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JEE Main Practice Test- 11 - JEE MCQ


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75 Questions MCQ Test - JEE Main Practice Test- 11

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JEE Main Practice Test- 11 - Question 1

Consider the plane (x, y, z) = (0, 1, 1) + λ(1, -1,1) + μ(2, -1, 0). The distance of this plane from the originis

Detailed Solution for JEE Main Practice Test- 11 - Question 1




x(0 + 1) – y(0 – 2) + z(–1 + 2) = x + 2y + z hence equation of plane is x + 2y + z = 3;

JEE Main Practice Test- 11 - Question 2

If  are non zero vectors satisfying  then

Detailed Solution for JEE Main Practice Test- 11 - Question 2


JEE Main Practice Test- 11 - Question 3

Let P(a, b, c) be any point on the plane 3x + 2y + z = 7, then the least value of (a2 + b2 + c2), is

Detailed Solution for JEE Main Practice Test- 11 - Question 3

Clearly minimum value of a2 + b2 + c2


(This is possible when P(a, b, c) is foot of perpendicular from O(0, 0, 0) on the plane.)


Hence a2 + b2 + c2|least = 7/2

JEE Main Practice Test- 11 - Question 4

Let


and z = 1 + i (where i = √-1), then | w | and amp w respectively are

Detailed Solution for JEE Main Practice Test- 11 - Question 4

JEE Main Practice Test- 11 - Question 5

If ω is one of the imaginary cube root of unity then the value of the expression, (1 + 2ω + 2ω2)10 + (2 + ω + 2ω2)10 + (2 + 2ω + ω2)10 is:

JEE Main Practice Test- 11 - Question 6

Two tour guides are leading 6 tourist. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. Number of possiible different groupings of guides and tourist is

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


12 + 30 + 20 = 62
Alternatively: 1st tourist can go G1 or G2 in 2 ways all others. Hence required number of ways = 26 – 2 = 62

JEE Main Practice Test- 11 - Question 7

From 6 boys and 7 girls a committee of 5 is to be formed so as to include atleast one girl. The number of ways this can be done is

Detailed Solution for JEE Main Practice Test- 11 - Question 7

JEE Main Practice Test- 11 - Question 8

Urn A contains 9 red balls and 11 white balls. Urn B contains 12 red balls and 3 white balls. A person is to roll a single fair die. If the result is a one or a two, then he is to randomly select a ball from urn A.
Otherwise he is to randomly select a ball form urn B. The probability of obtaining a red ball, is

Detailed Solution for JEE Main Practice Test- 11 - Question 8


E : event of drawing a red ball;
E1 = 1 or 2 on die ⇒ P(E1) = 1/3
E2 = 3, 4, 5, 6 on die ⇒ P(E2) = 2/3
E = (E ∩ E1) + (E ∩ E2)
P(E) = P(E1) · P(E/E1) + P(E2) P(E/E2)

Using the law of total probabilities,
 

JEE Main Practice Test- 11 - Question 9

Two coins look similar, but have different probabilities of falling "head". One is a fair coin, with P (H) = 1/2, but the other is weighed so that P (H) = 4/5. One of the coin is chosen at random and is tossed 10 times, let X denotes the number of heads that of appear, and F is the event that the fair coin was drawn. If X = 7 is observed, the probability that the coin was fair, is

Detailed Solution for JEE Main Practice Test- 11 - Question 9

A : Coin randomly selected tossed 10 times, fell head wise 7 times
B1 : coin was a fair coin P(B1) = 1/2
B2 : Coin was a weighted coin P(B2) = 1/2

JEE Main Practice Test- 11 - Question 10

A taxi was involved in a hit and run accident at night. There are two taxi companies in the city, namely Black Taxis and White Taxis. It is known that 85% of the taxis in the city are Black and 15% are White.
There was a witness to the accident and, according to the witness , the taxi involved in the accident was White. Further investigation of the reliability of the witness showed that, the witness was able to identify correctly the colour of a taxi, 80% of the time. The probability that the taxi involved was Black, is

Detailed Solution for JEE Main Practice Test- 11 - Question 10

Let B1 : Taxi is black 0.85
B2 : Taxi is white 0.15
A: witness says that taxi involved in the hit and run accident was White.
P(A/B1) = 0.2
P(A/B2) = 0.8

