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JEE Main 8 April 2019 Shift 1 Question Paper with Answers

8 April 2019 · April session · 86 questions

86 of the 90 questions from the JEE Main 8 April 2019 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

4 questions are held back from this paper while we re-check the transcription or the answer key. We would rather show you nothing than show you an answer we are not confident is right.

Physics
26
Chemistry
30
Mathematics
30

Physics — JEE Main 8 April 2019 Shift 1

Q1·PhysicsSingle correct
A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:
  1. (A)2.5 J
  2. (B)4 J
  3. (C)5 J
  4. (D)6.5 J

Correct answer: (D)

Step-by-step solution →
Q2·PhysicsSingle correct
Four particles A, B, C and D with masses mA=mm_A = mmA​=m, mB=2mm_B = 2mmB​=2m, mc=3mm_c = 3mmc​=3m and mD=4mm_D = 4mmD​=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:
  1. (A)a5(i^−j^)\dfrac{a}{5}(\hat{i} - \hat{j})5a​(i^−j^​)
  2. (B)Zero
  3. (C)a5(i^+j^)\dfrac{a}{5}(\hat{i} + \hat{j})5a​(i^+j^​)
  4. (D)a(i^+j^)a(\hat{i} + \hat{j})a(i^+j^​)

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8×1028 \times 10^{2}8×102 kg/m3^{3}3 and specific heat of 2000 J kg−1^{-1}−1 K−1^{-1}−1 while liquid in B has density of 10310^{3}103 kg m−3^{-3}−3 and specific heat of 4000 J Kg−1^{-1}−1 K−1^{-1}−1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 N m−1^{-1}−1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω10\,\Omega10Ω and air drag negligible, N will be close to:
  1. (A)50000
  2. (B)10000
  3. (C)1000
  4. (D)5000

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is
  1. (A)2ln⁡2\dfrac{2}{\ln 2}ln22​
  2. (B)ln⁡2\ln 2ln2
  3. (C)12ln⁡2\dfrac{1}{2}\ln 221​ln2
  4. (D)2ln⁡22\ln 22ln2

Correct answer: (D)

Step-by-step solution →
Q6·PhysicsSingle correct
A wire of length 2L is made by joining two wires A and b of same lengths but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is:
  1. (A)1 : 4
  2. (B)1 : 2
  3. (C)3 : 5
  4. (D)4 : 9

Correct answer: (B)

Step-by-step solution →
Q7·PhysicsSingle correct
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g=3.1πg = 3.1\pig=3.1π m s−2^{-2}−2, what will be the tensile stress that would be developed in the wire?
  1. (A)6.2×1066.2 \times 10^{6}6.2×106 N m−2^{-2}−2
  2. (B)4.8×1064.8 \times 10^{6}4.8×106 N m−2^{-2}−2
  3. (C)5.2×1065.2 \times 10^{6}5.2×106 N m−2^{-2}−2
  4. (D)3.1×1063.1 \times 10^{6}3.1×106 N m−2^{-2}−2

Correct answer: (D)

Step-by-step solution →
Q8·PhysicsSingle correct
Voltage rating of a parallel plate capacitor is 500V. Its dielectric can withstand a maximum electric field of 106 Vm10^{6}\,\dfrac{V}{m}106mV​. The plate area is 10−410^{-4}10−4 m2^{2}2. What is the dielectric constant if the capacitance is 15 pF? (given ϵ0=8.86×10−12\epsilon_{0} = 8.86 \times 10^{-12}ϵ0​=8.86×10−12 C2^{2}2/N m2^{2}2)
  1. (A)3.8
  2. (B)6.2
  3. (C)4.5
  4. (D)8.5

Correct answer: (D)

Step-by-step solution →
Q9·PhysicsSingle correct
An alternating voltage v(t)=220sin⁡100πtv(t) = 220 \sin 100\pi tv(t)=220sin100πt volt is applied to a purely resistive load of 50 Ω50\,\Omega50Ω. The time taken for the current to rise from half of the peak value of the peak value is:
  1. (A)2.2 ms
  2. (B)3.3 ms
  3. (C)5 ms
  4. (D)7.2 ms

Correct answer: (B)

Step-by-step solution →
Q10·PhysicsSingle correct
The wavelength of the carrier waves in a modern optical fiber communication network is close to:
  1. (A)1500 nm
  2. (B)600 nm
  3. (C)2400 nm
  4. (D)900 nm

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m3^{3}3, coefficient of viscosity of water = 1 mPa s)
  1. (A)10310^{3}103
  2. (B)10610^{6}106
  3. (C)10210^{2}102
  4. (D)10410^{4}104

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 m s−1^{-1}−1. Neglect the change in the area of cross section of the cord while stretched. The Young's modulus of rubber is closest to:
  1. (A)10310^{3}103 N m−2^{-2}−2
  2. (B)10610^{6}106 N m−2^{-2}−2
  3. (C)10810^{8}108 N m−2^{-2}−2
  4. (D)10410^{4}104 N m−2^{-2}−2

Correct answer: (B)

