Jarvis OS
PYQ papersPricingSign inGet started
  1. Home
  2. /JEE Main PYQs
  3. /2019
  4. /9 Apr Shift 2

JEE Main 9 April 2019 Shift 2 Question Paper with Answers

9 April 2019 · April session · 80 questions

80 of the 90 questions from the JEE Main 9 April 2019 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

10 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
25
Chemistry
27
Mathematics
28

Physics — JEE Main 9 April 2019 Shift 2

Q1·PhysicsSingle correct
Two coils P and Q are separated by some distance. When a current of 3 A flows through coil P a magnetic flux of 10−310^{-3}10−3 Wb passes through Q. No current is passed through Q. When no current passes through P and a current of 2 A passes through Q, the flux through P is:
  1. (A)6.67×10−36.67 \times 10^{-3}6.67×10−3 Wb
  2. (B)6.67×10−46.67 \times 10^{-4}6.67×10−4 Wb
  3. (C)3.67×10−43.67 \times 10^{-4}3.67×10−4 Wb
  4. (D)3.67×10−33.67 \times 10^{-3}3.67×10−3 Wb

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
A metal wire of resistance 3Ω3\Omega3Ω is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle 60060^{0}600 at the centre, the equivalent resistance between these two points will be:
  1. (A)125Ω\dfrac{12}{5}\Omega512​Ω
  2. (B)53Ω\dfrac{5}{3}\Omega35​Ω
  3. (C)52Ω\dfrac{5}{2}\Omega25​Ω
  4. (D)72Ω\dfrac{7}{2}\Omega27​Ω

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 – 0.5 A?
  1. (A)0.2 ohm
  2. (B)0.002 ohm
  3. (C)0.02 ohm
  4. (D)0.5 ohm

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
The position of a particle as a function of time t, is given by x(t)=at+bt2−ct3x(t) = at + bt^{2} - ct^{3}x(t)=at+bt2−ct3 where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be:
  1. (A)a+b24ca + \dfrac{b^{2}}{4c}a+4cb2​
  2. (B)a+b2ca + \dfrac{b^{2}}{c}a+cb2​
  3. (C)a+b22ca + \dfrac{b^{2}}{2c}a+2cb2​
  4. (D)a+b23ca + \dfrac{b^{2}}{3c}a+3cb2​

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A moving coil galvanometer has a coil with 175 turns and area 1 cm2^{2}2 It uses a torsion band of torsion constant 10−610^{-6}10−6 N – m/rad. The coil is placed in a magnetic field B parallel to its plane. The coil deflects by 101^{0}10 for a current of 1 mA. The value of B (in Tesla) is approximately:-
  1. (A)10−310^{-3}10−3
  2. (B)10−110^{-1}10−1
  3. (C)10−410^{-4}10−4
  4. (D)10−210^{-2}10−2

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
A very long solenoid of radius R is carrying current I(t)=kte−αtI(t) = kte^{-\alpha t}I(t)=kte−αt (k>0)(k > 0)(k>0), as a function of time (t≥0)(t \geq 0)(t≥0). counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:-
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)
  1. (A)10−310^{-3}10−3 K
  2. (B)10−410^{-4}10−4
  3. (C)10−110^{-1}10−1 K
  4. (D)10−510^{-5}10−5 K

Correct answer: (D)

Step-by-step solution →
Q8·PhysicsSingle correct
A particle P is formed due to a completely inelastic collision of particles x and y having de – Broglie wavelengths λx\lambda_{x}λx​ and λy\lambda_{y}λy​ respectively. If x and y were moving in opposite directions, then the de – Broglie wavelength of P is:
  1. (A)λx+λy\lambda_{x} + \lambda_{y}λx​+λy​
  2. (B)λxλyλx+λy\dfrac{\lambda_{x}\lambda_{y}}{\lambda_{x}+\lambda_{y}}λx​+λy​λx​λy​​
  3. (C)λxλy∣λx−λy∣\dfrac{\lambda_{x}\lambda_{y}}{|\lambda_{x}-\lambda_{y}|}∣λx​−λy​∣λx​λy​​
  4. (D)λx−λy\lambda_{x} - \lambda_{y}λx​−λy​

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x1x_{1}x1​ and x2x_{2}x2​ (x1>x2)(x_{1} > x_{2})(x1​>x2​) from the lens. The ratio of x1x_{1}x1​ and x2x_{2}x2​ is:
  1. (A)5 : 3
  2. (B)2 : 1
  3. (C)4 : 3
  4. (D)3 : 1

