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JEE Main Mock- 7


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75 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Main Mock- 7

JEE Main Mock- 7 for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The JEE Main Mock- 7 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Mock- 7 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Mock- 7 below.
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JEE Main Mock- 7 - Question 1

Work done by the system in closed path ABCA, as shown in figure is

Detailed Solution for JEE Main Mock- 7 - Question 1

Work done = area of ΔABC

JEE Main Mock- 7 - Question 2

A body executes S.H.M. of period 20 seconds. Its velocity is 5 cm s-1, 2 seconds after it has passed the mean position. Find amplitude of the bob

Detailed Solution for JEE Main Mock- 7 - Question 2

JEE Main Mock- 7 - Question 3

Calculate the gas constant for 1g of a gas from the following data: cp = 0.245calg-1oC-1;cv = 0.165calg-1°C-1

Detailed Solution for JEE Main Mock- 7 - Question 3


JEE Main Mock- 7 - Question 4

A balloon is moving upwards with a speed of 20 m/s. When it is at a height of 14 m from ground in front of a plane mirror in as shown in figure, a boy drops himself from the balloon. Find the time duration for which he will see the image of source S placed symmetrically before plane mirror during free fall.

Detailed Solution for JEE Main Mock- 7 - Question 4




FC = 2 + 10 = 12 m

The boy has dropped himself at point F. So, his velocity is 20 m/s in upward direction.
Let us first find the time to move from F to topmost point and then from topmost point to point C. From

Solving this equation we get, t1 = 4.53 s.
Velocity of boy at point Q,
 (v2 = u2 - 2gh)
Time taken to move the boy from Q to topmost point and then from topmost point to Q will be. 

∴Time required time is : t = t1 - t2 = 1.7 s

JEE Main Mock- 7 - Question 5

Prism angle & refractive index for a prism are 60o & 1.414. Angle of minimum deviation will be

Detailed Solution for JEE Main Mock- 7 - Question 5

JEE Main Mock- 7 - Question 6

If a gas is heated at constant pressure then what percentage of total heat supplied is used for doing work ? (Given : γ for gas = 4/3)

Detailed Solution for JEE Main Mock- 7 - Question 6

Heat supplied dQ = nCpdT
Heat used for work = dw = nRdT

= 25%
Thermodynamics Process
The process of change of state of a system involves change of thermodynamic variables such as pressure P, volume V and temperature T of the system. This process is known as thermodynamic process

JEE Main Mock- 7 - Question 7

Four persons K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed  v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four persons will meet at a time .....

Detailed Solution for JEE Main Mock- 7 - Question 7

The velocity of K throughout the motion towards the centre of the square is  v cos45  and the displacement covered by this velocity will be KO.

JEE Main Mock- 7 - Question 8

Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is 29.0 × 10-3 kg

Detailed Solution for JEE Main Mock- 7 - Question 8

At N.T.P., P = 1.013 x 105 N m-2
volume of air, V = 22400 cm3 = 2.24 x 10-2 m3
mass of 1 mole of air M = 29.0 x 10-3 kg Therefore, density of air at N.T.P.,

JEE Main Mock- 7 - Question 9

A pendulum bob is suspended on a flat car that moves with velocity v0. The flat car is stopped by a bumper
(i) What is the angle through which the pendulum swings.
(ii) If the swing angle is θ = 60° and l = 10m, what was the initial speed of the flat car?

Detailed Solution for JEE Main Mock- 7 - Question 9

When the flat car collides with the bumper, due to inertia of motion the bob swings forward No work is done by tension of string on the bob therefore energy is conserved

JEE Main Mock- 7 - Question 10

Two slits, 4 mm apart, are illuminated by light of wavelength 6000Å. What will be the fringe width on a screen placed 2 m from the slits?

Detailed Solution for JEE Main Mock- 7 - Question 10

JEE Main Mock- 7 - Question 11

A car moves uniformly along a horizontal sine curve y = a sin (x/α), where a and α are certain constants. The coefficient of friction between the wheels and the road is equal to k. At what velocity will the car ride without sliding?

