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# JEE Main 2017 April 8 Paper & Solutions - JEE

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## 90 Questions MCQ Test JEE Main & Advanced Mock Test Series - JEE Main 2017 April 8 Paper & Solutions

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JEE Main 2017 April 8 Paper & Solutions - Question 1

### Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

JEE Main 2017 April 8 Paper & Solutions - Question 2

### Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

JEE Main 2017 April 8 Paper & Solutions - Question 3

### A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 3

k = 4π2
In parallel keq = 2k

JEE Main 2017 April 8 Paper & Solutions - Question 4

An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t→∞ is :

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 4

JEE Main 2017 April 8 Paper & Solutions - Question 5

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

JEE Main 2017 April 8 Paper & Solutions - Question 6

Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure.  A cavity DEF is cut out from the lamina, where D, E, F are the midpoints of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

JEE Main 2017 April 8 Paper & Solutions - Question 7

If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4 W. Radius of the Earth is 6400 km and g=10 m/s2.

JEE Main 2017 April 8 Paper & Solutions - Question 8

In an experiment, a sphere of aluminium of mass 0.20 kg is heated up to 150ºC. Immediately, it is put into water of volume 150 cc at 27ºC kept in a calorimeter of water equivalent to 0.025 kg.  Final temperature of the system is 40ºC. The specific heat of aluminium is :
(take 4.2 Joule=1 calorie)

JEE Main 2017 April 8 Paper & Solutions - Question 9

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by ∆T.  The net change in its length is zero.  Let l be the length of the rod, A it's area of cross-section, Y its Young’s modulus, and α it's coefficient of linear expansion. Then, F is equal to :

JEE Main 2017 April 8 Paper & Solutions - Question 10

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :
(Take Cv=1.5 R, where R is gas constant)

JEE Main 2017 April 8 Paper & Solutions - Question 11

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp) and at constant volume (Cv) is:

JEE Main 2017 April 8 Paper & Solutions - Question 12

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1. At, t=0 the displacement is 5 m. What is the maximum acceleration? The initial phase is π/4.

JEE Main 2017 April 8 Paper & Solutions - Question 13

Two wires W1 and W2 have the same radius r and respective densities ρ1 and ρ2 such that ρ2=4ρ1. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T.The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is :

JEE Main 2017 April 8 Paper & Solutions - Question 14

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60º with the direction of the field?

JEE Main 2017 April 8 Paper & Solutions - Question 15

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 µC charges, its radius will be:

JEE Main 2017 April 8 Paper & Solutions - Question 16

What is the conductivity of a semiconductor sample having electron concentration of 5×1018 m−3, hole concentration of 5×1019 m−3, electron mobility of 2.0 m2 V−1  s−1 and hole mobility of 0.01 m2 V−1 s−1?
(Take charge of electron as 1.6×10−19 C)

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 16

s = e (neμe + nnμn)
= 1.6 × 10-19 (5 × 1018 × 2 + 5 × 1019 × 0.01)
= 1.6 × 10–19 (1019  + 0.05 × 1019)
= 1.6 × 1.05
= 1.68

JEE Main 2017 April 8 Paper & Solutions - Question 17

A 9 V battery with internal resistance of 0.5 Ω is connected across an infinite network as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal.

JEE Main 2017 April 8 Paper & Solutions - Question 18

In a certain region static electric and magnetic fields exist. The magnetic field is given by  .  If a test charge moving with a velocity experiences no force in that region, then the electric field in the region, in SI units, is :

JEE Main 2017 April 8 Paper & Solutions - Question 19

A magnetic dipole in a constant magnetic field has:

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 19

PE = – PE cos θ
τ = PE sin θ
τmax when θ = 90°
PE = 0

JEE Main 2017 April 8 Paper & Solutions - Question 20

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are on the same plane. The outer loop of radius b carries an alternating current I=Io cos (ωt). The emf induced in the smaller inner loop is nearly :

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 20

JEE Main 2017 April 8 Paper & Solutions - Question 21

Magnetic field in a plane electromagnetic wave is given by

Expression for corresponding electric field will be :
Where c is speed of light.

JEE Main 2017 April 8 Paper & Solutions - Question 22

Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle is θC. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 900. Angle A is given by :

JEE Main 2017 April 8 Paper & Solutions - Question 23

A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ. If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum)

JEE Main 2017 April 8 Paper & Solutions - Question 24

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

JEE Main 2017 April 8 Paper & Solutions - Question 25

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n=principal quantum number)

JEE Main 2017 April 8 Paper & Solutions - Question 26

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron=1.1 MeV and for helium=7.0 MeV)

JEE Main 2017 April 8 Paper & Solutions - Question 27

The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is :

JEE Main 2017 April 8 Paper & Solutions - Question 28

A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct statement.