Step-by-step solution →
Q13·PhysicsSingle correct
Two particles move at right angle to each other. Their de Broglie wavelengths are λ1\lambda_1λ1​ and λ2\lambda_2λ2​ respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength λ\lambdaλ, of the final particle, is given by:
  1. (A)λ=λ1λ2\lambda = \sqrt{\lambda_1 \lambda_2}λ=λ1​λ2​​
  2. (B)λ=λ1+λ22\lambda = \dfrac{\lambda_1 + \lambda_2}{2}λ=2λ1​+λ2​​
  3. (C)2λ=1λ1+1λ2\dfrac{2}{\lambda} = \dfrac{1}{\lambda_1} + \dfrac{1}{\lambda_2}λ2​=λ1​1​+λ2​1​
  4. (D)1λ2=1λ12+1λ22\dfrac{1}{\lambda^{2}} = \dfrac{1}{\lambda_1^{2}} + \dfrac{1}{\lambda_2^{2}}λ21​=λ12​1​+λ22​1​

Correct answer: (D)

Step-by-step solution →
Q14·PhysicsSingle correct
Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?
  1. (A)1.35GMa1.35\sqrt{\dfrac{GM}{a}}1.35aGM​​
  2. (B)1.16GMa1.16\sqrt{\dfrac{GM}{a}}1.16aGM​​
  3. (C)1.41GMa1.41\sqrt{\dfrac{GM}{a}}1.41aGM​​
  4. (D)1.21GMa1.21\sqrt{\dfrac{GM}{a}}1.21aGM​​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
A circular coil having N turns and radius r carries a current. It is held in the XZ plane in a magnetic field Bi^B\hat{i}Bi^. The torque on the coil due to the magnetic field is:
  1. (A)Br2IπN\dfrac{Br^{2}I}{\pi N}πNBr2I​
  2. (B)zero
  3. (C)Bπr2IN\dfrac{B\pi r^{2}I}{N}NBπr2I​
  4. (D)Bπr2INB\pi r^{2}INBπr2IN

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
Ship A is sailing towards north-east with velocity v⃗=30i^+50j^\vec{v}=30\hat{i}+50\hat{j}v=30i^+50j^​ km/hr where i^\hat{i}i^ points east and j^\hat{j}j^​, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B ins:
  1. (A)2.2 hrs.
  2. (B)4.2 hrs.
  3. (C)2.6 hrs.
  4. (D)3.2 hrs.

Correct answer: (C)

Step-by-step solution →
Q17·PhysicsSingle correct
A thermally insulted vessel contains 150 g of water at 0°C0°C0°C. Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C0°C0°C itself. The mass of evaporated water will be closes to: (Latent heat of vaporization of water =2.10×106Jkg−1=2.10\times10^{6}Jkg^{-1}=2.10×106Jkg−1 and Laten heat of Fusion of water =3.36×105Jkg−1=3.36\times10^{5}Jkg^{-1}=3.36×105Jkg−1)
  1. (A)35 g
  2. (B)150 g
  3. (C)130 g
  4. (D)20 g

Correct answer: (D)

Step-by-step solution →
Q18·PhysicsSingle correct
Radiation coming from transition n = 2 to n = 1 of hydrogen atoms fall of He+He^{+}He+ ions in n = 1 and n = 2 states. The possible. Transition of helium ions as they absorb energy from the radiation is:
  1. (A)n=2→n=4n=2\rightarrow n=4n=2→n=4
  2. (B)n=2→n=5n=2\rightarrow n=5n=2→n=5
  3. (C)n=2→n=3n=2\rightarrow n=3n=2→n=3
  4. (D)n=1→n=4n=1\rightarrow n=4n=1→n=4

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
A 200Ω200\Omega200Ω resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be:
  1. (A)500Ω500\Omega500Ω
  2. (B)400Ω400\Omega400Ω
  3. (C)300Ω300\Omega300Ω
  4. (D)100Ω100\Omega100Ω

Correct answer: (A)

Step-by-step solution →
Q20·PhysicsSingle correct
The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit . The current IzI_zIz​ through the Zener is:
  1. (A)10 mA
  2. (B)15 mA
  3. (C)7 mA
  4. (D)17 mA

Correct answer: (A)

Step-by-step solution →
Q21·PhysicsSingle correct
A thin circular plate of mass M and radius R has its density varying as p(r)=p0rp(r)=p_0 rp(r)=p0​r with P0P_0P0​ as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I=aMR2I=aMR^{2}I=aMR2. The value of the coefficient a is:
  1. (A)85\dfrac{8}{5}58​
  2. (B)12\dfrac{1}{2}21​
  3. (C)35\dfrac{3}{5}53​
  4. (D)32\dfrac{3}{2}23​

Correct answer: (A)

Step-by-step solution →
Q22·PhysicsSingle correct
In SI units, the dimensions of ϵ0μ0\sqrt{\dfrac{\epsilon_0}{\mu_0}}μ0​ϵ0​​​ is:
  1. (A)AT−3ML3/2AT^{-3}ML^{3/2}AT−3ML3/2
  2. (B)A−1TML3A^{-1}TML^{3}A−1TML3
  3. (C)A2T3M−1L−2A^{2}T^{3}M^{-1}L^{-2}A2T3M−1L−2
  4. (D)AT2M−1L−1AT^{2}M^{-1}L^{-1}AT2M−1L−1

Correct answer: (C)

Step-by-step solution →
Q23·PhysicsSingle correct
For the circuit shown, with R1=1.0ΩR_1=1.0\OmegaR1​=1.0Ω, R2=2.0ΩR_2=2.0\OmegaR2​=2.0Ω, E1=2VE_1=2VE1​=2V and E2=E3=4VE_2=E_3=4VE2​=E3​=4V, the potential difference between the points 'a' and 'b' is approximately (in V):
  1. (A)3.3
  2. (B)2.3
  3. (C)3.7
  4. (D)2.7