Detailed Solution for JEE Main Mock- 7 - Question 11

Step I : Determine the radius of curvature of given curve at point P (x, y)

∴ radius of curvature is 

Step II : Relate the fnction and centnpetal acceleration In this case, centripetal acceleration is provided by force of fnction

From equation (i), for minimum value of radius of curvature,

JEE Main Mock- 7 - Question 12

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to h/2 and from h/2 to zero is

Detailed Solution for JEE Main Mock- 7 - Question 12

Time taken for the level to fall from H to H'

According to problem the time taken for the level to fall from h to h/2

and similarly time taken for the level to fall from h/2

JEE Main Mock- 7 - Question 13

A bullet of mass 2 g is having a charge of 2μC. The potential difference it must be accelerated through, starting from rest, to acquire a speed of 10 m/s is

Detailed Solution for JEE Main Mock- 7 - Question 13

JEE Main Mock- 7 - Question 14

A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time . The value of N is

Detailed Solution for JEE Main Mock- 7 - Question 14

In the first case

When length of the wire is doubled, resistance and mass both are doubled. Therefore, in the second case,

Dividing Eq.(ii) by (i) we get

JEE Main Mock- 7 - Question 15

The intensity of the light coming from one of the slits in YDSE is double the intensity from the other slit. Find the ratio of maximum intensity to minimum intensity in the interference fringe pattern observed.

Detailed Solution for JEE Main Mock- 7 - Question 15


JEE Main Mock- 7 - Question 16

Consider α-particles, β-particles and γ- rays each having an energy of 0.5 MeV. In increasing order of penetrating powers, the radiations are

Detailed Solution for JEE Main Mock- 7 - Question 16

Penetrating power is maximum for γ - rays, then of β -particles and then α - particles because basically it depends on the velocity. However, ionization power is in reverse order.

JEE Main Mock- 7 - Question 17

A battery is supplying power to a tape-recorder by cable of resistance of 0.02 Ω . If the battery is generating 50 W power at 5V, then power received by tape-recorder is :

Detailed Solution for JEE Main Mock- 7 - Question 17

P = VI,
50 = 5 × I
I = 10 A
Power lost in cable= I2R = 10 × 10 × 0·02 = 2W
Power supplied to T. R= 50  W - 2  W   = 48 W 

JEE Main Mock- 7 - Question 18

A uniform rod of mass m and length ℓ is rotating with constant angular velocity ω about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its Young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :

Detailed Solution for JEE Main Mock- 7 - Question 18


⇒ 

∴ Tension at mid point is :
 

JEE Main Mock- 7 - Question 19

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be ;

Detailed Solution for JEE Main Mock- 7 - Question 19

JEE Main Mock- 7 - Question 20

Two masses m1 and m2 are connected by a string of length l. They are held in a horizontal plane at a height H above two heavy plates A and B made of different material placed on the floor. Initially distance between two masses is a < l. When the masses are released under gravity they make collision with A and B co - efficient of restitution 0.8 and 0.4 respectively. The time after the collision when the string becomes tight is

Detailed Solution for JEE Main Mock- 7 - Question 20

String will become tight when


∴ 

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JEE Main Mock- 7 - Question 21

The difference between (n + 2)th Bohr radius and nth Bohr radius is equal to the (n – 2)th Bohr radius. The value of n is ?


Detailed Solution for JEE Main Mock- 7 - Question 21

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JEE Main Mock- 7 - Question 22

The figure shows an RC circuit with a parallel plate capacitor. Before switching on the circuit, plate A of the capacitor has a charge –Q0 while plate B has no net charge. Now, at t = 0, the circuit is switched on. How much time (in second) will elapse before the net charge on plate A becomes zero.

 

(GivenC=1μF, Q0=1mC, ε=1000V and 


Detailed Solution for JEE Main Mock- 7 - Question 22

Let at any time t charge flown through the plate B to plate A is Q and instantaneous current is I

Now for charge on plate A to zero q = Q0

Putting value of C1 ,Q0 ,∈ and R , we get t = 2 seconds

*Answer can only contain numeric values
JEE Main Mock- 7 - Question 23

A thin non conducting disc of mass M = 2kg, charge Q = 2x10–2 C and radius R = 1/6m is placed on a frictionless horizontal plane with its centre at the origin of the coordinate system. A non uniform, radial magnetic field  exists in space, where B0 = 10T and  is a unit vector in the radially outward direction. The disc is set in motion with an angular velocity w = x*102 rad/sec, about an axis passing through its centre and perpendicular to its plane, as shown in the figure. At what value of x, the disc will lift off from the surface.