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 28

=1/5 = 0.2
Frequency = 12 × 103 kHz F = 12.00 kHz
F1 = 1200 – 20 = 1180 kHz
F2 = 1200 + 20 = 1220 kHz

JEE Main 2017 April 8 Paper & Solutions - Question 29

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

JEE Main 2017 April 8 Paper & Solutions - Question 30

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length l1 cm from P when two way key K3 is plugged in between 2 and 1, while the balance point is at a length l2 cm from P when key K3 is plugged in between 3 and 1. The ratio of two resistances R1/R2 , is found to be :

JEE Main 2017 April 8 Paper & Solutions - Question 31

Among the following, correct statement is :

JEE Main 2017 April 8 Paper & Solutions - Question 32

Excess of NaOH (aq) was added to 100 mL of FeCl3 (aq) resulting into 2.14 g of Fe(OH)3. The molarity of FeCl3 (aq) is
(Given molar mass of Fe=56 g mol−1 and molar mass of Cl=35.5 g mol−1)

JEE Main 2017 April 8 Paper & Solutions - Question 33

Among the following, the incorrect statement is :

JEE Main 2017 April 8 Paper & Solutions - Question 34

For a reaction, A(g) → A(l); ∆H=−3RT. The correct statement for the reaction is :

JEE Main 2017 April 8 Paper & Solutions - Question 35

What is the standard reduction potential (Eo) for Fe3+ → Fe ?
Given that :
Fe2+ +2e- → Fe; Eo Fe2+/Fe = -0.47V
Fe3+ + e- → Fe2+ ; EFe3+/Fe2+ = +0.77V

JEE Main 2017 April 8 Paper & Solutions - Question 36

If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is:

JEE Main 2017 April 8 Paper & Solutions - Question 37

5 g of Na2SO4 was dissolved in x g of H2O. The change in freezing point was found to be 3.82oC. If Na2SO4 is 81.5% ionised, the value of x
(Kf for water=1.86oC kg mol−1) is approximate:
(molar mass of S=32 g mol−1 and that of Na=23 g mol−1)

JEE Main 2017 April 8 Paper & Solutions - Question 38

Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. If ionisation constant of HA is 10−5, the ratio of salt to acid concentration in the buffer solution will be:

JEE Main 2017 April 8 Paper & Solutions - Question 39

The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A.

JEE Main 2017 April 8 Paper & Solutions - Question 40

The enthalpy change on freezing of 1 mol of water at 5oC to ice at −5oC is :
(Given ∆fusH=6 kJ mol−1 at 0oC, Cp(H2O, l)=75.3 J mol−1 K−1, Cp(H2O, s)=36.8 J mol−1 K−1)

JEE Main 2017 April 8 Paper & Solutions - Question 41

Which of the following is paramagnetic?

JEE Main 2017 April 8 Paper & Solutions - Question 42

The pair of compounds having metals in their highest oxidation state is:

JEE Main 2017 April 8 Paper & Solutions - Question 43

sp3d2 hybridization is not displayed by :

JEE Main 2017 April 8 Paper & Solutions - Question 44

Identify the pollutant gases largely responsible for the discoloured and lustreless nature of marble of the Taj Mahal.

JEE Main 2017 April 8 Paper & Solutions - Question 45

In which of the following reactions, hydrogen peroxide acts as an oxidizing agent?

JEE Main 2017 April 8 Paper & Solutions - Question 46

Consider the following ionization enthalpies of two elements ‘A’ and ‘B’.

JEE Main 2017 April 8 Paper & Solutions - Question 47

Consider the following standard electrode potentials (Eo in volts) in aqueous solution:

Based on these data, which of the following statements is correct?

JEE Main 2017 April 8 Paper & Solutions - Question 48

A metal ‘M’ reacts with nitrogen gas to afford ‘M3N’. ‘M3N’ on heating at high temperature gives back ‘M’ and on reaction with water produces a gas ‘B’. Gas ‘B’ reacts with aqueous solution of CuSO4 to form a deep blue compound. ‘M’ and ‘B’ respectively are :

JEE Main 2017 April 8 Paper & Solutions - Question 49

The number of S=O and S−OH bonds present in peroxodisulphuric acid and pyrosulphuric acid respectively are:

JEE Main 2017 April 8 Paper & Solutions - Question 50

A solution containing a group-IV cation gives a precipitate on passing H2S. A solution of this precipitate in dil.HCl produces a white precipitate with NaOH solution and bluish-white precipitate with basic potassium ferrocyanide. The cation is :

JEE Main 2017 April 8 Paper & Solutions - Question 51

A mixture containing the following four compounds is extracted with 1M HCl. The compound that goes to aqueous layer is:

JEE Main 2017 April 8 Paper & Solutions - Question 52

The reason for “drug induced poisoning” is :

JEE Main 2017 April 8 Paper & Solutions - Question 53

Which of the following compounds will not undergo Friedel Craft’s reaction with benzene?