Correct answer: (A)

Step-by-step solution →
Q24·PhysicsSingle correct
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of −4 Q, the new potential difference between the same two surface is:
  1. (A)2 V
  2. (B)−2V
  3. (C)4 V
  4. (D)V

Correct answer: (D)

Step-by-step solution →
Q25·PhysicsSingle correct
In an interference experiment the ratio of amplitudes of coherent waves is a1a2=13\dfrac{a_1}{a_2}=\dfrac{1}{3}a2​a1​​=31​. The ratio of maximum and minimum intensities of fringes will be:
  1. (A)9
  2. (B)4
  3. (C)18
  4. (D)2

Correct answer: (B)

Step-by-step solution →
Q26·PhysicsSingle correct
The bob of a simple pendulum has mass 2g and a charge of 5.0μC5.0\mu C5.0μC. It is at rest in a uniform horizontal electric field of intensity 2000Vm2000\dfrac{V}{m}2000mV​. At equilibrium, the angle that the pendulum makes with the vertical is: (take g=10ms2g=10\dfrac{m}{s^2}g=10s2m​)
  1. (A)tan⁡−1(2.0)\tan^{-1}(2.0)tan−1(2.0)
  2. (B)tan⁡−1(0.2)\tan^{-1}(0.2)tan−1(0.2)
  3. (C)tan⁡−1(5.0)\tan^{-1}(5.0)tan−1(5.0)
  4. (D)tan⁡−1(0.5)\tan^{-1}(0.5)tan−1(0.5)

Correct answer: (D)

Step-by-step solution →

Chemistry — JEE Main 8 April 2019 Shift 1

Q27·ChemistrySingle correct
Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is
  1. (A)A2B2OA_2B_2OA2​B2​O
  2. (B)AB2O4AB_2O_4AB2​O4​
  3. (C)A4B2OA_4B_2OA4​B2​O
  4. (D)A2BO4A_2BO_4A2​BO4​

Correct answer: (B)

Step-by-step solution →
Q28·ChemistrySingle correct
Coupling of benzene diazonium chloride with 1 – naphthol in alkaline medium will give:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q29·ChemistrySingle correct
The size of the iso-electronic species Cl−Cl^-Cl−, Ar and Ca2+Ca^{2+}Ca2+ is affected by
  1. (A)Principal quantum number of valence shell
  2. (B)Azimuthal quantum number of valence shell
  3. (C)electron – electron interaction in the outer orbitals
  4. (D)nuclear charge

Correct answer: (D)

Step-by-step solution →
Q30·ChemistrySingle correct
In the following compounds, the decreasing order of basic strength will be:
  1. (A)C2H5NH2>NH3>(C2H5)2NHC_2H_5NH_2 > NH_3 > (C_2H_5)_2NHC2​H5​NH2​>NH3​>(C2​H5​)2​NH
  2. (B)NH3>C2H5NH2>(C2H5)2NHNH_3 > C_2H_5NH_2 > (C_2H_5)_2NHNH3​>C2​H5​NH2​>(C2​H5​)2​NH
  3. (C)(C2H5)2NH>C2H5NH2>NH3(C_2H_5)_2NH > C_2H_5NH_2 > NH_3(C2​H5​)2​NH>C2​H5​NH2​>NH3​
  4. (D)(C2H5)2NH>NH3>C2H5NH2(C_2H_5)_2NH > NH_3 > C_2H_5NH_2(C2​H5​)2​NH>NH3​>C2​H5​NH2​

Correct answer: (C)

Step-by-step solution →
Q31·ChemistrySingle correct
The correct order of the spin only magnetic moment of metal ions in the following low spin complexes, [V(CN)6]4−[V(CN)_6]^{4-}[V(CN)6​]4−, [Fe(CN)6]4−[Fe(CN)_6]^{4-}[Fe(CN)6​]4−, [Ru(NH3)6]3+[Ru(NH_3)_6]^{3+}[Ru(NH3​)6​]3+, and [Cr(NH3)6]2+[Cr(NH_3)_6]^{2+}[Cr(NH3​)6​]2+, is:
  1. (A)Cr2+>Ru3+>Fe2+>V2+Cr^{2+} > Ru^{3+} > Fe^{2+} > V^{2+}Cr2+>Ru3+>Fe2+>V2+
  2. (B)V2+>Cr2+>Ru3+>Fe2+V^{2+} > Cr^{2+} > Ru^{3+} > Fe^{2+}V2+>Cr2+>Ru3+>Fe2+
  3. (C)Cr2+>V2+>Ru3+>Fe2+Cr^{2+} > V^{2+} > Ru^{3+} > Fe^{2+}Cr2+>V2+>Ru3+>Fe2+
  4. (D)V2+>Ru3+>Cr2+>Fe2+V^{2+} > Ru^{3+} > Cr^{2+} > Fe^{2+}V2+>Ru3+>Cr2+>Fe2+

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
An organic compound 'X' showing the following solubility profile is:
  1. (A)Oleic acid
  2. (B)o – Toluidine
  3. (C)Benzamide
  4. (D)m – Cresol

Correct answer: (D)

Step-by-step solution →
Q33·ChemistrySingle correct
Diborane (B2H6B_2H_6B2​H6​) reacts independently with O2O_2O2​ and H2OH_2OH2​O to produce, respectively:
  1. (A)H3BO3H_3BO_3H3​BO3​ and B2O3B_2O_3B2​O3​
  2. (B)B2O3B_2O_3B2​O3​ and H3BO3H_3BO_3H3​BO3​
  3. (C)HBO2HBO_2HBO2​ and H3BO3H_3BO_3H3​BO3​
  4. (D)B2O3B_2O_3B2​O3​ and [BH4]−[BH_4]^-[BH4​]−