Detailed Solution for JEE Main Mock- 7 - Question 23

The force an any small part of the disc is in the vertically upward direction

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JEE Main Mock- 7 - Question 24

All springs, string and pulley shown in figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of block m is  calculate x


Detailed Solution for JEE Main Mock- 7 - Question 24

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JEE Main Mock- 7 - Question 25

In Young’s Double slit experiment, a thin glass mica strip of thickness (t = 8λ) is pasted infront of slit S1. If the same strip is now shifted in front of other slit S2. If the number of fringes which will cross the central point on the screen is N. Find N? (d >> D, λ << d and nmica = 1.5)


Detailed Solution for JEE Main Mock- 7 - Question 25

(μ - 1)t = nλ
n = number of fringes  shifted
(1.5 - 1)8λ = nλ
n = 4
If the number of fringes which will cross the central point on the screen is  N
N, then 
N = 2 n = 8
Hence the total number of fringes shifted is 
8

JEE Main Mock- 7 - Question 26

A saturated aqueous solution of sparingly soluble salt AB3 has the vapour pressure 0.08 mm lesser than the vapour pressure 17.33 mm of solvent at 25oC. The solubility product of AB3 is :

Detailed Solution for JEE Main Mock- 7 - Question 26


JEE Main Mock- 7 - Question 27

Photoelectric emission is observed from a surface for frequencies v1 and v2 of the incident radiation (v1 > v2). If the maximum kinetic energies of the photoelectrons in the two cases are in the ration l : k then the threshold frequency v0 is given by :

Detailed Solution for JEE Main Mock- 7 - Question 27

JEE Main Mock- 7 - Question 28

In the following electron dot structure calculate the formal charge from left to right nitrogen atom ?

Detailed Solution for JEE Main Mock- 7 - Question 28

1.Left N
⇒ 5 - 4 - 1/2 (4) = - 1
2.Central N
⇒ 5 - 0 - 1/2 (8) = + 1
3.Right N
⇒ 5 - 4 - 1/2 (4) = - 1

JEE Main Mock- 7 - Question 29

A 50 litre vessel is equally divided into three parts with the help of two stationary semi permeable membrane (SPM). The vessel contains 60 g H2 gas in the left chamber, 160 g O2 in the middle and 140 g N2 in the right one. The left SPM allows transfer of only H2 gas while the right one allows the transfer of both H2 and N2. The final ratio of pressure in the three chambers.

Detailed Solution for JEE Main Mock- 7 - Question 29


JEE Main Mock- 7 - Question 30

Acetamide is treated separately with the following reagents. Which of these would give methylamine ?

Detailed Solution for JEE Main Mock- 7 - Question 30

JEE Main Mock- 7 - Question 31

 White fumes. Metal (M) can be

Detailed Solution for JEE Main Mock- 7 - Question 31

Li, Mg and Al when burn in air produces nitrides whose hydrolysis will liberate NH3. NH3 gives white fumes with HCl.

JEE Main Mock- 7 - Question 32

Copper ore is heated in a blast furnace after mixing with silica. Iron oxide slags off as iron silicate and copper is produced in the form of

Detailed Solution for JEE Main Mock- 7 - Question 32

During smelting, the roasted ore is mixed with coke and silica in a small blast furnace. The changes occurring are

Most of
FeS is oxidised to ferrous oxide

FeO removed as slag
 (slag) at the lowest point of furnace, motion mass is Cu2S plus little FeS.

JEE Main Mock- 7 - Question 33

The ionization isomer of [Cr(H2O)4Cl(NO2 )]Cl is

Detailed Solution for JEE Main Mock- 7 - Question 33

Ionisation isomers are the complexes that produce different ions in solution, i.e, they have ions interchanged inside and outside the coordination sphere.
Cr(H2O)4CI(NO2)]Cl and [Cr(H2O)4Cl2](NO2) have different ions outside the coordination sphere and they are isomers. Therefore, they are ionisation isomers.