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm. Coming from a distant object, the limit of resolution of the telescope is close to:-
  1. (A)1.5×10−71.5 \times 10^{-7}1.5×10−7 rad
  2. (B)2.0×10−72.0 \times 10^{-7}2.0×10−7 rad
  3. (C)3.0×10−73.0 \times 10^{-7}3.0×10−7 rad
  4. (D)4.5×10−74.5 \times 10^{-7}4.5×10−7 rad

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
Moment of inertia of a body about a given axis is 1.5 kg m2^{2}2 Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad/s2^{2}2 must be applied about the axis of rotation for a duration of:
  1. (A)2 s
  2. (B)5 s
  3. (C)2.5 s
  4. (D)3 s

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
The logic gate equivalent to the given logic circuit is:
  1. (A)OR
  2. (B)AND
  3. (C)NOR
  4. (D)NAND

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
The physical sizes of the transmitter and receiver antenna in a communication system are:
  1. (A)Proportional of carrier frequency
  2. (B)Inversely proportional to modulation frequency
  3. (C)Inversely proportional to carrier frequency
  4. (D)Independent of both carrier and modulation frequency

Correct answer: (C)

Step-by-step solution →
Q14·PhysicsSingle correct
Four point charges −q-q−q, +q+q+q, +q+q+q and −q-q−q are placed on y axis at y = -2d, y = -d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x −-− axis at x = D, with D >>>>>> d, will vary as:
  1. (A)E∝1DE \propto \dfrac{1}{D}E∝D1​
  2. (B)E∝1D3E \propto \dfrac{1}{D^{3}}E∝D31​
  3. (C)E∝1D2E \propto \dfrac{1}{D^{2}}E∝D21​
  4. (D)E∝1D4E \propto \dfrac{1}{D^{4}}E∝D41​

Correct answer: (D)

Step-by-step solution →
Q15·PhysicsSingle correct
The position vector of a particle changes with time according to the relation r⃗(t)=15t2i^+(4−20t2)j^\vec{r}(t) = 15t^{2}\hat{i} + (4 - 20t^{2})\hat{j}r(t)=15t2i^+(4−20t2)j^​. What is the magnitude of the acceleration at t = 1?
  1. (A)40
  2. (B)100
  3. (C)25
  4. (D)50

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r)=Kr2\rho(r) = \dfrac{K}{r^{2}}ρ(r)=r2K​. Identify the correct relation between the radius R of the particle's orbit and its period T:
  1. (A)T/R2^{2}2 is a constant
  2. (B)TR is constant
  3. (C)T2^{2}2/R3^{3}3 is a constant
  4. (D)T/R is a constant

Correct answer: (D)

Step-by-step solution →
Q17·PhysicsSingle correct
A wooden block floating in a bucket of water has 45\dfrac{4}{5}54​ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:-
  1. (A)0.5
  2. (B)0.7
  3. (C)0.6
  4. (D)0.8

Correct answer: (C)

Step-by-step solution →
Q18·PhysicsSingle correct
Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms−1^{-1}−1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source of car B? (speed of sound in air = 340 ms−1^{-1}−1)
  1. (A)2250 Hz
  2. (B)2060 Hz
  3. (C)2150 Hz
  4. (D)2300 Hz

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:
  1. (A)2v27g\dfrac{2v^{2}}{7g}7g2v2​
  2. (B)v2g\dfrac{v^{2}}{g}gv2​
  3. (C)2v25g\dfrac{2v^{2}}{5g}5g2v2​
  4. (D)v22g\dfrac{v^{2}}{2g}2gv2​

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
A He+ ion is in its first excited state. Its ionization energy is:
  1. (A)6.04 eV
  2. (B)13.60 eV
  3. (C)54.40 eV
  4. (D)48.36 eV

Correct answer: (B)

Step-by-step solution →
Q21·PhysicsSingle correct
Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are θ2\theta_{2}θ2​ and θ1\theta_{1}θ1​ respectively (θ2>θ1)(\theta_{2} > \theta_{1})(θ2​>θ1​). The temperature at the interface is:
  1. (A)θ2+θ12\dfrac{\theta_{2} + \theta_{1}}{2}2θ2​+θ1​​
  2. (B)θ110+9θ210\dfrac{\theta_{1}}{10} + \dfrac{9\theta_{2}}{10}10θ1​​+109θ2​​
  3. (C)θ13+2θ23\dfrac{\theta_{1}}{3} + \dfrac{2\theta_{2}}{3}3θ1​​+32θ2​​
  4. (D)θ16+5θ26\dfrac{\theta_{1}}{6} + \dfrac{5\theta_{2}}{6}6θ1​​+65θ2​​