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
The lanthanoide that would show colour is:
  1. (A)Gd3+Gd^{3+}Gd3+
  2. (B)La3+La^{3+}La3+
  3. (C)Lu3+Lu^{3+}Lu3+
  4. (D)Sm3+Sm^{3+}Sm3+

Correct answer: (D)

Step-by-step solution →
Q35·ChemistrySingle correct
The major product of the following reaction
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q36·ChemistrySingle correct
100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of CaCO3CaCO_3CaCO3​ is: (molar mass of calcium bicarbonate is 162 g mol−1162\ g\ mol^{-1}162 g mol−1 and magnesium bicarbonate is 146 g mol−1146\ g\ mol^{-1}146 g mol−1)
  1. (A)10,000 ppm
  2. (B)1,000 ppm
  3. (C)5,000 ppm
  4. (D)100 ppm

Correct answer: (A)

Step-by-step solution →
Q37·ChemistrySingle correct
An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent and gives positive iodoform test. The compound is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
For the reaction 2A+B→C2A + B \rightarrow C2A+B→C, the values of initial rate at different reactant concentrations are given in the table below: The rate law for the reaction is:
[A] (mol L−1^{-1}−1)[B] (mol L−1^{-1}−1)Initial Rate (mol L−1^{-1}−1s−1^{-1}−1)
0.050.050.045
0.100.050.090
0.200.100.72
  1. (A)Rate = k[A]2[B]2k[A]^2[B]^2k[A]2[B]2
  2. (B)Rate = k[A][B]2k[A][B]^2k[A][B]2
  3. (C)Rate = k[A][B]k[A][B]k[A][B]
  4. (D)Rate = k[A]2[B]k[A]^2[B]k[A]2[B]

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
The major product of the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q40·ChemistrySingle correct
Which is wrong with respect to our responsibility as a human being to protect our environment?
  1. (A)Restricting the use of vehicles
  2. (B)Using plastic bags
  3. (C)Setting up compost tin in gardens
  4. (D)Avoiding the use of floodlighted facilities.

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
The major product of the following reaction
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
For silver CP(JK−1mol−1)=23+0.01TC_P (JK^{-1} mol^{-1}) = 23 + 0.01TCP​(JK−1mol−1)=23+0.01T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of ΔH\Delta HΔH will be close to:
  1. (A)13 kJ
  2. (B)62 kJ
  3. (C)16 kJ
  4. (D)21 kJ

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
The correct order of hydration enthalpies of alkali metal ions is:
  1. (A)Li+>Na+>K+>Cs+>Rb+Li^+ > Na^+ > K^+ > Cs^+ > Rb^+Li+>Na+>K+>Cs+>Rb+
  2. (B)Na+>Li+>K+>Rb+>Cs+Na^+ > Li^+ > K^+ > Rb^+ > Cs^+Na+>Li+>K+>Rb+>Cs+
  3. (C)Na+>Li+>K+>Cs+>Rb+Na^+ > Li^+ > K^+ > Cs^+ > Rb^+Na+>Li+>K+>Cs+>Rb+
  4. (D)Li+>Na+>K+>Rb+>Cs+Li^+ > Na^+ > K^+ > Rb^+ > Cs^+Li+>Na+>K+>Rb+>Cs+

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot of log⁡xm\log \dfrac{x}{m}logmx​ versus log⁡p\log plogp is shown in the given graph, xm\dfrac{x}{m}mx​ is proportional to:
  1. (A)p2/3p^{2/3}p2/3
  2. (B)p2p^2p2
  3. (C)p3p^3p3
  4. (D)p3/2p^{3/2}p3/2

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are:
  1. (A)500 mmHg, 0.4, 0.6
  2. (B)500 mmHg, 0.5, 0.5
  3. (C)450 mmHg, 0.5, 0.5
  4. (D)450 mmHg, 0.4, 0.6

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
Given that EO2/H2O0=+1.23VE^0_{O_2/H_2O} = +1.23VEO2​/H2​O0​=+1.23V; ES2O82−/SO42−0=2.05VE^0_{S_2O_8^{2-}/SO_4^{2-}} = 2.05VES2​O82−​/SO42−​0​=2.05V; EBr2/Br−0=+1.09VE^0_{Br_2/Br^-} = +1.09VEBr2​/Br−0​=+1.09V; EAu3+/Au0=1.4VE^0_{Au^{3+}/Au} = 1.4VEAu3+/Au0​=1.4V. The strongest oxidizing agent is:
  1. (A)O2O_2O2​
  2. (B)S2O82−S_2O_8^{2-}S2​O82−​
  3. (C)Au3+Au^{3+}Au3+
  4. (D)Br2Br_2Br2​

Correct answer: (B)

Step-by-step solution →
Q47·ChemistrySingle correct
The quantum number of four electrons are given below: I. n=4,l=2,ml=−2,ms=−1/2n=4, l=2, m_l=-2, m_s=-1/2n=4,l=2,ml​=−2,ms​=−1/2 II. n=3,l=2,ml=1,m8=+1/2n=3, l=2, m_l=1, m_8=+1/2n=3,l=2,ml​=1,m8​=+1/2 III. n=4,l=1,ml=0,ms=+1/2n=4, l=1, m_l=0, m_s=+1/2n=4,l=1,ml​=0,ms​=+1/2 IV. n=3,l=1,ml=1,ms=−1/2n=3, l=1, m_l=1, m_s=-1/2n=3,l=1,ml​=1,ms​=−1/2 The correct order of their increasing energies will be:
  1. (A)I < III < II < IV
  2. (B)I < II < III < IV
  3. (C)IV < II < III < I
  4. (D)IV < III < II < I