JEE Main Mock- 7 - Question 34

What is the pH of 0.01 M glycine solution ? For glycine 

Detailed Solution for JEE Main Mock- 7 - Question 34

For glycine H2N - CH2 - COOH which can act as zwitter ion


JEE Main Mock- 7 - Question 35

Which one of the following cannot be prepared from B2H6 ?

Detailed Solution for JEE Main Mock- 7 - Question 35

In diborane (B2H6) molecule, only four terminal hydrogen atoms are replaceable. The two bridge H - atoms can not be substituted. Hence B2(CH3)6 cannot be prepared from B2H6.

JEE Main Mock- 7 - Question 36

Titration of I2 produced from 0.1045 g of primary standard KIO3 required 30.72 mL of sodium thiosulphate as shown below :


The molarity of sodium thiosulphate ion is :

Detailed Solution for JEE Main Mock- 7 - Question 36



JEE Main Mock- 7 - Question 37

The standard reduction potentials of Cu2+ / Cu and Cu2+ / Cu+ are 0.337 V and 0.153 V respectively. The standard electrode potential of Cu+ / Cu half cell is

Detailed Solution for JEE Main Mock- 7 - Question 37



JEE Main Mock- 7 - Question 38

The electron energy in hydrogen atom is given by  Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength (in cm) of light that can be used to cause this transition?

Detailed Solution for JEE Main Mock- 7 - Question 38

The required transition is n1 = 2to n2 = ∞ and corresponding transition energy is 1erg = 10-7 joule

As the electron is to be ejected from the atom, the final state will have 0 energy as n2 tends to infinity Hence, the amount of energy required for t

1 erg = 10-7 joule
The longest wavelength that can cause above transition can be determined as 

JEE Main Mock- 7 - Question 39

An element has fcc structure with edge length 200 pm, calculate the density if 200g of this element contains 24 × 1023 atoms. (N=  6 × 1023​)

Detailed Solution for JEE Main Mock- 7 - Question 39

JEE Main Mock- 7 - Question 40

A compound that gives a positive iodoform test is

Detailed Solution for JEE Main Mock- 7 - Question 40


JEE Main Mock- 7 - Question 41

1.44 g of Titanium (Ti) reacted with an excess of O2 and produced x gm of a non-stoichiometric compound Ti1.44O1. The value of x is :

Detailed Solution for JEE Main Mock- 7 - Question 41


JEE Main Mock- 7 - Question 42

A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

Detailed Solution for JEE Main Mock- 7 - Question 42



JEE Main Mock- 7 - Question 43

One desires to prepare a positively charged solution of silver iodide. This can be achieved by

Detailed Solution for JEE Main Mock- 7 - Question 43

KI + AgNO3 → AgI + KNO3
AgNO3 → Ag+ + NO3
AgI(s) + Ag+ → [AgI] + Ag+.

JEE Main Mock- 7 - Question 44

Anhydrous AlCl3. How will it behave in Aqueous solution?

Detailed Solution for JEE Main Mock- 7 - Question 44



It will behave ionic.

JEE Main Mock- 7 - Question 45

The ionisation energy of solid NaCl is 180 kcal per mol.The dissolution of the solid in water in the form of ions is endothermic to the extent of 1 kcal per mol. If the solvation energies of Na+ and Cl- ions are in the ratio 6 : 5, what is the enthalpy of hydration of sodium ion ?

Detailed Solution for JEE Main Mock- 7 - Question 45


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JEE Main Mock- 7 - Question 46

In gas phase what is the maximum number of coplanar atoms in X.


Detailed Solution for JEE Main Mock- 7 - Question 46

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JEE Main Mock- 7 - Question 47

A 200 ml aqueous solution of KCl was electrolysed for 16 min and 5 sec. If the pH of the final solution was 13 and volume of solution remains practically unchanged, then the average current used in ampere is.


