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JEE Main 2018 Question Paper With Solutions (8 April)


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JEE Main 2018 Question Paper With Solutions (8 April) - Question 1

The density of a material in the shape of a cube is determines by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 1

JEE Main 2018 Question Paper With Solutions (8 April) - Question 2

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 2

In graph ‘2’ initial slope is zero which is not possible, since initial velocity is non zero in all other three graphs.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 3

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 3

JEE Main 2018 Question Paper With Solutions (8 April) - Question 4

A particle is moving in a circular path of radius a under the action of an attractive potential   Its total energy is :  

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 4


‘ – ‘ sign of force implies attractive force So,

JEE Main 2018 Question Paper With Solutions (8 April) - Question 5

In a collinear collisio n, a particle with an init ial speed ν0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 5

By cons of linear momentum,




So relative velocity :

Hence the Solution is Option (2)

JEE Main 2018 Question Paper With Solutions (8 April) - Question 6

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 6

Moment of inertia of each disc about the given axis is,


JEE Main 2018 Question Paper With Solutions (8 April) - Question 7

From a uniform circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 7

Mass of disc = Volume x Density
9M = A x T x ρ (Area x thickness x density)

(i) Divided by (ii) 

Moment of inertia of complete disc about an axis passes through O.

Moment of inertia of cut off disc about an axis passes through O

So, moment of inertia of remaining disc = I1 -I2

JEE Main 2018 Question Paper With Solutions (8 April) - Question 8

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 8


JEE Main 2018 Question Paper With Solutions (8 April) - Question 9

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, (dr/r) is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 9

Bulk Modulus,

JEE Main 2018 Question Paper With Solutions (8 April) - Question 10

Two moles of an ideal monoatomic gas occupies a volume V at 270C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 10

Initially n = 2, v, T= 300k
Finally Vd = 2v
Gas is monoatomic, So, r = 5/3
So, 


Since gas undergoes expensed.

 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 11

The mass of a hydrogen molecule is 3.32 x 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 450 to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly : 

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 11

Change in momentum normal to the wall 


JEE Main 2018 Question Paper With Solutions (8 April) - Question 12

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other ? (Mole wt. of silver = 108 and Avagadro number = 6.02 x 1023 gm mole-1)

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 12


JEE Main 2018 Question Paper With Solutions (8 April) - Question 13

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 x 103 kg/m3 and its young's modulus is 9.27 x 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 13

Since rod is clamped at centre. So centre it behaves as node & end it behave as antinode.
So, 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 14

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densit ies +σ ,-σ and +σ respectively. The potent ial of shell B is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 14

Charge in sphere 


JEE Main 2018 Question Paper With Solutions (8 April) - Question 15

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be : 

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 15

qi = C0V
= 90 x 10-12 x 20
= 1800 x 10-12
= 1.8nC

JEE Main 2018 Question Paper With Solutions (8 April) - Question 16

In an a.c. circuit, the instantaneous e.m.f. and current are given by: 
e = 100 sin 30 t 
 .
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 16




JEE Main 2018 Question Paper With Solutions (8 April) - Question 17

Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10Ω. The internal resistances of the two batteries are 1Ω and 2Ω respectively. The voltage across the load lies between :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 17

The circuit may be drawn as shown in the figure.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 18

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 18

JEE Main 2018 Question Paper With Solutions (8 April) - Question 19

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B2. The ratio B1/B2 is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 19

Magnetic moment, and magnetic field at the centre of circle

JEE Main 2018 Question Paper With Solutions (8 April) - Question 20

For an RLC circuit driven with voltage of amplitude and frequency  the current exhibits resonance. The quality factor, Q is given by  

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 20


Alternate solution
 is the only dimensionless  quantity, hence must be the quality factor.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 21

An EM wave from air enters a medium. The electric fields are  in air and  in medium, where the wave number k and frequency refer to their values in air. The medium is non-magnetic. ∈r1 and ∈r2 refer to relative permitivit ies of air and medium respectively, which of the following options is correct ?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 21


Where

So volume in medium 1 = C
Volume in medium 2 = C/2 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 22

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be 1/2. Now  another identical polarizer C is placed between A and B. The intensity beyond B is now found to be 1/8 The angle between polarizer A and C is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 22

Unpolarized light of intensity I, when passed through a polarizer A, its intensity becomes I/2
Since intensity of light emerging from polarizer B = I/2
So, A & B are parallel placed.
Let, C makes angle θ with A.
So,

JEE Main 2018 Question Paper With Solutions (8 April) - Question 23

The angular width of the central maximum in a single slit diffraction pattern is 600. The width of the slit is 1μm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance of 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ?
(i.e. distance between the centres of each slit.)

