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JEE Main Mock- 8


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75 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Main Mock- 8

JEE Main Mock- 8 for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The JEE Main Mock- 8 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Mock- 8 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Mock- 8 below.
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JEE Main Mock- 8 - Question 1

In the figure shown the acceleration of A is, , then the acceleration of B is : (A remains in contact with B)

Detailed Solution for JEE Main Mock- 8 - Question 1

From wedge constraint


JEE Main Mock- 8 - Question 2

The speed of sound in hydrogen gas at N.T.P. is 1,328 ms-1. What will be its value in air at N.T.P., if density of hydrogen is 1/16th that of air?

Detailed Solution for JEE Main Mock- 8 - Question 2


Let vair be the velocity of sound in air at N.T.P



JEE Main Mock- 8 - Question 3

A balloon that is initially flat, is inflated by filling it from a tank of compressed air. The final volume of the balloon is 5m3. The barometer reads 95 kPa. The work done in this process is

Detailed Solution for JEE Main Mock- 8 - Question 3

W = P Δ V⁡ = 95 × 103 × (5-0)
= 4.75 × 105 J

JEE Main Mock- 8 - Question 4

Two bodies of same mass tied with an inelastic string of length   together on a horizontal surface. One a horizontal surface of them is projected vertically upwards with velocity  ⁡Find the maximum height up to which the centre of mass of system of the two masses rises.

Detailed Solution for JEE Main Mock- 8 - Question 4


Velocity of B when string is just taut

After string in taut both will move up with same speed, 
By this time centre of mass in at 
Further rise in 

Hence maximum height 

JEE Main Mock- 8 - Question 5

The electric potential at a point (x, y, z) is given by V = -x2y - xz3 + 4 The electric field  at that point is

Detailed Solution for JEE Main Mock- 8 - Question 5

The electric potential at a point,

JEE Main Mock- 8 - Question 6

Binding energy per nucleon versus mass number curve for nuclei is shown in figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is

Detailed Solution for JEE Main Mock- 8 - Question 6

Energy is released in a process when total binding energy of the nucleus (= binding energy per nucleon x number of nucleons) is increased or we can say, when total binding energy of products is more than the reactants.
Binding energy of reactants = 120 x 7. 5 = 900 MeV
and binding energy of products = 2 (60 x 8. 5)
= 1020 MeV > 900 MeV.

JEE Main Mock- 8 - Question 7

A wire of length 1.0 m and radius 10-3 m is carrying a heavy current and is assumed to radiate as a black body. At equilibrium, its temperature is 900 K while that of the surroundings is 300 K. The resistivity of the material of the wire at 300 K is π2 × 10-8 ohm-m and its temperature coefficient of resistance is 7.8× 10−3 Co. Find the current in the wire. [Given Stefan's constant = 5.68 × 10-8 W/m2K4]

Detailed Solution for JEE Main Mock- 8 - Question 7

According to Stefan's law power radiated by a black body is given by.


Now if I is the current in the resistance R,

According to the given problem Equations (i) and (ii) represent the same. 

JEE Main Mock- 8 - Question 8

50 V battery is supplying a steady current of 10 amp when connected to an external resistor. If the efficiency of the battery at this current is 25%, then internal resistance of battery is:

Detailed Solution for JEE Main Mock- 8 - Question 8


JEE Main Mock- 8 - Question 9

A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it. A charge +Q is now given to its positive plate. Now, the potential difference across the capacitor is.

Detailed Solution for JEE Main Mock- 8 - Question 9

Initially

After charge Q is given

Charge distribution is

JEE Main Mock- 8 - Question 10

Energy from the sun falls on the earth at a rate of 1353 W/m2, which is known as solar constant, i.e., the power incident per unit area per second at the top of atmosphere. Find the r.m.s values of the electric and magnetic fields in the sunlight reaching the top of the atmosphere.