JEE Main Practice Test- 11 - Question 11

If a variable takes the discrete values

then the median is

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

Arrange the data in increasing order as,

p + 4 , p + 5.
As, number of observations = 8
So, median =

JEE Main Practice Test- 11 - Question 12

Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball of the total , 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 24 played all the three games. The number of boys who play only cricket is

Detailed Solution for JEE Main Practice Test- 11 - Question 12


V = 800
Total playing game = 640
800 – 640 = 160

JEE Main Practice Test- 11 - Question 13

Let x1, x2, … …, xn be n observat ions such that  ∑x2i = 400 and ∑xi = 80. Then a possible value of n among the following is

Detailed Solution for JEE Main Practice Test- 11 - Question 13

Since, root mean square ≥ arithmetic mean

Hence, possible value of n = 18.

JEE Main Practice Test- 11 - Question 14

The statement p → (q → p) is equivalent to

Detailed Solution for JEE Main Practice Test- 11 - Question 14

JEE Main Practice Test- 11 - Question 15

A flagstaff 5m high is placed on a building 25 m high. If the flag and building both subtend equal angles on the observer at a height 30 m, the distance between the observer and the top of the flag is

Detailed Solution for JEE Main Practice Test- 11 - Question 15

In ΔOBC, we have
tan α = 5/x   ..(i) 
Also, tan 2α = 30/x    ....(ii) 
Dividing (ii) by (i), we have 



JEE Main Practice Test- 11 - Question 16

A line 'L' passes through a point with position vector ar and is perpendicular to the plane containing the two intersecting lines  If L intersects a plane  at the point R then the postion vector of the point R, is 

Detailed Solution for JEE Main Practice Test- 11 - Question 16

Equation of the line is



hence the position vector of R is

JEE Main Practice Test- 11 - Question 17

Equation of the line in the plane x + 3y – z = 9, which is perpendicular to the line 

and passing through a point where the plane P meets the given line, is

Detailed Solution for JEE Main Practice Test- 11 - Question 17

Vector perpendicular to  and


Any general point on the line is (1 + 2λ, 1 + λ, 1 - λ) at their point of intersection. This point satisfies equation of plane
(1 + 2λ) + 3(1 + λ) - (1 - λ) = 9 ⇒  λ = 1
∴ Point of intersection is (3, 2, 0).
Hence required line is

JEE Main Practice Test- 11 - Question 18

For any complex number w = a + bi,where a, b ∈ R.
If w = cos 40° + i sin40°, then | w + 2w2 + 3w3 + ..... + 9w9 |–1 equals

Detailed Solution for JEE Main Practice Test- 11 - Question 18

S = w + 2w2 + 3w3 + ..... + 9w9



JEE Main Practice Test- 11 - Question 19

The vector z = - 4 + 5i is turned counter clockwise through an angle of 180º & stretched 1.5 times. The complex number corresponding to the newly obtained vector is:

JEE Main Practice Test- 11 - Question 20

The total number of combinations 6 at a time which can be formed from 6 alike white, 6 alike blue, 6 alike green and 6 alike red balls is

Detailed Solution for JEE Main Practice Test- 11 - Question 20

Treat W, B, G, R as beggar
0 0 0 0 0 0 Ø Ø Ø = 9C3 = 84
or co-eff. of x6 in
(1 + x + x2 + x3 + x4 + x5 + x6)4

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 21

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

If  then the value of a+ b5 must be


Detailed Solution for JEE Main Practice Test- 11 - Question 21

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JEE Main Practice Test- 11 - Question 22

If  where [.] denotes the greatest integer function, then the value of 128I must be


Detailed Solution for JEE Main Practice Test- 11 - Question 22

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JEE Main Practice Test- 11 - Question 23

If f(x) + f(y) =  for all x, y ∈ R and xy ≠ 1 and  then the value of  must be 


Detailed Solution for JEE Main Practice Test- 11 - Question 23

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JEE Main Practice Test- 11 - Question 24

If f(x) =  is continuous at x = 3, then the value of 8100λ must be


Detailed Solution for JEE Main Practice Test- 11 - Question 24


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JEE Main Practice Test- 11 - Question 25

The equation of a curve whose slope at any point is thrice its abscissa and which passes through (–1, –3) is 2y = λ (x2 − 3)2y = λ(x2 − 3), then the value of λ must be