Correct answer: (B)

Step-by-step solution →
Q22·PhysicsSingle correct
A thin smooth rod of length L and mass M is rotating freely with angular speed ω0\omega_{0}ω0​ about an axis perpendicular to the rod and passing through its centre. Two beads of mass m and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be:-
  1. (A)Mω0M+3m\dfrac{M\omega_{0}}{M + 3m}M+3mMω0​​
  2. (B)Mω0M+m\dfrac{M\omega_{0}}{M + m}M+mMω0​​
  3. (C)Mω0M+2m\dfrac{M\omega_{0}}{M + 2m}M+2mMω0​​
  4. (D)Mω0M+6m\dfrac{M\omega_{0}}{M + 6m}M+6mMω0​​

Correct answer: (D)

Step-by-step solution →
Q23·PhysicsSingle correct
The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is:
  1. (A)VK+n\dfrac{V}{K + n}K+nV​
  2. (B)V
  3. (C)(n+1)V(K+n)\dfrac{(n + 1)V}{(K + n)}(K+n)(n+1)V​
  4. (D)nVK+n\dfrac{nV}{K + n}K+nnV​

Correct answer: (C)

Step-by-step solution →
Q24·PhysicsSingle correct
In a conductor, if the number of conduction electrons per unit volume is 8.5 ×\times× 1028^{28}28 m−3^{-3}−3 and mean free time is 25fs (femto second), its approximate resistivity is: (me=9.1×10−31kg)(m_{e} = 9.1 \times 10^{-31} kg)(me​=9.1×10−31kg)
  1. (A)10−5^{-5}−5 Ω\OmegaΩm
  2. (B)10−6^{-6}−6 Ω\OmegaΩm
  3. (C)10−7^{-7}−7 Ω\OmegaΩm
  4. (D)10−8^{-8}−8 Ω\OmegaΩm

Correct answer: (D)

Step-by-step solution →
Q25·PhysicsSingle correct
A string 2.0 m long and fixed at its end is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:
  1. (A)320 m/s, 120 Hz
  2. (B)180 m/s, 80 Hz
  3. (C)180m/s, 120 Hz
  4. (D)320 m/s, 80 Hz

Correct answer: (D)

Step-by-step solution →

Chemistry — JEE Main 9 April 2019 Shift 2

Q26·ChemistrySingle correct
Increasing order of reactivity of the following compounds for SN_{N}N​1 substitution is:
  1. (A)(b) < (c) < (d) < (a)
  2. (B)(a) < (b) < (d) < (c)
  3. (C)(b) < (a) < (d) < (c)
  4. (D)(b) < (c) < (a) < (d)

Correct answer: (C)

Step-by-step solution →
Q27·ChemistrySingle correct
The one that is not a carbonate is:
  1. (A)bauxite
  2. (B)siderite
  3. (C)calamine
  4. (D)malachite

Correct answer: (A)

Step-by-step solution →
Q28·ChemistrySingle correct
During compression of a spring the work done is 10kJ and 2kJ escaped to the surroundings as heat. The change in internal energy, ΔU\Delta UΔU (in kJ) is:
  1. (A)8
  2. (B)12
  3. (C)-12
  4. (D)-8

Correct answer: (A)

Step-by-step solution →
Q29·ChemistrySingle correct
The amorphous form of silica is:
  1. (A)quartz
  2. (B)kieselguhr
  3. (C)cristobalite
  4. (D)tridymite

Correct answer: (B)

Step-by-step solution →
Q30·ChemistrySingle correct
Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by a0_00​)
  1. (A)The electron can be found at a distance 2a0_00​ from the nucleus
  2. (B)The probability density of finding the electron is maximum at the nucleus
  3. (C)The magnitude of potential energy is double that of its kinetic energy on an average
  4. (D)The total energy of the electron is maximum when it is at a distance a0_00​ from the nucleus

Correct answer: (D)

Step-by-step solution →
Q31·ChemistrySingle correct
The maximum possible denticities of a ligand given below towards a common transition and inner – transition metal ion, respectively, are:
  1. (A)6 and 8
  2. (B)8 and 6
  3. (C)8 and 8
  4. (D)6 and 6

Correct answer: (A)

Step-by-step solution →
Q32·ChemistrySingle correct
The correct statements among I to III regarding group 13 element oxides are, I. Boron trioxide is acidic II. Oxides of aluminium and gallium are amphoteric III. Oxides of indium and thallium are basic
  1. (A)I, II and III
  2. (B)II and III only
  3. (C)I and III only
  4. (D)I and II only