Detailed Solution for JEE Main Mock- 8 - Question 10

For an electromagnetic wave of sinusoidal form



The mean value of energy flux is intensity

[The mean value of cos2θ over on cycle is 1/2] 

Hence   

JEE Main Mock- 8 - Question 11

The size of the image of an object, which is at infinity, is formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image

Detailed Solution for JEE Main Mock- 8 - Question 11


Image formed by convex lens at ^ will act as a virtual object for concave lens. For concave lens

Magnification for concave lens 

As height of the image at h is 2 cm.
Therefore, height of image at I2 will be 2 x 1.25 = 2.5 cm

JEE Main Mock- 8 - Question 12

A network of Four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C, are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is

Detailed Solution for JEE Main Mock- 8 - Question 12



All the capacitors in upper branch are in series so the charge on each capacitor is 
Also charge on capacitor C4 is Q = 4CV

JEE Main Mock- 8 - Question 13

A rod AD, consisting of three segments AB, BC and CD joined together, is hanging vertically from a fixed support at A. The lengths of the segments are respectively 0.1 m, 0.2 m and 0.15 m. The cross - section of the rod is uniform 10-4 m2. A weight of 10 kg is hung from D. Calculate the displacements of point D if YAB = 2.5 x 1010 N/m2, YBC = 4 x 1010 N/m2 and YCD = 1 x 1010 N/m2. (Neglect the weight of the rod.)

Detailed Solution for JEE Main Mock- 8 - Question 13

By defination of Young's modulus,


JEE Main Mock- 8 - Question 14

A block of mass m & charge q is released on a long smooth inclined plane. Magnetic field B is constant, uniform, horizontal and out of the plane of paper as shown. Find the time from start when block loses contact with the surface.

Detailed Solution for JEE Main Mock- 8 - Question 14

Block will loose contact with surface when force due to magnetic field will become equal to mg cos θ

 (along the inclined plane)

JEE Main Mock- 8 - Question 15

A battery of internal resistance 4Ω is connected to the network of resistances as shown in figure. In order that the maximum power can be delivered to the network, the value of R in $$ should be

Detailed Solution for JEE Main Mock- 8 - Question 15

The given circuit is a balanced Wheatstone's bridge.

Thus, no current will flow across 6R of the side CD. The given circuit will now be equivalent to

 

For maximum power, net external resistance
= Total internal resistance
or 2R = 4
or R = 2Ω. 

JEE Main Mock- 8 - Question 16

In the circuit shown in diagram, the equivalent resistance between point A and B is

Detailed Solution for JEE Main Mock- 8 - Question 16

The circuit shown in diagram (1) can be redrawn as shown in diagram (2).

∴  RAB = 5R/8

JEE Main Mock- 8 - Question 17

Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when they are 300 m apart. Graphs given below show their velocities as a function of time as they slow down. The separation between the trains, when both have stopped, is:

Detailed Solution for JEE Main Mock- 8 - Question 17

Initial distance between trains is 300 m. Displacement of 1st train is calculated by area under V-t.


Displacement of train Which means it moves towards left.
∴ Distance between the two is = 300 - 280 = 20 m

JEE Main Mock- 8 - Question 18

A tuning fork sends out waves of wavelength 68.75 cm and 3 m in air and hydrogen gas respectively. If the velocity of sound in air is 330 ms-1, find the velocity of sound in hydrogen. Also, find the frequency of the tuning fork

Detailed Solution for JEE Main Mock- 8 - Question 18

In air : λa = 68.75 cm = 0.6875 m ; va = 330 ms-1 Let v be the frequency of the tuning fork. Then,

If vH is velocity of sound in hydrogen, then

JEE Main Mock- 8 - Question 19

A particle executes S.H.M. given by x = 0 · 24 cos (400 t - 0.5) in SI units. Find amplitude

Detailed Solution for JEE Main Mock- 8 - Question 19

Here, x = 0.24 cos (4001 - 0.5) ...(i)
The standard equation for S.H.M. is
 ... (ii)
Comparing the equations (i) and (ii),we have
r = 0.24 m

JEE Main Mock- 8 - Question 20

A lens (μ = 1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection from its surface at λ = 4800 Å. Find the minimum thickness of the film which will minimise the intensity of the reflected light. (Assume near normal incidence)

Detailed Solution for JEE Main Mock- 8 - Question 20


*Answer can only contain numeric values
JEE Main Mock- 8 - Question 21

A ray of light from a liquid (μ = √3) is incident on a system of two right angled prism of refractive indices √3 and √2 as shown in the figure. The light suffers zero net deviation when it emerges into air from surface CD. If the angle of incidence (in degrees) is 5n. Find n ?