Detailed Solution for JEE Main Mock- 7 - Question 47

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JEE Main Mock- 7 - Question 48

Reaction of hydrated ferric chloride (FeCl3. 6H2O) with thionyl chloride gives anhydrous ferric chloride with evolution of hydrochloric acid (HCl) and sulphur dioxide (SO2) gases. The number of sulphur dioxide (SO2) molecules involved in the balanced chemical equation is.


Detailed Solution for JEE Main Mock- 7 - Question 48

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JEE Main Mock- 7 - Question 49

A complex compound is represented as CoCl3. xNH3. Its 0.1 M solution in water shows depression in freezing point equal to 0.0558K. Assuming 100% ionisation of complex and coordination number of Co to be six, calculate the value of x. Kf for H2O is 1.86 K kgmol–1.


Detailed Solution for JEE Main Mock- 7 - Question 49

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JEE Main Mock- 7 - Question 50

How many stereoisomers of Pt(gly)2Cl2 are possible?


Detailed Solution for JEE Main Mock- 7 - Question 50

JEE Main Mock- 7 - Question 51

Detailed Solution for JEE Main Mock- 7 - Question 51



JEE Main Mock- 7 - Question 52

ABC is an acute - angled triangle with circumcentre 'O' and orthocentre H. If AO = AH, then angle A is

Detailed Solution for JEE Main Mock- 7 - Question 52

As we know in triangle, the distance of the ortho-centre from vertex A is 2R cos A
In the question it is given distance of the circum-centre and ortho-centre from the vertex A is equal.

JEE Main Mock- 7 - Question 53

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Detailed Solution for JEE Main Mock- 7 - Question 53

Let p (h, k) be the mid point of the line segment joining the focus (a, 0) and a general point Q (x, y) on the parabola. Then

Put these values of x and y in y2 = 4ax, we get

JEE Main Mock- 7 - Question 54

The eccentricity of the ellipse which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lie along the axes of coordinates, is :

Detailed Solution for JEE Main Mock- 7 - Question 54


Let ellipse be 
∵ Ellipse meets the straight line  on the axis of x.

and meets the straight line  on the axis of y,

i.e., -b = -5
⇒ b = 5
∴ b2 = a2 (1 - e2)
⇒ 
∴ 
∴ 

JEE Main Mock- 7 - Question 55

A circle is described whose centre is the vertex and whose diameter is three-quarters of the latus rectum of a parabola y2 = 4ax. The common chord of the circle and parabola is

Detailed Solution for JEE Main Mock- 7 - Question 55



 is the required circle ......(1)
now given parabola is 


⇒ x = a/2 common chord of circle and parabola.

JEE Main Mock- 7 - Question 56

A (3, 2, 0), B (5, 3, 2) and C (-9, 6, -3) are three points forming a triangle and AD is bisector of the angle  AD meets BC at the point :

Detailed Solution for JEE Main Mock- 7 - Question 56

The bisector of ∠BAC i.e., AD divides the side BC in the ratio AB : AC

Let co-ordinates of D (x: y, z)

JEE Main Mock- 7 - Question 57

If p, q ∈{1,2,3,4} the number of equations of the form px+ qx + 1 = 0 having real roots is

Detailed Solution for JEE Main Mock- 7 - Question 57

For real roots, we must have

Thus, there are 7 values of (p,q).

JEE Main Mock- 7 - Question 58

Detailed Solution for JEE Main Mock- 7 - Question 58


JEE Main Mock- 7 - Question 59

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

Detailed Solution for JEE Main Mock- 7 - Question 59

Let the equation of the circle is (x - 1)2 + (y - k)2 = k2
It passes through (2, 3) ⇒ (2 - 1)2 + (3 - k)2 = k2 

JEE Main Mock- 7 - Question 60

If f(x) = a - (x - 3)8/9, then maximum value of f(x) is:

Detailed Solution for JEE Main Mock- 7 - Question 60


∵  
∴  
At x = 3: f' (x) is not defined, 
hence sign scheme of f' (x) is

∴  f(x) is maximum at x = 3
Hence maximum value of f (x) is equal to "a"

JEE Main Mock- 7 - Question 61

The number of terms in the expansion of  which are integers, is given by

Detailed Solution for JEE Main Mock- 7 - Question 61



  should be integers so R be even
⇒ R = 0,2,4,........,250
∴ Number of integers terms = 251.