Detailed Solution for JEE Main Practice Test- 11 - Question 25

JEE Main Practice Test- 11 - Question 26

A ray of light falls perpendicularly at the surface of composite glass slab, made of two transparent prism of small angle of refractive index µ1 and µ2 respectively, as shown in figure. The correct deviation δ is

Detailed Solution for JEE Main Practice Test- 11 - Question 26

δ1 = (µ2 - 1)θ
δ2 = -(µ1 - 1)θ
δ = (µ2 - µ1

JEE Main Practice Test- 11 - Question 27

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

JEE Main Practice Test- 11 - Question 28

Object distance from the pole of a concave mirror is equal to its radius of curvature . The image must be:

JEE Main Practice Test- 11 - Question 29

When a certain metallic surface is irradiated with monochromatic light wavelength λ, the stopping potential for photoelectric current is 3 V0. When the same surface is irradiated with light of wavelength 2 λ, the stopping potential is V0. The threshold wavelength for the given surface is

Detailed Solution for JEE Main Practice Test- 11 - Question 29


where hc/λ0 = ϕ (λ0 - threshold wavelength)

JEE Main Practice Test- 11 - Question 30

Ram is looking at his face in a mirror kept 10 cm away & he finds that his image is erect and magnified (m = 1.8). If he holds the mirror 50cm away.

Detailed Solution for JEE Main Practice Test- 11 - Question 30


1.8 f + 18 = f
18 = – 0.8 f
f = – 22.5 cm in second case, u = – 50
⇒ Obj. is beyond C.
⇒ Image is invereted and diminished.

JEE Main Practice Test- 11 - Question 31

An electromagnetic wave has an electric field given by the expression (in Cartesian co-ordinates) :

What is the direction of the magnetic field at time t = 0 and position x = 0?

Detailed Solution for JEE Main Practice Test- 11 - Question 31

JEE Main Practice Test- 11 - Question 32

In the figure shown, O is the centre of the glass sphere. Spot P on the sphere when viewed almost normally appears :

Detailed Solution for JEE Main Practice Test- 11 - Question 32

JEE Main Practice Test- 11 - Question 33

A beam of light of wavelength 400nm and power 1.55mW is directed at the cathode of a photoelectric cell. If only 10% of the incident photons effectively produce photoelectrons, find the current due to these electrons.

Detailed Solution for JEE Main Practice Test- 11 - Question 33

JEE Main Practice Test- 11 - Question 34

In the figure shown a point object O is placed in air. A spherical boundary separates various media of radius of curvature 1.0 m. AB is principal axis. The refractive index above AB is 1.6 and below AB is 2.0. The separation between the images formed due to refraction at spherical surface is:

Detailed Solution for JEE Main Practice Test- 11 - Question 34


JEE Main Practice Test- 11 - Question 35

A parallel beam of monochromatic light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

JEE Main Practice Test- 11 - Question 36

A beam of light passes from medium 1 to medium 2 to medium 3 as shown in the diagram. What may be concluded about the three indexes of refraction, n1, n2 and n3?

JEE Main Practice Test- 11 - Question 37

A hydrogen atom in its ground state absorbs a photon of energy 10.2eV and gets excited. The change in angular momentum of the electrons in this process is (in kgm2/s) nearly :

JEE Main Practice Test- 11 - Question 38

A ray of light is incident at an angle of 75° from air into a medium having refractive index μ. The reflected and the refracted rays are found to suffer equal deviations in opposite direction μ equals

JEE Main Practice Test- 11 - Question 39

In a YDSE experiment λ = 540 nm, D = 1m, d = 1mm. A thin film is pasted on upper slit and the central maxima shifts to the point just in front of the upper slit. What is the path difference at the centre of the screen?

Detailed Solution for JEE Main Practice Test- 11 - Question 39

Infront of upper slint

at centre on the screen

JEE Main Practice Test- 11 - Question 40

Light from denser medium 1 passes to a rarer medium 2. When the angle of incidence is θ the partially reflected and refracted rays are mutually perpendicular. The critical angle will be

Detailed Solution for JEE Main Practice Test- 11 - Question 40


JEE Main Practice Test- 11 - Question 41

The ratio of magnetic moment to the angular momentum is a universal constant for hydrogen like atoms and ions. The value of this constant is

JEE Main Practice Test- 11 - Question 42

Three polaroids are kept coaxially. Angle between the first and third polaroid is 90°. Angle between the first and second polaroid is 60°. If unpolarized light energy incident on the first polaroid is I0. Light energy that emerges from the system is

Detailed Solution for JEE Main Practice Test- 11 - Question 42

Accordin to Malus law, I = I0 cos2 θ

JEE Main Practice Test- 11 - Question 43

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40 cm. The area of the image is 9 times that of the square. The focal length of the lens is

JEE Main Practice Test- 11 - Question 44

The radius of the shortest orbit in a one electron system is 18pm. It may be :

JEE Main Practice Test- 11 - Question 45

What should be the value of distance d so that final image is formed on the object itself. (focal lengths of the lenses are written on the lenses.)