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
Among the following species, the diamagnetic molecule is
  1. (A)O2_22​
  2. (B)NO
  3. (C)B2_22​
  4. (D)CO

Correct answer: (D)

Step-by-step solution →
Q34·ChemistrySingle correct
The peptide that gives positive ceric ammonium nitrate and carbylamine tests is:
  1. (A)Lys - Asp
  2. (B)Ser – Lys
  3. (C)Gln - Asp
  4. (D)Asp – Gln

Correct answer: (B)

Step-by-step solution →
Q35·ChemistrySingle correct
Assertion : For the extraction of iron, haematite ore is used Reason : Haematite is a carbonate ore of iron
  1. (A)Only the reason is correct.
  2. (B)Both the assertion and reason are correct and the reason is the correct explanation for the assertion.
  3. (C)Only the assertion is correct
  4. (D)Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
Consider the given plot of enthalpy of the following reaction between A and B. A + B →\rightarrow→ C + D Identify the incorrect statement
  1. (A)C is the thermodynamically stable product
  2. (B)Formation of A and B from C has highest enthalpy of activation
  3. (C)D is kinetically stable product
  4. (D)Activation enthalpy to form C is 5kJ mol−1^{-1}−1 less than that to form D

Correct answer: (D)

Step-by-step solution →
Q37·ChemistrySingle correct
At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as P=RTV−bP=\dfrac{RT}{V-b}P=V−bRT​ at T. Here, b is the van der Waals constant. Which gas will exhibit steeper increase in the plot of Z (compression factor) versus P?
  1. (A)Ne
  2. (B)Ar
  3. (C)Xe
  4. (D)Kr

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
A solution of Ni(NO3_33​)2_22​ is electrolysed between platinum electrodes using 0.1 Faraday electricity. How many mole of Ni will be deposited at the cathode?
  1. (A)0.20
  2. (B)0.05
  3. (C)0.10
  4. (D)0.15

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
In the following reaction Carbonyl compound + MeOH ⇌HCl\overset{\text{HCl}}{\rightleftharpoons}⇌HCl​ acetal Rate of the reaction is the highest for:
  1. (A)Acetone as substrate and methanol in stoichiometric amount
  2. (B)Proponal as substrate and methanol in stoichiometric amount
  3. (C)Acetone as substrate and methanol in excess
  4. (D)Propanal as substrate and methanol in excess

Correct answer: (D)

Step-by-step solution →
Q40·ChemistrySingle correct
The structures of beryllium chloride in the solid state and vapour, phase, respectively, are:
  1. (A)chain and dimeric
  2. (B)chain and chain
  3. (C)dimeric and dimeric
  4. (D)dimeric and chain

Correct answer: (A)

Step-by-step solution →
Q41·ChemistrySingle correct
Which of the following potential energy (PE) diagrams represents the SN1S_N1SN​1 reaction?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
The maximum number of possible oxidation states of actinoids are shown by
  1. (A)berkelium (Bk) and californium (Cf)
  2. (B)nobelium (No) and lawrencium (Lr)
  3. (C)actinium (Ac) and thorium (Th)
  4. (D)neptunium (Np) and plutonium (Pu)

Correct answer: (D)

Step-by-step solution →
Q43·ChemistrySingle correct
Molal depression constant for a solvent is 4.0 K Kg mol−1^{-1}−1. The depression in the freezing point of the solvent for 0.03 mol kg−1^{-1}−1 solution of K2_22​SO4_44​ is: (Assume complete dissociation of the electrolyte)
  1. (A)0.12 K
  2. (B)0.36 K
  3. (C)0.18 K
  4. (D)0.24 K

Correct answer: (B)

Step-by-step solution →
Q44·ChemistrySingle correct
Noradrenaline is a/an
  1. (A)Neurotransmitter
  2. (B)Antidepresessant
  3. (C)Antihistamine
  4. (D)Antacid

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
Hinsberg's reagent is:
  1. (A)C6_66​H5_55​SO2_22​Cl
  2. (B)C6_66​H5_55​COCl
  3. (C)SOCl2_22​
  4. (D)(COCl)2_22​

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
The layer of atmosphere between 10 km to 50 km above the sea level is called as:
  1. (A)troposphere
  2. (B)mesosphere
  3. (C)stratosphere
  4. (D)thermosphere

Correct answer: (C)