Detailed Solution for JEE Main Mock- 8 - Question 21


Hence 5*9 = 45

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 22

A drop water of mass = 4.0 g is placed between two clean glass plates, the distance between the plates is 0.01cm. Find the force (103N) required to pull the plates away. Surface tension of water = 0.08 N/m and density of water is 1000 kg/m3


Detailed Solution for JEE Main Mock- 8 - Question 22

Let R be the radius of the circular layer of water. then πR2.d x r = m(l)
The pressure inside the water.

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 23

A car is accelerating horizontally with constant acceleration a=10m/s2. One end of a light string is attached to the roof of the ceiling and there is a small bob at other end of string. The bob is given an initial velocity such that it continues to move in uniform circular motion with respect to an observer inside the car. The bob moves such the maximum vertical separation between two points of its path is h=1m. The length of the string is  and acceleration due to gravity g=10m/s2. If the angular speed of the bob in rad/s is √x .find the value of x.


Detailed Solution for JEE Main Mock- 8 - Question 23

First we will drive a result for conical pendulum in stationary car. see figure

Now in acceleration car, with respect to an inside observer, there will be pseudo force acting on the particle opposite
to the acceleration of the car, and hence perpendicular to the weight. since a=g, the effective gravity will be
  inclined at an angle of 450 with the verticle axis.

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 24

Find the current (in A) through the battery after the switch S is closed if L/R = RC = 1 ms.


Detailed Solution for JEE Main Mock- 8 - Question 24

Since the battery is across the two branches in parallel the current through the RL branch is unaffected by the current of the RC branch

i.e there will be no transient current through the battery in this case

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 25

Assuming that the law of gravitation is of the form  and attractive. A body of mass m revolves in a circular path of radius r around a fixed body of mass M. Find on what power of r will the square of time period depend.


Detailed Solution for JEE Main Mock- 8 - Question 25

The  centrepetal  acceleration is due  to the gravitational force

JEE Main Mock- 8 - Question 26

Place the following alcohols in decreasing order of rate of dehydration with concentrated H2SO4 :
1. CH3CH2CH(OH)CH2CH2CH3
2. (CH3)2C(OH)CH2CH2CH3
3. (CH3)2C(OH)CH(CH3)2
4. CH3CH2CH(OH)CH(CH3)2
​5. CH3CH2CH2CH2CH2CH2OH

Detailed Solution for JEE Main Mock- 8 - Question 26

The alcohols (3) and (2) are both 3o, but alcohol (3) gives a more substituted alkene. Alcohol (4) and (1) are both 2o, but alcohol (4) can give a more substituted alkene and alcohol (5) is 1o. Rate of dehydration of alcohols with concentrated H2SO4 follows the order 3o > 2o > 1o.

JEE Main Mock- 8 - Question 27

1.2 g of a salt with its empirical formula KxHy(C2O4)z was dissolved in 50 mL of water and its 10 mL portion required 11 mL of a 0.1 M HCl solution to reach the equivalence point. In a separate titration, 15 mL of the stock solution required 20 mL 0.2475 M KOH to reach the equivalence point. Identify the correct option.

Detailed Solution for JEE Main Mock- 8 - Question 27





∴ y = 3x.

JEE Main Mock- 8 - Question 28

The structure of H2O2 is

Detailed Solution for JEE Main Mock- 8 - Question 28

In H2O2, the O - H groups are not in the same plane. So it has non - planar structure. If has a half - opened book structure in which the two O - H groups lie on the two pages of the book. The angle between two pages of the book is 94o and H - O - O bond angle is 97o.

JEE Main Mock- 8 - Question 29

In nitroprusside ion the iron and NO exist as Fe II and NOrather than Fe III and NO. These forms can be differentiated by

Detailed Solution for JEE Main Mock- 8 - Question 29

Fe II and Fe III will have different values of magnetic moment due to different number of unpaired electrons in their d-orbitals.

JEE Main Mock- 8 - Question 30

Among the following pair of oxides, which pair cannot be reduced by carbon to give the respective metals ?

Detailed Solution for JEE Main Mock- 8 - Question 30

Potassium and calcium are strong reductant, hence their oxides cannot be reduced by carbon.