Correct answer: (C)

Step-by-step solution →
Q48·ChemistrySingle correct
If solubility product of Zr3(PO4)4Zr_3(PO_4)_4Zr3​(PO4​)4​ is denoted by KSPK_{SP}KSP​ and its molar solubility is denoted by S, then which of the following relation between S and KSPK_{SP}KSP​ is correct?
  1. (A)S=(KSP6912)1/7S = \left(\dfrac{K_{SP}}{6912}\right)^{1/7}S=(6912KSP​​)1/7
  2. (B)S=(KSP144)1/6S = \left(\dfrac{K_{SP}}{144}\right)^{1/6}S=(144KSP​​)1/6
  3. (C)S=(KSp929)1/9S = \left(\dfrac{K_{Sp}}{929}\right)^{1/9}S=(929KSp​​)1/9
  4. (D)S=(KSP216)1/7S = \left(\dfrac{K_{SP}}{216}\right)^{1/7}S=(216KSP​​)1/7

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
Which of the following amines can be prepared by Gabriel phthalimide reaction?
  1. (A)t – butylamine
  2. (B)n – butylamine
  3. (C)neo – pentylamine
  4. (D)triethylamine

Correct answer: (B)

Step-by-step solution →
Q50·ChemistrySingle correct
Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non–expansion work is zero)
  1. (A)Adiabatic process: ΔU=−w\Delta U = -wΔU=−w
  2. (B)Isochoric process: ΔU=q\Delta U = qΔU=q
  3. (C)Cyclic process: q=−wq = -wq=−w
  4. (D)Isothermal process: q=−wq = -wq=−w

Correct answer: (A)

Step-by-step solution →
Q51·ChemistrySingle correct
The following ligand is:
  1. (A)tridentate
  2. (B)bidentate
  3. (C)tetradentate
  4. (D)hexadentate

Correct answer: (C)

Step-by-step solution →
Q52·ChemistrySingle correct
The IUPAC name of the following compound is:
  1. (A)3-Hydroxy – 4 – methylpentaonic acid
  2. (B)4 – Methyl – 3 – hydroxypentanoic acid
  3. (C)2 – Methyl – 3 – hydroxylpentan-5-oic acid
  4. (D)4, 4 – Dimethyl – 3 – hydroxybutanoic acid

Correct answer: (A)

Step-by-step solution →
Q53·ChemistrySingle correct
In order to oxidize a mixture of one mole of each of FeC2O4FeC_2O_4FeC2​O4​, Fe2(C2O4)3Fe_2(C_2O_4)_3Fe2​(C2​O4​)3​, FeSO4FeSO_4FeSO4​ and Fe2(SO4)3Fe_2(SO_4)_3Fe2​(SO4​)3​ in acidic medium, the number of moles of KMnO4KMnO_4KMnO4​ required is:
  1. (A)1
  2. (B)1.5
  3. (C)2
  4. (D)3

Correct answer: (C)

Step-by-step solution →
Q54·ChemistrySingle correct
Assertion : Ozone is destroyed by CFCs in the upper stratosphere. Reason : Ozone holes increase the amount of UV radiation reaching the earth.
  1. (A)Assertion and reason are incorrect
  2. (B)Assertion is false, but the reason is correct
  3. (C)Assertion and reasons are both correct, and the reason is the correct explanation for the assertion.
  4. (D)Assertion and reason are correct, but the reason is not the explanation for the assertion.

Correct answer: (D)

Step-by-step solution →
Q55·ChemistrySingle correct
Maltose on treatment with dilute HCl gives:
  1. (A)D – Fructose
  2. (B)D – Galactose
  3. (C)D – Glucose and D – Fructose
  4. (D)D – Glucose

Correct answer: (D)

Step-by-step solution →
Q56·ChemistrySingle correct
With respect to an ore, Ellingham diagram helps to predict the feasibility of its
  1. (A)Electrolysis
  2. (B)Thermal reduction
  3. (C)Vapour phase refining
  4. (D)Zone refining

Correct answer: (B)

Step-by-step solution →

Mathematics — JEE Main 8 April 2019 Shift 1

Q57·MathematicsSingle correct
The magnitude of the projection of the vector 2i^+3j^+k^2\hat{i}+3\hat{j}+\hat{k}2i^+3j^​+k^ on the vector perpendicular to the plane containing the vectors i^+j^+k^\hat{i}+\hat{j}+\hat{k}i^+j^​+k^ and i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k}i^+2j^​+3k^, is:
  1. (A)363\sqrt{6}36​
  2. (B)32\frac{\sqrt{3}}{2}23​​
  3. (C)6\sqrt{6}6​
  4. (D)32\sqrt{\frac{3}{2}}23​​

Correct answer: (D)

Step-by-step solution →
Q58·MathematicsSingle correct
The shortest distance between the line y=xy=xy=x and the curve y2=x−2y^{2}=x-2y2=x−2 is:
  1. (A)1142\frac{11}{4\sqrt{2}}42​11​
  2. (B)222
  3. (C)742\frac{7}{4\sqrt{2}}42​7​
  4. (D)78\frac{7}{8}87​