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 23


JEE Main 2018 Question Paper With Solutions (8 April) - Question 24

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λng be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let ∧n be the wavelength of the emitted photon in the transit ion fro m the nth state to the ground state. For large n, (A, B are constants)

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 24

2πr = nλn



From equation (1) and (2)

JEE Main 2018 Question Paper With Solutions (8 April) - Question 25

If the series limit frequency of the Lyman series is then the series limit frequency of the Pfund series is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 25

Series limit frequency of the Lyman series is given by

Series limit frequency of the Pfund series 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 26

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 26


 (from conservation of momentum)
and K0 = K1 + K2 (for elastic collision)
So after solving

JEE Main 2018 Question Paper With Solutions (8 April) - Question 27

The reading of the ammeter for a silicon diode in the given circuit is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 27


JEE Main 2018 Question Paper With Solutions (8 April) - Question 28

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz ?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 28

No. of telephonic channels that can be transmitted simultaneously

JEE Main 2018 Question Paper With Solutions (8 April) - Question 29

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5Ω, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 29

When the cell is shunted by a resistance of 5 Ω

JEE Main 2018 Question Paper With Solutions (8 April) - Question 30

On interchanging the resistances, the balane point of a meter bridge shifts to the left by 10cm. The resistance of their series combinations is 1 kΩ. How much was the resistance on the left slot before interchanging the resistances?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 30

     (i)
      (ii)
From (i) and (ii)
⇒ l = 55 cm
    (1)
and  R1 + R 2 = 1000 Ω       (iii)
from  (i) and (iii)
R = 550 Ω

JEE Main 2018 Question Paper With Solutions (8 April) - Question 31

The ratio of mass present of C and H of an organic compound (CXHYOZ) is 6 : 1. If one molecule of the above compound (CXHYOZ) contains half as much oxygen as required to burn one molecule of compound CXHY completely to CO2 and H2O. The empirical formula of compound CXHYOZ is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 31




JEE Main 2018 Question Paper With Solutions (8 April) - Question 32

Which type of ‘defect’ has the presence of cations in the interstitial sites?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 32

In Frenkel defect, smaller ion displaces from its actual lattice site into the interstitial sites.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 33

According to molecular orbital theory, which of the following will not be a viable molecule? 

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 33

 electronic configuration 
Number of electrons =  
Molecule does not exist.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 34

Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 34


For exothermic reaction ΔH = -ve.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 35

The combustion of benzene (1) gives CO2(g) and H2O(I). Given that heat of combustion of benzene at constant volume is -3263.9 kJ mol-1 at 250 C; heat of combust ion (in kJ mol-1) of benzene at constant pressure will be :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 35

JEE Main 2018 Question Paper With Solutions (8 April) - Question 36

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 36


JEE Main 2018 Question Paper With Solutions (8 April) - Question 37

An aqueous solution contains 0.10 M H2S and 0.20 M HCl. If the equilibrium constants for the format ion of HS- from H2S is 1.0 x 10-7 and that of S2- from HS- ions is 1.2 x 10-13 then the concentration of S2- ions in aqueous solution is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 37


JEE Main 2018 Question Paper With Solutions (8 April) - Question 38

An aqueous solution contains an unknown concentration of Ba2+. When 50 mL of a 1M solution of Na2SO4 is added, BaSO4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO4 is 1 x 10-10. What is the original concentration of Ba2+ ?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 38



JEE Main 2018 Question Paper With Solutions (8 April) - Question 39

At 5180C, the rate of decomposition of a sample of gaseous acetaldehyde, initially ar a pressure of 363 Torr, was 1.00 Torr s-1 when 5% had reacted and 0.5 Torr s-1 when 33% had reacted. The order of the reaction is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 39