JEE Main Mock- 8 - Question 31

Two liquids A and B are mixed. The partial vapour pressures of A and B in pure state are 100 and 200 mm respectively. If they are mixed in 1 : 4 mole ratio, assuming that mixture obeys Raoult's law, the mole fractions of A and B present in gaseous state in equilibrium of above solution are :

Detailed Solution for JEE Main Mock- 8 - Question 31


JEE Main Mock- 8 - Question 32

Identify the final product (Z) in the following sequence of reactions :

Detailed Solution for JEE Main Mock- 8 - Question 32


JEE Main Mock- 8 - Question 33

In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is

Detailed Solution for JEE Main Mock- 8 - Question 33

In FCC  arrangement
after removal of atom from face centre.
No. of A atoms per unit cell = 1/8 × 8 = 1
No. of B atoms per uni cell = = 1/2 ×5= 5/2
so formula  is  A2B5

JEE Main Mock- 8 - Question 34

The standard e.m.f. of a cell, involving one electron change is found to be 0.591 V at 25. The equilibrium constant of the reaction is-
(F = 96500 C mol-1 ,R = 8.314 JK-1 mol-1

Detailed Solution for JEE Main Mock- 8 - Question 34

∆G° = ∆G + RT lnQ
-nFE° = -nFE + RT lnQ
ECell = E°Cell - RT/nF lnQ
At equilibrium, E = 0
0 = 0.591 - (0.0591/1)× logKC
-0.591 = -0.0591 logKC
log KC = 0.591/0.0591 = 10
KC = antilog 10 = 1×1010

JEE Main Mock- 8 - Question 35

For the indicator HIn the ratio [In-]/[HIn] is 7.0 at pH of 4.3. Keq for the indicator is [Given log 7 = 0.845 and Antilogo (0.545) = 3.5

Detailed Solution for JEE Main Mock- 8 - Question 35


JEE Main Mock- 8 - Question 36

Match the hybrid bond orbitals  of list I with the species of the list II and pick out the correct ?

Detailed Solution for JEE Main Mock- 8 - Question 36

JEE Main Mock- 8 - Question 37

The electrochemical cell shown below is a concentration cell. 
M|M2+ (saturated solution of a sparingly soluble salt, MX2) ||M2+ (0.001 mol dm3) | M
The emf of the cell depends on the difference in concentrations of M2+ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.
The value of Δ G (kJ mol-1) for the given cell is (Take 1 F = 96500 C mol-1)

Detailed Solution for JEE Main Mock- 8 - Question 37



JEE Main Mock- 8 - Question 38

First and second ionization energies of Magnesium are 7.646 and 15.035 eV respectively. The amount of energy in KJ needed to convert all the atoms of Magnesium into Mg2+ ions present in 12 mg of Magnesium vapours is :
[Given : 1 eV = 96.5 kJ mol-1]

Detailed Solution for JEE Main Mock- 8 - Question 38

JEE Main Mock- 8 - Question 39

The enthalpy change of the reaction is -57.3 kJ mol-1. If the enthalpies of Formation of  are zero and -285.84 kJ mol-1 respectively, then the enthalpy of formation of 

Detailed Solution for JEE Main Mock- 8 - Question 39

JEE Main Mock- 8 - Question 40

Amongst the halides
(1) BCl3
(2) AlCl3
(3) GaCl3 
(4) InCl3
The order of decreasing Lewis acid character is

Detailed Solution for JEE Main Mock- 8 - Question 40

Lewis acid strength of group 13 halides follow the order : BCl3 > AlCl3 > GaCl3 > InCl3.
As we move down the group, the size of atom increases, and as a result, the tendency to attract electrons decreases. This leads to a decrease in Lewis acid nature down the group 

JEE Main Mock- 8 - Question 41

A cationic colloidal electrolyte forms micelle at 10-4 M concentration in water. If 1 mm3 solution contains 1012 micelle structure, then the no. of cations involved in one micelle are NA = 6 × 1023.

Detailed Solution for JEE Main Mock- 8 - Question 41

No. of particles of cationic colloidal electrolyte/litre before micelle formation = 10-4 × 6 × 1023 = 6 × 1019
∴  No. of particles of cationic colloidal electrolyte/mm3 = 6 × 1019 ​× 10-6 = 6  × 1013
Number of micelles formed = 1012 /mm3
∴ Number of cations in one micelle = 6 × 1013/1012 = 60

JEE Main Mock- 8 - Question 42

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be

Detailed Solution for JEE Main Mock- 8 - Question 42

JEE Main Mock- 8 - Question 43


Which of the above compounds are enantiomers?

Detailed Solution for JEE Main Mock- 8 - Question 43

(i),(ii),(iv) have plane of symmetry, so they'll be meso compound. So its mirror image is identical.