JEE Main 2017 April 8 Paper & Solutions - Question 54

Among the following, the essential amino acid is:

JEE Main 2017 April 8 Paper & Solutions - Question 55

The major product expected from the following reaction is:

JEE Main 2017 April 8 Paper & Solutions - Question 56

The major product of the following reaction is :

JEE Main 2017 April 8 Paper & Solutions - Question 57

Which of the following statements is not true about partition chromatography?

JEE Main 2017 April 8 Paper & Solutions - Question 58

The IUPAC name of the following compound is :

JEE Main 2017 April 8 Paper & Solutions - Question 59

The major product of the following reaction is:

JEE Main 2017 April 8 Paper & Solutions - Question 60

The major product of the following reaction is:

JEE Main 2017 April 8 Paper & Solutions - Question 61

Let f(x)=210⋅x+1 and g(x)=310⋅x−1. If (fog)(x)=x, then x is equal to :

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 61

JEE Main 2017 April 8 Paper & Solutions - Question 62

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x−1 and it leaves remainder 6 when divided by x+1; then :

JEE Main 2017 April 8 Paper & Solutions - Question 63

Let z∈C, the set of complex numbers. Then the equation, 2|z+3i|−|z−i|=0 represents :

JEE Main 2017 April 8 Paper & Solutions - Question 64

The number of real values of λ for which the system of linear equations
2x+4y−λz=0
4x+λy+2z=0
λx+2y+2z=0
has infinitely many solutions, is :

JEE Main 2017 April 8 Paper & Solutions - Question 65

Let A be any 3×3 invertible matrix. Then which one of the following is not always true?

JEE Main 2017 April 8 Paper & Solutions - Question 66

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

Detailed Solution for JEE Main 2017 April 8 Paper & Solutions - Question 66

JEE Main 2017 April 8 Paper & Solutions - Question 67

If (27)999 is divided by 7, then the remainder is :

JEE Main 2017 April 8 Paper & Solutions - Question 68

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then a+b / a-b is equal to:

JEE Main 2017 April 8 Paper & Solutions - Question 69

If the sum of the first n terms of the series √3 + √75 + √243 + √507 + .... + 435√3 then n equals :

JEE Main 2017 April 8 Paper & Solutions - Question 70

is equal to:

JEE Main 2017 April 8 Paper & Solutions - Question 71

The tangent at the point (2, −2) to the curve, x2y2−2x=4(1−y) does not pass through the point :

JEE Main 2017 April 8 Paper & Solutions - Question 72

If then  is equal to :

JEE Main 2017 April 8 Paper & Solutions - Question 73

If a point P has co-ordinates (0, −2) and Q is any point on the circle, x2+y2−5x−y+5=0, then the maximum value of (PQ)2 is :

JEE Main 2017 April 8 Paper & Solutions - Question 74

The integral  is equal to :
(where C is a constant of integration)

JEE Main 2017 April 8 Paper & Solutions - Question 75

The integral equals :

JEE Main 2017 April 8 Paper & Solutions - Question 76

The area (in sq. units) of the smaller portion enclosed between the curves, x2+y2=4 and y2=3x, is :

JEE Main 2017 April 8 Paper & Solutions - Question 77

The curve satisfying the differential equation, ydx−(x+3y2)dy=0 and passing through the point (1, 1), also passes through the point :

JEE Main 2017 April 8 Paper & Solutions - Question 78

The locus of the point of intersection of the straight lines,
tx−2y−3t=0
x−2ty+3=0  (t ∈ R), is :

JEE Main 2017 April 8 Paper & Solutions - Question 79

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos -1 (1/7) and sec-1 (7) at the centre respectively, then the distance between these chords, is :

JEE Main 2017 April 8 Paper & Solutions - Question 80

If the common tangents to the parabola, x2=4y and the circle, x2+y2=4 intersect at the point P, then the distance of P from the origin, is :

JEE Main 2017 April 8 Paper & Solutions - Question 81

Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is 3/5 and thedistance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :

JEE Main 2017 April 8 Paper & Solutions - Question 82

The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines,  and  is :

JEE Main 2017 April 8 Paper & Solutions - Question 83

The line of intersection of the planes  and  is :

JEE Main 2017 April 8 Paper & Solutions - Question 84

The area (in sq. units) of the parallelogram whose diagonals are along the vectors  and  is:

JEE Main 2017 April 8 Paper & Solutions - Question 85

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place.  If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

JEE Main 2017 April 8 Paper & Solutions - Question 86

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 3/4, 1/2 and 5/8 respectively, then the probability that the target is hit by P or Q but not by R is :

JEE Main 2017 April 8 Paper & Solutions - Question 87

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:

JEE Main 2017 April 8 Paper & Solutions - Question 88

If
then  is equal to :

JEE Main 2017 April 8 Paper & Solutions - Question 89

The value of   is equal to :

JEE Main 2017 April 8 Paper & Solutions - Question 90

The proposition (~p) ∨ (p ∧ ~q) is equivalent to :

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