JEE Main Mock- 7 - Question 62

In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ is

Detailed Solution for JEE Main Mock- 7 - Question 62


JEE Main Mock- 7 - Question 63

There are unlimited number of identical balls of four different colours. How many arrangements of at most 8 balls in row can be made by using them?

Detailed Solution for JEE Main Mock- 7 - Question 63

The number of arrangements of one ball = 4,
because there are only four different balls.
The number of arrangements of two balls = 4 x 4 = 42 , etc.
∴ the required number of arrangements

JEE Main Mock- 7 - Question 64

The value of ii is :

Detailed Solution for JEE Main Mock- 7 - Question 64

JEE Main Mock- 7 - Question 65

For what value of  'a' is the area bounded by the curve y = a2x2 + ax + 1 and the straight line y = 0, x = 0 & x = 1 the least ?

Detailed Solution for JEE Main Mock- 7 - Question 65



 upward parabola with vertex 

JEE Main Mock- 7 - Question 66

If a1, a2, a3,....a20 are AMs between 13 and 67, then the maximum value of product a1 a2 a3 ....a20 is.

Detailed Solution for JEE Main Mock- 7 - Question 66



∴  Maximum value of a1 a2 a3 .......a20 is (40)20.

JEE Main Mock- 7 - Question 67

The area bounded by the curvesy = (x - 1)2 ,  y = (x+1) 2 and y = 1/4 is

Detailed Solution for JEE Main Mock- 7 - Question 67

The curves y = (x - 1)2, y = (x + 1)2 and y = 1/4 are shown as

where point of intersection are


JEE Main Mock- 7 - Question 68

Let z and ω be two non-zero complex numbers such that z = ω and arg z + arg ω = π, then z equals

Detailed Solution for JEE Main Mock- 7 - Question 68

JEE Main Mock- 7 - Question 69

If two distinct chords, drawn from the point (p, q) on the circle x2 + y2 = px + qy (where pq ≠ 0) are bisected by the x-axis, then

Detailed Solution for JEE Main Mock- 7 - Question 69

Let (h,0) be the mid-point of chord then its equation is
T = S,

this line passes through
(p,q)

D > 0 (Since these are two such chords)

JEE Main Mock- 7 - Question 70

If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is

Detailed Solution for JEE Main Mock- 7 - Question 70

Let the third vertex C be (x1. y1) since 0(0, 0) is the orthocenter







⇒ x1 = - 4
y1 = - 7
Hence the third vertex is
(-4, -7)

*Answer can only contain numeric values
JEE Main Mock- 7 - Question 71

The summation of series  upto infinite terms is equal to length of latus rectum of standard hyperbola with e = 2. If r is radius of director circle of its conjugate hyperbola, then r2 =


Detailed Solution for JEE Main Mock- 7 - Question 71

⇒ radius of director circle of conjugate hyperbola is given by

r2= b2-a2  = 2

*Answer can only contain numeric values
JEE Main Mock- 7 - Question 72

Let  Find tr(A2012)


Detailed Solution for JEE Main Mock- 7 - Question 72

A3 = 0, using CHT

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JEE Main Mock- 7 - Question 73

Let P, Q be points of the ellipse 16x2 + 25y2 = 400 so that PQ = 96/25 and P, Q lie above major axis. Circle drawn with PQ as diameter touch major axis at positive focus. If m is slope of PQ then find the value of 1/|m|


Detailed Solution for JEE Main Mock- 7 - Question 73

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JEE Main Mock- 7 - Question 74


Detailed Solution for JEE Main Mock- 7 - Question 74



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JEE Main Mock- 7 - Question 75

if sin−1x + sin−1y + sin−1z =π/2 then the value of x2+y2+z2+2xyz is equal to


Detailed Solution for JEE Main Mock- 7 - Question 75

sin−1x + sin−1y + sin−1z =π/2
put
sin−1 x = α, sin−1y=β, sin−1z=γ

(Given) or

cos α cos β - sin α sin β = sin γ    ... (1)
and, we have
sin α = x ,
Similarly,

∴  From equation (i), we get

 Squaring both sides, we have
x2 + y2 + z2 + 2xyz = 1

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