Non-Mirror image to each other so III and V are enantiomers.

JEE Main Mock- 8 - Question 44

Give the IUPAC name of :

Detailed Solution for JEE Main Mock- 8 - Question 44

JEE Main Mock- 8 - Question 45

When H2O2 is added to ice cold solution of acidified potassium dichromate in ether and the contents are shaken and allowed to stand

Detailed Solution for JEE Main Mock- 8 - Question 45

When H2O2 is added acidified potassium dichromate in ether solution, potassium dichromate is oxidised to blue peroxide of chromium (CrO5) which is soluble in ether and produces blue coloured solution.
K2Cr2O7 + H2SO4 + 4H2O2 2CrO5 + K2SO4 + 5H2O

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 46

Identify the compounds in given set which can form enol.


Detailed Solution for JEE Main Mock- 8 - Question 46

Only 3, 4, 5, 7 and 10 can form enol.

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 47

A reaction takes place at 300K. When catalyst is added, rate of reaction increases. How much temperature should be increased (in C) which can create same affect as produced by catalyst. (Experimentally it is known that catalyst change the activation energy by20%).


Detailed Solution for JEE Main Mock- 8 - Question 47

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 48

The vapour pressure of a certain liquid is given by the equation  Where P is vapour pressure in mmHg and T is temperature in K. Calculate latent heat of vaporisation (in cal mol−1) at 75 .

K(R=2calmol−1K−1)


Detailed Solution for JEE Main Mock- 8 - Question 48

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 49

How many of total isomers are possible for the complex [Co(NH3)4(NO2)2]NO3?


Detailed Solution for JEE Main Mock- 8 - Question 49

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 50

How many atoms will have positive charge due to delocalization in given structure. Give answer including carbon on which charge is shown.


JEE Main Mock- 8 - Question 51

If the area bounded by  y = ax2 and x = ay2,  a > 0, is 1, then a is equal to

Detailed Solution for JEE Main Mock- 8 - Question 51


solving simultaneously 

∴ (0,0) and  are the points of intersection
∴ area between the given curves

JEE Main Mock- 8 - Question 52

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel, is :

Detailed Solution for JEE Main Mock- 8 - Question 52

Out of 11 letters in the word PROBABILITYO,A,I and I are the vowels.
So probability that the letter selected is a vowel, is 4/11

JEE Main Mock- 8 - Question 53

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.

Detailed Solution for JEE Main Mock- 8 - Question 53

Let the events be :
A : Number on the card drawn is even.
B : Number on the card is more than 3.
We are to find P(A/B).
We have : S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8,10}
and B = {4, 5, 6, 7, 8, 9, 10}

JEE Main Mock- 8 - Question 54

Detailed Solution for JEE Main Mock- 8 - Question 54


JEE Main Mock- 8 - Question 55

Detailed Solution for JEE Main Mock- 8 - Question 55


JEE Main Mock- 8 - Question 56

A point R with x-co-ordinate 4 lies on the line segment joining the points  P (2, - 3, 4) and Q (8, 0,10). Find the co-ordinates of the point R.

Detailed Solution for JEE Main Mock- 8 - Question 56



JEE Main Mock- 8 - Question 57

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are

Detailed Solution for JEE Main Mock- 8 - Question 57


Let the coordinates of A be (a. 0). Then the slope of the reflected ray is

Then the slope of the incident ray

From Eqs. (i) and (ii),

Thus, the coordinate of A is 

JEE Main Mock- 8 - Question 58

The points A, B and C represent the complex numbers z1, z2, (1−i)z1+iz2 (where ) respectively on the complex plane. The triangle ABC is :

Detailed Solution for JEE Main Mock- 8 - Question 58






Hence the triangle is isosceles and right angled.

JEE Main Mock- 8 - Question 59

In the expansion of  the term containing same powers of a and b is -

Detailed Solution for JEE Main Mock- 8 - Question 59




∴ 13th term contains same power of a & b.