Correct answer: (C)

Step-by-step solution →
Q59·MathematicsSingle correct
If α\alphaα and β\betaβ be the roots of the equation x2−2x+2=0x^{2}-2x+2=0x2−2x+2=0, then the least value of n for which (αβ)n=1\left(\frac{\alpha}{\beta}\right)^{n}=1(βα​)n=1 is:
  1. (A)444
  2. (B)222
  3. (C)555
  4. (D)333

Correct answer: (A)

Step-by-step solution →
Q60·MathematicsSingle correct
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is:
  1. (A)180180180
  2. (B)175175175
  3. (C)162162162
  4. (D)160160160

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
∫sin⁡5x2sin⁡x2dx\int \frac{\sin\frac{5x}{2}}{\sin\frac{x}{2}}dx∫sin2x​sin25x​​dx is equal to: (where c is a constant of integration).
  1. (A)x+2sin⁡x+2sin⁡2x+cx+2\sin x+2\sin 2x+cx+2sinx+2sin2x+c
  2. (B)2x+sin⁡x+2sin⁡2x+c2x+\sin x+2\sin 2x+c2x+sinx+2sin2x+c
  3. (C)x+2sin⁡x+sin⁡2x+cx+2\sin x+\sin 2x+cx+2sinx+sin2x+c
  4. (D)2x+sin⁡x+sin⁡2x+c2x+\sin x+\sin 2x+c2x+sinx+sin2x+c

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
Let O (0, 0) and A (0, 1) be two fixed points. Then the locus of a point P such that the perimeter of △AOP\triangle AOP△AOP, is 4, is:
  1. (A)9x2−8y2+8y=169x^{2}-8y^{2}+8y=169x2−8y2+8y=16
  2. (B)8x2+9y2−9y=188x^{2}+9y^{2}-9y=188x2+9y2−9y=18
  3. (C)9x2+8y2−8y=169x^{2}+8y^{2}-8y=169x2+8y2−8y=16
  4. (D)8x2−9y2+9y=188x^{2}-9y^{2}+9y=188x2−9y2+9y=18

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
If cos⁡(α+β)=35\cos(\alpha+\beta)=\frac{3}{5}cos(α+β)=53​, sin⁡(α−β)=513\sin(\alpha-\beta)=\frac{5}{13}sin(α−β)=135​ and 0<α,β<π40<\alpha,\beta<\frac{\pi}{4}0<α,β<4π​, then tan⁡(2α)\tan(2\alpha)tan(2α) is equal to:
  1. (A)6352\frac{63}{52}5263​
  2. (B)3352\frac{33}{52}5233​
  3. (C)6316\frac{63}{16}1663​
  4. (D)2116\frac{21}{16}1621​

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Let A=(cos⁡α−sin⁡αsin⁡αcos⁡α)A=\begin{pmatrix}\cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha\end{pmatrix}A=(cosαsinα​−sinαcosα​), (α∈R)(\alpha \in R)(α∈R) such that A32=(0−110)A^{32}=\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}A32=(01​−10​). Then a value of α\alphaα is:
  1. (A)000
  2. (B)π16\frac{\pi}{16}16π​
  3. (C)π32\frac{\pi}{32}32π​
  4. (D)π64\frac{\pi}{64}64π​

Correct answer: (D)

Step-by-step solution →
Q65·MathematicsSingle correct
If f(x)=log⁡e(1−x1+x)f(x)=\log_{e}\left(\frac{1-x}{1+x}\right)f(x)=loge​(1+x1−x​), ∣x∣<1|x|<1∣x∣<1, then f(2x1+x2)f\left(\frac{2x}{1+x^{2}}\right)f(1+x22x​) is equal to:
  1. (A)2f(x)2f(x)2f(x)
  2. (B)(f(x))2\left(f(x)\right)^{2}(f(x))2
  3. (C)2f(x2)2f(x^{2})2f(x2)
  4. (D)−2f(x)-2f(x)−2f(x)

Correct answer: (A)

Step-by-step solution →
Q66·MathematicsSingle correct
If 2y=(cot⁡−1(3cos⁡x+sin⁡xcos⁡x−3sin⁡x))22y=\left(\cot^{-1}\left(\frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x}\right)\right)^{2}2y=(cot−1(cosx−3​sinx3​cosx+sinx​))2, x∈(0,π2)x \in \left(0,\frac{\pi}{2}\right)x∈(0,2π​) then dydx\frac{dy}{dx}dxdy​ is equal to
  1. (A)π6−x\frac{\pi}{6}-x6π​−x
  2. (B)π3−x\frac{\pi}{3}-x3π​−x
  3. (C)x−π6x-\frac{\pi}{6}x−6π​
  4. (D)2x−π32x-\frac{\pi}{3}2x−3π​

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
The sum of the solutions of the equation ∣x−2∣+x(x−4)+2=0\left|\sqrt{x}-2\right|+\sqrt{x}\left(\sqrt{x}-4\right)+2=0∣x​−2∣+x​(x​−4)+2=0, (x>0)(x>0)(x>0) is equal to:
  1. (A)999
  2. (B)444
  3. (C)101010
  4. (D)121212

Correct answer: (C)

Step-by-step solution →
Q68·MathematicsSingle correct
lim⁡x→0sin⁡2x2−1+cos⁡x\displaystyle\lim_{x\to 0}\frac{\sin^{2}x}{\sqrt{2}-\sqrt{1+\cos x}}x→0lim​2​−1+cosx​sin2x​ equals
  1. (A)2\sqrt{2}2​
  2. (B)424\sqrt{2}42​
  3. (C)444
  4. (D)222\sqrt{2}22​