JEE Main 2018 Question Paper With Solutions (8 April) - Question 40

How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane?
(Atomic weight of B = 10.8 u)

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 40



Moles of O2 required = 3
Gram equivalent of O2 = 3 x 4= 12
Gram equivalent 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 41

The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting [3Ca3 (PO4)2 . Ca(OH)2]

JEE Main 2018 Question Paper With Solutions (8 April) - Question 42

Which of the following compounds contain(s) no covalent bond(s)?
KCl, PH3, O2, B2H6, H2SO4

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 42

KCl is an ionic compound. It cannot from covalent bond. Elements of s – block & p – block combine to form ionic compounds.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 43

Which of the following are Lewis acids?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 43

Both BCl3 and AlCl3 are Lewis acids as both ‘B’ and ‘Al’ has vacant p-orbitals. SiCl4 is also a Lewis acid as silicon atom has vacant 3d-orbital.
Therefore,both b and d options are possible.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 44

Total number of lone pair of electrons in I-3 ion is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 44

The total number of lone pair of electrons is I-3 is 9

JEE Main 2018 Question Paper With Solutions (8 April) - Question 45

Which of the following salts is the most basic in aqueous solution?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 45

CH3COOK is a salt of weak acid and strong base. Hydrolysis of potassium acetate gives strong base KOH

JEE Main 2018 Question Paper With Solutions (8 April) - Question 46

Hydrogen peroxide oxides [Fe(CN)6 ]4- to [Fe(CN)6]3-  in acidic medium but reduces [Fe(CN)6 ]3- to [Fe(CN)6]4- in alkaline medium. The other products formed are, respectively:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 46



JEE Main 2018 Question Paper With Solutions (8 April) - Question 47

The oxidation states of Cr in [Cr(H2O)6] Cl3 , [Cr(C6H6)2] and K2[Cr(CN)2 (O)2 (O2) NH3 ] respectively are :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 47

The Oxidation state of Cr in 
[Cr(H2O)6]CI3
x + 6(0) - 3 = 0
x = +3
[Cr(C6H6)2]
x + 2(0) = 0
x = 0
K2 [Cr (CN )2 (O)2 (O2) NH3]
+2 + x + 2 (-1) + 2 (-2) +1 (-2) + 0
= 6
∴ x =+6

JEE Main 2018 Question Paper With Solutions (8 April) - Question 48

The compound that does not produce nitrogen gas by the thermal decomposition is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 48

JEE Main 2018 Question Paper With Solutions (8 April) - Question 49

When metal ‘M’ is treated with NaOH, a white gelatinous precipitate ‘X’ is obtained, which is soluble in excess of NaOH. Compound ‘X’ when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal ‘M’ is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 49

The Gelatinous precipitate formed in Al(OH)3 ; Al(OH)3 on strong heating gives Al2O3 which is used in chromatography as an adsorbent. So the metal is A1.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 50

Consider the following reaction and statements:
[Co(NH3)4Br2]+ +Br→ [Co(NH3)3Br3] + NH3
(I) Two isomers are produced if the reactant complex ion is a cis-isomer.
(II) Two isomers are produced if the reactant complex ion is a trans-isomer.
(III) Only one isomer is produced if the reactant complex ion is a trans-isomer.
(IV) Only one isomer is produced if the reactant complex ion is a cis-isomer.
The correct statements are :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 50



As all the NH3 posit ions are identical only one product can be formed.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 51

Glucose on prolonged heating with HI gives :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 51


 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 52

The trans-alkenes are formed by the reduction of alkynes with :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 52

Trans alkenes are formed by the reaction of alkynes with Na/liq. NH3 (birch Reduction)

JEE Main 2018 Question Paper With Solutions (8 April) - Question 53

Which of the following compounds will be suitable for Kjeldahl’s method for nitrogen estimation?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 53

Kjeldahl’s method:-
Organic compounds nitrogen + 

Nitro compounds, A2O compounds & Nitrogen part of the aromatic ring will not give positive result for Kjeldahl’s method. Aniline is the best suitable to estimate nitrogen using Kjeldahl’s method.  