JEE Main Mock- 8 - Question 60

All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is

Detailed Solution for JEE Main Mock- 8 - Question 60


So the required probability that are comes in 4th draw

JEE Main Mock- 8 - Question 61

Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven coupons are selected at random one at a time with replacement. The  probability that the largest number appearing on a selected coupons is at most 9, is :

Detailed Solution for JEE Main Mock- 8 - Question 61

Total coupons  = 15
1 <  selected coupon number < 9
i.e., 1, 2, 3, 4, 5, 6,, 7, 8, 9

∴ Probability of one selected coupon to have number 
Hence, the required probability
= (3/5) x (3/5) x ....... 7 times = (3/5)7   (Using multiplicative principle for independent events)

JEE Main Mock- 8 - Question 62

Find the value(s) of the parameter 'a'(a>0) for each of which the area of the figure bounded by the straight line,  the parabola  is the greatest

Detailed Solution for JEE Main Mock- 8 - Question 62


point of intersection of (i) and (ii)


f(a) is max is when

JEE Main Mock- 8 - Question 63

Detailed Solution for JEE Main Mock- 8 - Question 63



JEE Main Mock- 8 - Question 64

The parameter on which the value of the determinant


does not depend upon, is

Detailed Solution for JEE Main Mock- 8 - Question 64





⇒ Δ = (1 + a2 - 2a cos dx) [sin (p + d)x cos px - sin px cos (p + d) x] 
⇒ Δ = (1 + a2 - 2a cos dx) sin dx
Which is independent of p.

JEE Main Mock- 8 - Question 65

If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)n may have the greatest coefficient also is

Detailed Solution for JEE Main Mock- 8 - Question 65


⇒  
and 


⇒ 
Hence, 

JEE Main Mock- 8 - Question 66

The equation of the common tangent to the curves y⁡2 = 8 x and xy ⁡= -1 is

Detailed Solution for JEE Main Mock- 8 - Question 66

Tangent to the curve y2 = 8x is 
So, it must satisfy xy = - 1. 
⇒ 
⇒ 
Since, it has equal roots.
∴  D = 0
Hence, equation of common tangent is y = x + 2

JEE Main Mock- 8 - Question 67

If ABC be a triangle with  and AB = x such that (AB) (AC) = 1. If x varies, then the longest possible length of the angle bisector AD is 

Detailed Solution for JEE Main Mock- 8 - Question 67



⇒ ymax = 1/2 since the minimum value of the denominator is 2 if x > 0.

JEE Main Mock- 8 - Question 68

The locus of the midpoint of the portion of the line x cos α + y sin α = p intercepted between the axes is

Detailed Solution for JEE Main Mock- 8 - Question 68


If M(h, k) is the mid-point then 



Hence the requried locus is 

JEE Main Mock- 8 - Question 69

Find the derivative with respect to x of the function :

Detailed Solution for JEE Main Mock- 8 - Question 69




JEE Main Mock- 8 - Question 70

A lady wants to select one cotton saree and one polyester saree from a textile shop. If there are 10 cotton varieties and 12 polyester varieties, in how many ways can she choose the two sarees ?

Detailed Solution for JEE Main Mock- 8 - Question 70

There are 10 cotton sarees. The lady can select the cotton saree in 10 different ways. Corresponding to each of the above 10 different ways, she can select the polyester saree in 12 different ways because there are 12 polyester sarees.. Hence the no. of different ways of selecting the two sarees 
= 10 × 12 = 120

*Multiple options can be correct
JEE Main Mock- 8 - Question 71

Two lines   and  are coplanar. then find the value of  α

Detailed Solution for JEE Main Mock- 8 - Question 71

Direction ratios of L1 are (0, α – 3, 2) and it passes through the point (5, 0, 0) and direction ratios of L2 are (0, 1, α – 2) and it passes through the point (α, 0, 0) If L1 & L2 are coplanar then


so α = 1,4,5

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 72

A man will take 3 steps forward or 3 steps backward he will fall in the well. Given the probability of steps forward is 1/2 and steps backward is 1/2. If probability that he fells in well in the 5th steps is p/2q when p and q are co-prime, then find the value of q+p.


Detailed Solution for JEE Main Mock- 8 - Question 72

FFBFF X 3 + BBFBB X 3

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 73

The sum of the areas of n squares in n2. If the areas of the squares can be put in A.P. What is the length of the side of the 25th square?


Detailed Solution for JEE Main Mock- 8 - Question 73

*Answer can only contain numeric values
JEE Main Mock- 8 - Question 74

If   where p and q are co-prime, then find the value of p+q.


*Answer can only contain numeric values
JEE Main Mock- 8 - Question 75

 

If A is a square matrix of order n such that   then find the possible value of n.


Detailed Solution for JEE Main Mock- 8 - Question 75

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