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 46

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

How far from the mirror (in cm), the image is formed in the context shown in the figure?


Detailed Solution for JEE Main Practice Test- 11 - Question 46

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 47

A non-conducting non-magnetic rod having a circular cross section of radius R is suspended from a rigid support as shown in figure. A light and small coil of 300 turns is wrapped tightly at the left end of the rod where uniform magnetic field B exists in vertically downward direction. Air of density ρρ hits the half of the right part of the rod with velocity v as shown in the figure. What should be the current in the clockwise direction (as seen from O) in the coil so that the rod remains horizontal? Given answer in mA. Given,


Detailed Solution for JEE Main Practice Test- 11 - Question 47

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JEE Main Practice Test- 11 - Question 48

The magnetic field of a cylindrical magnet that has a pole face radius 2.8 cm can be varied sinusoidally between the minimum value 16.8 T and the maximum value 17.2 T at a frequency of (50/π) Hz. Cross section of the magnetic field created by the magnet is shown in the figure. At a radial distance of 2 cm from the axis, find the amplitude of the electric field (in units of x 102m NC-1) induced by the magnetic field variation.


Detailed Solution for JEE Main Practice Test- 11 - Question 48

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JEE Main Practice Test- 11 - Question 49

A circular coil of wire consists of exactly 100 turns with a total resistance 0.20Ω. The area of the coil is 100 cm2. The coil is kept in a uniform magnetic field B as shown in figure. The magnetic field is increased at a constant rate of 2 Ts–1. Find the induced current in the coil in A.


Detailed Solution for JEE Main Practice Test- 11 - Question 49

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JEE Main Practice Test- 11 - Question 50

There is a point object and a plane mirror. If the mirror is moved by 10 cm away from the object, find the distance (in cm) which the image will move.


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JEE Main Practice Test- 11 - Question 51

There is 34 g H2O2 in its 2L aqueous solution. The volume strength of the solution is:

Detailed Solution for JEE Main Practice Test- 11 - Question 51


∴ Volume strength of the solution =

JEE Main Practice Test- 11 - Question 52

Syn gas is a mixture of:

Detailed Solution for JEE Main Practice Test- 11 - Question 52

Syn gas or water gas ⇒ CO + H2

JEE Main Practice Test- 11 - Question 53

Which order is incorrect according to their resonance energy:

Detailed Solution for JEE Main Practice Test- 11 - Question 53

Negative charged O-atom has more electron donating power than neutral O-atom therefore resonance energy.

JEE Main Practice Test- 11 - Question 54

The ratio of mass percent of C and H of an organic compound CxHyOz is 7.5 : 1. If the percentage of oxygen in the compound is 32%. Then, the empirical formula of the compound is :

Detailed Solution for JEE Main Practice Test- 11 - Question 54

Let, % of C be 7.5 x % and H be x %
∴ 7.5 x + x + 32 = 100
∴ x = 8
∴ % of C = 60%, H = 8 % and O = 32 %

JEE Main Practice Test- 11 - Question 55

The correct order in which the O–O bond length increases in the following is :

Detailed Solution for JEE Main Practice Test- 11 - Question 55

O2 → B.O. ⇒ [O = O] = 2

JEE Main Practice Test- 11 - Question 56

Which of the following group has the maximum hyperconjugation effect when attached to benzene ring?