Correct answer: (B)

Step-by-step solution →
Q69·MathematicsSingle correct
2⋅20C0+5⋅20C1+8⋅20C2+11⋅20C3+....+62⋅20C202\cdot {}^{20}C_{0}+5\cdot {}^{20}C_{1}+8\cdot {}^{20}C_{2}+11\cdot {}^{20}C_{3}+....+62\cdot {}^{20}C_{20}2⋅20C0​+5⋅20C1​+8⋅20C2​+11⋅20C3​+....+62⋅20C20​ is equal to
  1. (A)2232^{23}223
  2. (B)2262^{26}226
  3. (C)2242^{24}224
  4. (D)2252^{25}225

Correct answer: (D)

Step-by-step solution →
Q70·MathematicsSingle correct
Let y=y(x)y=y(x)y=y(x) be the solutions of the differential equation, (x2+1)2dydx+2x(x2+1)y=1\left(x^{2}+1\right)^{2}\frac{dy}{dx}+2x\left(x^{2}+1\right)y=1(x2+1)2dxdy​+2x(x2+1)y=1 such that y(0)=0y(0)=0y(0)=0. If a y(1)=π32\sqrt{a}\,y(1)=\frac{\pi}{32}a​y(1)=32π​, then the value of 'a' is
  1. (A)12\frac{1}{2}21​
  2. (B)111
  3. (C)116\frac{1}{16}161​
  4. (D)14\frac{1}{4}41​

Correct answer: (C)

Step-by-step solution →
Q71·MathematicsSingle correct
If f(x)=2−xcos⁡x2+xcos⁡xf(x)=\frac{2-x\cos x}{2+x\cos x}f(x)=2+xcosx2−xcosx​ and g(x)=log⁡ex,(x>0)g(x)=\log_{e}x,(x>0)g(x)=loge​x,(x>0) then the value of the integral ∫−π/4π/4g(f(x))dx\displaystyle\int_{-\pi/4}^{\pi/4} g\left(f(x)\right)dx∫−π/4π/4​g(f(x))dx is:
  1. (A)log⁡e1\log_{e}1loge​1
  2. (B)log⁡e2\log_{e}2loge​2
  3. (C)log⁡ee\log_{e}eloge​e
  4. (D)log⁡e3\log_{e}3loge​3

Correct answer: (A)

Step-by-step solution →
Q72·MathematicsSingle correct
The area (in sq. units) of the region A={(x,y)∈R×R∣0≤x≤3,0≤y≤4,y≤x2+3x}A=\{(x,y)\in R\times R \mid 0\le x\le 3, 0\le y\le 4, y\le x^{2}+3x\}A={(x,y)∈R×R∣0≤x≤3,0≤y≤4,y≤x2+3x} is:
  1. (A)263\dfrac{26}{3}326​
  2. (B)596\dfrac{59}{6}659​
  3. (C)536\dfrac{53}{6}653​
  4. (D)8

Correct answer: (B)

Step-by-step solution →
Q73·MathematicsSingle correct
The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is:
  1. (A)40
  2. (B)45
  3. (C)49
  4. (D)48

Correct answer: (D)

Step-by-step solution →
Q74·MathematicsSingle correct
The length of the perpendicular from the point (2, −1, 4) on the straight line, x+310=y−2−7=z1\dfrac{x+3}{10}=\dfrac{y-2}{-7}=\dfrac{z}{1}10x+3​=−7y−2​=1z​ is:
  1. (A)greater than 2 but less than 3
  2. (B)less than 2
  3. (C)greater than 4
  4. (D)greater than 3 but less than 4

Correct answer: (D)

Step-by-step solution →
Q75·MathematicsSingle correct
The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:
  1. (A)If you are a citizen of India, then you are born in India
  2. (B)If your are not a citizen of India, then you are not born in India
  3. (C)If you are no born in India, then you are not a citizen of India
  4. (D)If you are born in India, then you are not a citizen of India

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
The sum of all natural numbers 'n' such that 100<n<200100<n<200100<n<200 and H.C. F (91, n) > 1 is:
  1. (A)3221
  2. (B)3303
  3. (C)3203
  4. (D)3121

Correct answer: (D)

Step-by-step solution →
Q77·MathematicsSingle correct
If S1S_{1}S1​ and S2S_{2}S2​ are respectively the sets of local minimum and local maximum points of the function. f(x)=9x4+12x3−36x2+25,x∈Rf(x)=9x^{4}+12x^{3}-36x^{2}+25, x\in Rf(x)=9x4+12x3−36x2+25,x∈R, then
  1. (A)S1={−2,1};S2={0}S_{1}=\{-2,1\};S_{2}=\{0\}S1​={−2,1};S2​={0}
  2. (B)S1={−2,0};S2={1}S_{1}=\{-2,0\};S_{2}=\{1\}S1​={−2,0};S2​={1}
  3. (C)S1={−2};S2={0,1}S_{1}=\{-2\};S_{2}=\{0,1\}S1​={−2};S2​={0,1}
  4. (D)S1={−1};S2={0,2}S_{1}=\{-1\};S_{2}=\{0,2\}S1​={−1};S2​={0,2}