JEE Main 2018 Question Paper With Solutions (8 April) - Question 54

Phenol on treatment with CO2 in the presence of NaOH followed by acidification produces compound X as the major product. X on treatment with (CH3CO)2O in the presence of catalytic amount of H2SO4 produces :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 54

JEE Main 2018 Question Paper With Solutions (8 April) - Question 55

An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 55

When a weak base is titrated with string acid with methyl orange as an indicator then at end point The colour change will be yellow to pinkish red.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 56

The predominant form of histamine present in human blood is (pka , Histidine = 6.0)

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 56

JEE Main 2018 Question Paper With Solutions (8 April) - Question 57

Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br2 to form product B. A and B are respectively :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 57

JEE Main 2018 Question Paper With Solutions (8 April) - Question 58

The increasing order of basicity of the following compounds is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 58

Order of base nature depends on electron donation tendency.

It compounds (b) nitrogen is sp2 hybridized so least basic among all given compound

Compound (c) is a very strong nitrogeneous organic base as a lone pair of one nitrogen delocalize in resonance and make another nitrogen negatively charged and conjugate acid have two equivalent resonating structure.
Thus it is most basic in given compound.

(d) is secondary amin more than (a) which is a primary amine.

 

Order of base nature depends on electron donation tendency.

It compounds (b) nitrogen is sp2 hybridized so least basic among all given compound

Compound (c) is a very strong nitrogeneous organic base as a lone pair of one nitrogen delocalize in resonance and make another nitrogen negatively charged and conjugate acid have two equivalent resonating structure.
Thus it is most basic in given compound.

(d) is secondary amin more than (a) which is a primary amine

JEE Main 2018 Question Paper With Solutions (8 April) - Question 59

The major product formed in the following reaction is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 59

JEE Main 2018 Question Paper With Solutions (8 April) - Question 60

The major product of the following reaction is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 60

JEE Main 2018 Question Paper With Solutions (8 April) - Question 61

Let S= {x ∈ R : x ≥ 0 and 2 | √x - 3| + √x (√x - 6) + 6 = 0} . Then S :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 61



There are exactly two elements in the given set.

JEE Main 2018 Question Paper With Solutions (8 April) - Question 62

If α ,β ∈ c are the distinct roots, of the equation x2 -x +1 =0 , then α101 + β107 is equal to :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 62

x2 – x+ 1 = 0 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 63

Let a1 , a2 , a3 , ......, a49 be in A.P. such that  = 416 a9 + a43  = 66. 
If a12 + a22 + .... + a172 = 140m then m is equal to:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 63

a1 + a5 + a9 = 416 ⇒ a + 24d = 32 ......(i)
a9 + a43 = 66 ⇒ a + 25d = 33......(ii)
From (i) and (ii) d = 1 and a = 8

JEE Main 2018 Question Paper With Solutions (8 April) - Question 64

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series
1 + 2•22 + 32 + 2•42 + 52 + 2•62 + .....
If  B-2A=100λ, then λ is equal to:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 64

A = 12 + 2.22 + 32 + 2.42+ ………+ A2+2.202
= (12 + 2.22 + 32 + 42+ ………+202)+ (22+ 42+ ………+ 202)

= 2870 + 1540 = 4410 = 2870 + 1540 = 4410

= 540 x 41 + 41 x 280 = 41 x 820 = 33620
33620 - 8820 = 100λ
100λ = 24800
λ = 248

JEE Main 2018 Question Paper With Solutions (8 April) - Question 65

If the curve y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is: 

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 65

2yy’= 6


JEE Main 2018 Question Paper With Solutions (8 April) - Question 66

The integral is equal to:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 66




