tangent to y2 = 4ax is  It touches x2 = 4ay if
has equal roots.
So m3 + 1 = 0, i e , m = -1 Hence, the common tangent is y = - x - a

JEE Main Practice Test- 6 - Question 55

A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:

Detailed Solution for JEE Main Practice Test- 6 - Question 55

Let α , β , γ be the angles, which the line makes with the positive directions of x-axis, y-axis and z-axis respectively

Hence the line makes an angle of 60° with the positive direction of z-axis

JEE Main Practice Test- 6 - Question 56

If ln(x + y) = 2xy, then y′ (0) is equal to

Detailed Solution for JEE Main Practice Test- 6 - Question 56

JEE Main Practice Test- 6 - Question 57

If the fourth term of is equal to 200 and x > 1, then x is equal to

Detailed Solution for JEE Main Practice Test- 6 - Question 57

∴  x = 10-4, 101

JEE Main Practice Test- 6 - Question 58

If the line 3x + 2y = 13 divides the area enclosed by the curve, 9x+ 4y− 18x − 16y − 11 = 0 into two parts then the ratio of the larger area to the smaller area is

Detailed Solution for JEE Main Practice Test- 6 - Question 58

E quation o f given curve is
It can be reduced to  which is the equation of ellipse having it’s principal axis parallel to coordinate axes
⇒  lt's area = πab = π (2) ( 3) = 6π
From the figure we can see that points of intersection of  and line 3x + 2y = 13, have x = 1, 3
⇒ Smaller area between ellipse and line

JEE Main Practice Test- 6 - Question 59

The third vertex of the triangle whose centroid is (7,−2, 5) and whose other two vertices are (2, 6, −4)  and (4,−2, 3)  is

Detailed Solution for JEE Main Practice Test- 6 - Question 59

Let A (2, 6, - 4) and B (4, - 2, 3) be the two given vertices of the triangle. Let C (α , β, γ) be the third vertex
Since G (7, - 2, 5) is the centroid of ΔABC,

Hence C (15, - 10,16) is the third vertex

JEE Main Practice Test- 6 - Question 60

The least positive integral value of m, if

Detailed Solution for JEE Main Practice Test- 6 - Question 60

⇒ m is a multiple of 4.
Hence the smallest positive value of m is 4.

JEE Main Practice Test- 6 - Question 61

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r is equal to

Detailed Solution for JEE Main Practice Test- 6 - Question 61

From figure it is clear that ΔPRQ and ΔRSP are similar

JEE Main Practice Test- 6 - Question 62

If a3 + b6 = 2, then the maximum value of the term independent of x in the expansion of (ax1/3 + bx-1/6)9 (a > 0, b > 0) is

Detailed Solution for JEE Main Practice Test- 6 - Question 62

Let (r + 1) th term be independent of x, then

As Tr + 1 is independent of x

JEE Main Practice Test- 6 - Question 63

The co-ordinates of the point which divides the line segment joining the points (5,4, 2) and (−1,−2, 4) in the ratio 2 : 3 externally is

Detailed Solution for JEE Main Practice Test- 6 - Question 63

Let A (5 , 4 , 2) and B (- 1, - 2, 4) be the given points.
Let P (x , y, z) be the point, which divides the line segment [AB] in the ratio - 2 : 3

JEE Main Practice Test- 6 - Question 64

The area of an expanding rectangle is increasing at the rate of 48 cm2/sec. The length of the rectangle is always equal to the square of the breadth. At the instant when the breadth is 4.5 cm, The length is increasing at the rate of

Detailed Solution for JEE Main Practice Test- 6 - Question 64

JEE Main Practice Test- 6 - Question 65

If nP= 1680 and nC= 70, then 69 n + r! is equal to

Detailed Solution for JEE Main Practice Test- 6 - Question 65

From equation (i) and (ii), we get

On putting the value of r in equation (i), we get

JEE Main Practice Test- 6 - Question 66

Consider the straight line ax + by = c, where a, b, c ∈ Rthis line meets the coordinate axes at A and B respectively. If the area of the ΔOAB, O being origin, is always a constant equal to half, then

Detailed Solution for JEE Main Practice Test- 6 - Question 66

Given line is ax + by = c

⇒ This line cut the coordinate axes as points

Equating this area to half, we get,
c2 = ab
Therefore, a, c, b are in GP

JEE Main Practice Test- 6 - Question 67

If for a ΔABC, cot A⋅cot B⋅cot C>0 then the triangle is

Detailed Solution for JEE Main Practice Test- 6 - Question 67

cot A⋅cot B⋅cot C>0⇒cot A>0, cot B>0, cot C > 0

Because two or more of cot A, cot B, cot C cannot be negative at the same time in a triangle, as no two angle could be more than 90 degree.

JEE Main Practice Test- 6 - Question 68

The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x+ y2 = 9 is

Detailed Solution for JEE Main Practice Test- 6 - Question 68

Any circle passing through the points of intersection of the given line and circle has the equation x2 + y2 - 9 + λ (x + y - 1) = 0. Its centre
The circle is the smallest if center

Putting this value for λ, the equation of the smallest circle is x2 + y2 - 9 - (x + y - 1) = 0
⇒ x2 + y2 - x - y - 8 = 0

JEE Main Practice Test- 6 - Question 69

Detailed Solution for JEE Main Practice Test- 6 - Question 69

So given integration

JEE Main Practice Test- 6 - Question 70

be two perpendicular unit vectors such that

Detailed Solution for JEE Main Practice Test- 6 - Question 70

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JEE Main Practice Test- 6 - Question 71

The probability of a bomb hitting a bridge is 1/2 and two direct hits are needed to destroy it. Find the least number of bombs required so that the probability of the bridge being destroyed is greater than 0.9.

Detailed Solution for JEE Main Practice Test- 6 - Question 71

Let n ne the number of bombs required and X the number of bombs that hit the bridge.
Then X follows a bionomial distribution with parameters n and p=1/2. Now

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JEE Main Practice Test- 6 - Question 72

If sin 3αα= 4 sin αα sin (x+ a) sin (x - αα), then 864 sin2 x+ 3620 cos2 x is equal to

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JEE Main Practice Test- 6 - Question 73

If  than 8190 cot S is equal to

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JEE Main Practice Test- 6 - Question 74

If  and f(1) = 2, then f(101) equals

Detailed Solution for JEE Main Practice Test- 6 - Question 74

we have
and f(1) = 2,
f(101) = f(1) + 100 x 1/2 = 2 + 50
f(101) = 52

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JEE Main Practice Test- 6 - Question 75

If points (0,0,9), (1,1,8), (1,0,7) and (2,2, λ) are coplanar, then λ =

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