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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

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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 (a^{2} + b^{2} + c^{2}), is

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JEE Main Practice Test- 11 - Question 4

Let

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

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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 + 2ω^{2})^{10} + (2 + ω + 2ω^{2})^{10} + (2 + 2ω + ω^{2})^{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

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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

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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

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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

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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

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JEE Main Practice Test- 11 - Question 11

If a variable takes the discrete values

then the median is

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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

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JEE Main Practice Test- 11 - Question 13

Let x_{1}, x_{2}, … …, x_{n} be n observat ions such that ∑x^{2}_{i} = 400 and ∑x_{i} = 80. Then a possible value of n among the following is

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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

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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

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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

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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 + 2w^{2} + 3w^{3} + ..... + 9w^{9} |^{–1} equals

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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

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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^{4 }+ b^{5} must be

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JEE Main Practice Test- 11 - Question 22

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

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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

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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

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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 (x^{2} − 3)2y = λ(x^{2} − 3), then the value of λ must be

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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 µ_{1} and µ_{2} respectively, as shown in figure. The correct deviation δ is

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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 V_{0}. When the same surface is irradiated with light of wavelength 2 λ, the stopping potential is V_{0}. The threshold wavelength for the given surface is

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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.

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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?

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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 :

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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.

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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:

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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, n_{1}, n_{2} and n_{3}?

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 kgm^{2}/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?

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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

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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 I_{0}. Light energy that emerges from the system is

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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.)

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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?

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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,

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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 10^{2}m NC^{-1}) induced by the magnetic field variation.

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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 cm^{2}. 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.

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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 H_{2}O_{2} in its 2L aqueous solution. The volume strength of the solution is:

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JEE Main Practice Test- 11 - Question 53

Which order is incorrect according to their resonance energy:

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JEE Main Practice Test- 11 - Question 54

The ratio of mass percent of C and H of an organic compound C_{x}H_{y}O_{z} is 7.5 : 1. If the percentage of oxygen in the compound is 32%. Then, the empirical formula of the compound is :

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JEE Main Practice Test- 11 - Question 55

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

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JEE Main Practice Test- 11 - Question 56

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

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JEE Main Practice Test- 11 - Question 57

3L mixture of O_{2}(g) and N_{2}(g) is passed through ozonizer. The gas mixture obtained contains O_{2}, O_{3} and N_{2} 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 O_{2}(g) and N_{2}(g) in the original mixture respectively is -

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JEE Main Practice Test- 11 - Question 58

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

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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?

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JEE Main Practice Test- 11 - Question 61

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

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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?

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JEE Main Practice Test- 11 - Question 64

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

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JEE Main Practice Test- 11 - Question 65

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

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JEE Main Practice Test- 11 - Question 66

Which of the following forms a positively charged sol?

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JEE Main Practice Test- 11 - Question 68

Structural isomers of the compound with molecular formula C_{4}H_{10}O are -

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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 × 10^{6}m s^{-1}

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JEE Main Practice Test- 11 - Question 72

Calculate the energy required (in Joules) to convert all atoms of Mg to Mg^{2+} ions present in 48 mg of Mg vapours. IE_{1} and IE_{2} of Mg are 740 and 1450 kJ mol^{–1} respectively.

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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 ______

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JEE Main Practice Test- 11 - Question 74

A 12 g mixture of Na_{2}CO_{3} and CaCO_{3} and clay when heated gave 1.792 L of CO_{2} and in another experiment same amount of mixture required 19.8 L of 0.01 N HCI for complete neutralization. Calculate weight of Na_{2}CO_{3 }present in sample.

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JEE Main Practice Test- 11 - Question 75

The compound(s) with TWO lone pairs of electrons on the central atom is(are)

BrF_{5}; ClF_{3}; XeF_{4}; SF_{4}

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