JEE Main 2018 Question Paper With Solutions (8 April) - Question 67

Let g(x) = cos x2 ,f(x) = √x, and α ,β (α < β) be the roots of the quadratic equation 18x2 - 9πx +π2 = 0. Then the area (in sq. units) bounded by the curve  y = (gof )(x) and the lines x =α , x = β and y = 0 , is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 67

g(x) = cos x2
f(x) = √x
g(f (x)) = cos x

JEE Main 2018 Question Paper With Solutions (8 April) - Question 68

Let y=y(x) be the solution of the differential equation

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 68


Integrating both sides we get y sin x = 2x2+ C

JEE Main 2018 Question Paper With Solutions (8 April) - Question 69

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 69

Let R = (h,k)
P = (0, k)
Q = (h,0)
Equation of line would be, 


2k + 3h = hk
Locus of (h, k) is 2y + 3x = xy

JEE Main 2018 Question Paper With Solutions (8 April) - Question 70

Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB=θ, then a value of tanq is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 70

The equation of tangent at P


The normal is y = y – 16 = -2(x – 16) 
B = (24, 0)

AB is the diameter
Centre of the circle C = (4, 0)
lope of PB = -2 = m1

JEE Main 2018 Question Paper With Solutions (8 April) - Question 71

Tangents are drawn to the hyperbola 4x2 -y2= 36 at the points P and Q. If these tangents intersects at the point T(0, 3) then the area (in sq. units) of ΔPTQ is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 71

Equation of PQ, 
4x.(0) -3y = 36

Y = -12 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 72

Let be a vector coplanar with the vectors  and  perpendicular to  then, is equal to :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 72



JEE Main 2018 Question Paper With Solutions (8 April) - Question 73

PQR is a triangular park with PQ=PR=200 m. A T.V. tower stands at the mid-point of QR. If the angle of elevation of the top of the tower at P,Q and R are respectively 450, 300 and 300 then the height of tower (in m) is :

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 73



200 = 3h2 +h2
4h= (200)2
4h= 40000
h = 100

JEE Main 2018 Question Paper With Solutions (8 April) - Question 74

The Boolean expression ~(p ν q) ν (~p ∧ q) is equivalent to:

Detailed Solution for JEE Main 2018 Question Paper With Solutions (8 April) - Question 74

JEE Main 2018 Question Paper With Solutions (8 April) - Question 75

Two sets A and B are as under :
A={(a, b) ∈ R x R : |a - 5| <1 and |b - 5|<1};
B={(a, b) ∈ R x R : 4(a - 6)2 + 9(b - 5)2 ≤ 36 }. Then :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 76

If  = ( A + Bx)( x- A)2 , then the ordered pair (A, B) is equal to :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 77

If the system of linear equations
x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0
has a non-zero solution (x, y, z), then xz/y2 is equal to:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 78

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 79

The sum of the co-efficients of all odd degree terms in the expansion of  

JEE Main 2018 Question Paper With Solutions (8 April) - Question 80

For each t ∈ R, let [t] be the greatest integer less than or equal to t. Than 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 81

Let S={t ∈ R:f(x)= |x - π| • (e|x| - 1) sin |x| is not different iable at t}. Then the set S is equal to:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 82

 Let  and g(x) = x - 1/x, x∈R - {-1, 0,1} . If  then the local minimum value of value of h(x) is :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 83

The value of  dx is: 

JEE Main 2018 Question Paper With Solutions (8 April) - Question 84

Let the orthocenter and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, than the radius of the circle having line segment AC as diameter, is :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 85

If the tangent at (1,7) to the curve x2 =y- 6 touches  the circle x2 + y2 +16x +12 y + c = 0 than the value of c is :

JEE Main 2018 Question Paper With Solutions (8 April) - Question 86

If L1 is the line of intersect ion of the planes  2x - 2y + 3z = 0, x - y + z = 0 and L2 is the line of intersection of the planes x + 2y - z - 3 = 0, 3x - y + 2z = 0 then the distance of the origin fro m the plane, containing the lane L1 and L2 , is:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 87

The length of the project ion of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x + y + z = 7 is:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 88

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two addit ional balls of the same colour is returned to the bag. If now a ball is drawn at random from the bag, then probability that this drawn ball is red, is:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 89

If  and  then the standard deviation of the 9 items x1 x2, …., x9 is:

JEE Main 2018 Question Paper With Solutions (8 April) - Question 90

If sum of all the solution of equation  in [0,π ] is kπ ,then k is equal  to :

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