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsSingle correct
The sum of the co-efficient of all even degree terms in x in the expansion of (x+x3−1)6+(x−x3−1)6,(x>1)\left(x+\sqrt{x^{3}-1}\right)^{6}+\left(x-\sqrt{x^{3}-1}\right)^{6},(x>1)(x+x3−1​)6+(x−x3−1​)6,(x>1) is equal to:
  1. (A)26
  2. (B)24
  3. (C)32
  4. (D)29

Correct answer: (B)

Step-by-step solution →
Q79·MathematicsSingle correct
A point on the straight line, 3x+5y=153x+5y=153x+5y=15 which is equidistant from the coordinate, axes will lie only in:
  1. (A)4th quadrant
  2. (B)1st, 2nd and 4th quadrants
  3. (C)1st quadrant
  4. (D)1st and 2nd quadrants

Correct answer: (D)

Step-by-step solution →
Q80·MathematicsSingle correct
If the tangents on the ellipse 4x2+y2=84x^{2}+y^{2}=84x2+y2=8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2a^{2}a2 is equal to:
  1. (A)217\dfrac{2}{17}172​
  2. (B)417\dfrac{4}{17}174​
  3. (C)6417\dfrac{64}{17}1764​
  4. (D)12817\dfrac{128}{17}17128​

Correct answer: (A)

Step-by-step solution →
Q81·MathematicsSingle correct
If α=cos⁡−1(35),β=tan⁡−1(13)\alpha=\cos^{-1}\left(\dfrac{3}{5}\right), \beta=\tan^{-1}\left(\dfrac{1}{3}\right)α=cos−1(53​),β=tan−1(31​), where 0<α,β<π20<\alpha,\beta<\dfrac{\pi}{2}0<α,β<2π​, then α−β\alpha-\betaα−β is equal to:
  1. (A)sin⁡−1(9510)\sin^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)sin−1(510​9​)
  2. (B)cos⁡−1(9510)\cos^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)cos−1(510​9​)
  3. (C)tan⁡−1(9510)\tan^{-1}\left(\dfrac{9}{5\sqrt{10}}\right)tan−1(510​9​)
  4. (D)tan⁡−1(914)\tan^{-1}\left(\dfrac{9}{14}\right)tan−1(149​)

Correct answer: (A)

Step-by-step solution →
Q82·MathematicsSingle correct
The equation of a plane containing the line of intersection of the planes 2x−y−4=02x-y-4=02x−y−4=0 and y+2z−4=0y+2z-4=0y+2z−4=0 and passing through the point (1, 1, 0) is:
  1. (A)x+3y+z=4x+3y+z=4x+3y+z=4
  2. (B)2x−z=22x-z=22x−z=2
  3. (C)x−3y−2z=−2x-3y-2z=-2x−3y−2z=−2
  4. (D)x−y−z=0x-y-z=0x−y−z=0

Correct answer: (D)

Step-by-step solution →
Q83·MathematicsSingle correct
The sum of the squares of the lengths of the chords intercepted on the circle, x2+y2=16x^{2}+y^{2}=16x2+y2=16, by the lines, x+y=n,n∈Nx+y=n, n\in Nx+y=n,n∈N, where N is the set of all natural numbers is:
  1. (A)320
  2. (B)160
  3. (C)105
  4. (D)210

Correct answer: (D)

Step-by-step solution →
Q84·MathematicsSingle correct
The greatest value of c∈Rc\in Rc∈R for which the system of linear equations x−cy−cz=0x-cy-cz=0x−cy−cz=0 cx−y+cz=0cx-y+cz=0cx−y+cz=0 cx+cy−z=0cx+cy-z=0cx+cy−z=0 has a non-trivial solution, is:
  1. (A)-1
  2. (B)2
  3. (C)12\dfrac{1}{2}21​
  4. (D)0

Correct answer: (C)

Step-by-step solution →
Q85·MathematicsSingle correct
Let f:[0,2]→Rf:[0,2]\to Rf:[0,2]→R be a twice differentiable function such that f′′(x)>0f''(x)>0f′′(x)>0, for all x∈(0,2)x\in(0,2)x∈(0,2). If ϕ(x)=f(x)+f(2−x)\phi(x)=f(x)+f(2-x)ϕ(x)=f(x)+f(2−x), then ϕ\phiϕ is:
  1. (A)increasing on (0, 2)
  2. (B)decreasing on (0, 2)
  3. (C)decreasing on (0, 1) and increasing on (1, 2)
  4. (D)increasing on (0, 1) and decreasing on (1, 2)

Correct answer: (C)

Step-by-step solution →
Q86·MathematicsSingle correct
Let A and b be two non-null events such that A⊂BA\subset BA⊂B. Then, which of the following statements is always correct?
  1. (A)P(A∣B)=1P(A|B)=1P(A∣B)=1
  2. (B)P(A∣B)≤P(A)P(A|B)\le P(A)P(A∣B)≤P(A)
  3. (C)P(A∣B)=P(B)−P(A)P(A|B)=P(B)-P(A)P(A∣B)=P(B)−P(A)
  4. (D)P(A∣B)≥P(A)P(A|B)\ge P(A)P(A∣B)≥P(A)

Correct answer: (D)

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Application of Derivatives 139/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • Quadratic Equations 148/186
  • Work, Energy and Power 132/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Alcohols and Ethers 106/186
  • Alternating Currents 108/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Solid State 63/186
  • Diazonium Salts and Reactions 53/186
  • IUPAC Nomenclature 37/186
  • Mathematical Reasoning 26/186
  • Communication Systems 11/186
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