Detailed Solution for JEE Main Practice Test- 11 - Question 56

JEE Main Practice Test- 11 - Question 57

3L mixture of O2(g) and N2(g) is passed through ozonizer. The gas mixture obtained contains O2, O3 and N2 gases only. This obtained mixture is passed through alkaline pyrogallol and then through turpentine oil, there were 1100 mL and 600 mL volume contractions respectively. The volume of O2(g) and N2(g) in the original mixture respectively is -

Detailed Solution for JEE Main Practice Test- 11 - Question 57



t = 0   x = mL      0
t = tf   (x–3u)mL  (2u)mL= 600mL
∴ u = 300
⇒ x – 3 × 300 = 1100
∴ x = 2000 ∴ Eqn (1) ⇒ y = 1000 V

JEE Main Practice Test- 11 - Question 58

In the solvay process of manufacturing of Sodium Bicarbonate, the final by-product is :

Detailed Solution for JEE Main Practice Test- 11 - Question 58

In solvay process manufacture of sodium bicarbonate, the final biproduct is :

JEE Main Practice Test- 11 - Question 59

Which comparison is not correct as indicated?

Detailed Solution for JEE Main Practice Test- 11 - Question 59

JEE Main Practice Test- 11 - Question 60

15 g of a gas present in 5L vessel exerts a pressure of 0.1 bar. What is the root mean square speed of the gasmolecules?

Detailed Solution for JEE Main Practice Test- 11 - Question 60

JEE Main Practice Test- 11 - Question 61

In which of the following pair both the chlorides do not impart colour to the flame?

Detailed Solution for JEE Main Practice Test- 11 - Question 61

Be and Mg does not impart colour to the flame due to their high Ionisation energy

JEE Main Practice Test- 11 - Question 62

Which species has dipole moment?

Detailed Solution for JEE Main Practice Test- 11 - Question 62

JEE Main Practice Test- 11 - Question 63

An open container of volume 5L contains air at 27°C and 1 atm. The container is heated to T K. The amount of air expelled from the container is found to be 1.5L at – 33°C and 1atm. What is the value of temperature T K?

Detailed Solution for JEE Main Practice Test- 11 - Question 63

JEE Main Practice Test- 11 - Question 64

The stability of +1 oxidation state increases in the sequence.

Detailed Solution for JEE Main Practice Test- 11 - Question 64

Due to inert pair effect as we more down the group stability of (+1) oxidation state increases.

JEE Main Practice Test- 11 - Question 65

The most stable conformational isomer of cis 1-Bromo-2-chloro cyclohexane is

Detailed Solution for JEE Main Practice Test- 11 - Question 65

Chlorine atom lies at equatorial position because of its smaller size, bond length is shorter than Bromine to avoid 1, 3 diaxial repulsion.

JEE Main Practice Test- 11 - Question 66

Which of the following forms a positively charged sol?

JEE Main Practice Test- 11 - Question 67

Phosphine is prepared by the action of :

Detailed Solution for JEE Main Practice Test- 11 - Question 67

JEE Main Practice Test- 11 - Question 68

Structural isomers of the compound with molecular formula C4H10O are -

Detailed Solution for JEE Main Practice Test- 11 - Question 68

4 isomers with alcohol functional group


3 isomers with ether functional group

JEE Main Practice Test- 11 - Question 69

Which of the following is NOT correct?

JEE Main Practice Test- 11 - Question 70


In above reaction 'X' will be :

Detailed Solution for JEE Main Practice Test- 11 - Question 70


* Manufacture of H2SO4 by "Contact process"

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 71

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

Calculate the atomic number of hydrogen like species which can be ionized by an electron moving with a velocity, v = 6.56 × 106m s-1


Detailed Solution for JEE Main Practice Test- 11 - Question 71

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 72

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- 11 - Question 72

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JEE Main Practice Test- 11 - Question 73

5.6 litre of the gas have 1 g weight at STP. Then atomic weight of the gas is ______


Detailed Solution for JEE Main Practice Test- 11 - Question 73

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JEE Main Practice Test- 11 - Question 74

A 12 g mixture of Na2CO3 and CaCO3 and clay when heated gave 1.792 L of CO2 and in another experiment same amount of mixture required 19.8 L of 0.01 N HCI for complete neutralization. Calculate weight of Na2COpresent in sample.


Detailed Solution for JEE Main Practice Test- 11 - Question 74

Na2CO3 does not get decomposed due to ignition.  CaCO3 decomposes to form CaO and CO2  
100 g of CaCO3 produced 22.4 L CO2
1.792 CO2 produced by = 100 x 1.792 / 22.4 = 8 g

*Answer can only contain numeric values
JEE Main Practice Test- 11 - Question 75

The compound(s) with TWO lone pairs of electrons on the central atom is(are)
BrF5; ClF3; XeF4; SF4


Detailed Solution for JEE Main Practice Test- 11 - Question 75

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