Step-by-step solution →
Q47·ChemistrySingle correct
HF has highest boiling point among hydrogen halides, because it has:
  1. (A)lowest dissociation enthalpy
  2. (B)strongest van der Waals' interactions
  3. (C)strongest hydrogen bonding
  4. (D)lowest ionic character

Correct answer: (C)

Step-by-step solution →
Q48·ChemistrySingle correct
What would be the molality of 20% (mass/mass) aqueous solution of KI? (molar mass of KI = 166 g mol−1^{-1}−1)
  1. (A)1.08
  2. (B)1.48
  3. (C)1.51
  4. (D)1.35

Correct answer: (C)

Step-by-step solution →
Q49·ChemistrySingle correct
Which of the following compounds is a constituent of the polymer?
  1. (A)Formaldehyde
  2. (B)Ammonia
  3. (C)Methylamine
  4. (D)N – methyl urea

Correct answer: (A)

Step-by-step solution →
Q50·ChemistrySingle correct
The correct statements among I to III are: I. Valence bond theory cannot explain the color exhibited by transition metal complexes II. Valence bond theory can predict quantitatively the magnetic properties of transition metal complexes III. Valence bond theory cannot distinguish ligands as weak and strong field ones
  1. (A)I and II only
  2. (B)I, II and III
  3. (C)I and III only
  4. (D)II and III only

Correct answer: (C)

Step-by-step solution →
Q51·ChemistrySingle correct
In an acid – base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titration mixture in this experiment?
  1. (A)(a)
  2. (B)(c)
  3. (C)(d)
  4. (D)(b)

Correct answer: (A)

Step-by-step solution →
Q52·ChemistrySingle correct
p-Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →

Mathematics — JEE Main 9 April 2019 Shift 2

Q53·MathematicsSingle correct
If the tangent to the parabola y2=xy^{2} = xy2=x at a point (α,β)(\alpha,\beta)(α,β), (β>0)(\beta > 0)(β>0) is also a tangent to the ellipse, x2+2y2=1x^{2} + 2y^{2} = 1x2+2y2=1, then α\alphaα is equal to
  1. (A)22+12\sqrt{2} + 122​+1
  2. (B)2−1\sqrt{2} - 12​−1
  3. (C)2+1\sqrt{2} + 12​+1
  4. (D)22−12\sqrt{2} - 122​−1

Correct answer: (C)

Step-by-step solution →
Q54·MathematicsSingle correct
Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is
  1. (A)190
  2. (B)262
  3. (C)225
  4. (D)157

Correct answer: (A)

Step-by-step solution →
Q55·MathematicsSingle correct
If f:R→Rf:R \rightarrow Rf:R→R is a differentiable function and f(2)=6f(2)=6f(2)=6, then lim⁡x→2∫6f(x)2t dt(x−2)\displaystyle\lim_{x\to 2}\int_{6}^{f(x)}\dfrac{2t\,dt}{(x-2)}x→2lim​∫6f(x)​(x−2)2tdt​ is:
  1. (A)000
  2. (B)2f′(2)2f'(2)2f′(2)
  3. (C)12f′(2)12f'(2)12f′(2)
  4. (D)24f′(2)24f'(2)24f′(2)

Correct answer: (C)

Step-by-step solution →
Q56·MathematicsSingle correct
If the system of equations 2x+3y−z=02x + 3y - z = 02x+3y−z=0, x+ky−2z=0x + ky - 2z = 0x+ky−2z=0 and 2x−y+z=02x - y + z = 02x−y+z=0 has a non-trivial solution (x,y,z)(x, y, z)(x,y,z), then xy+yz+zx+k\dfrac{x}{y} + \dfrac{y}{z} + \dfrac{z}{x} + kyx​+zy​+xz​+k is equal to
  1. (A)34\dfrac{3}{4}43​
  2. (B)−4-4−4
  3. (C)12\dfrac{1}{2}21​
  4. (D)−14-\dfrac{1}{4}−41​

Correct answer: (C)

Step-by-step solution →
Q57·MathematicsSingle correct
The common tangent to the circles x2+y2=4x^{2} + y^{2} = 4x2+y2=4 and x2+y2+6x+8y−24=0x^{2} + y^{2} + 6x + 8y - 24 = 0x2+y2+6x+8y−24=0 also passes through the point
  1. (A)(−4,6)(-4, 6)(−4,6)
  2. (B)(6.−2)(6. -2)(6.−2)
  3. (C)(−6,4)(-6, 4)(−6,4)
  4. (D)(4,−2)(4, -2)(4,−2)

Correct answer: (B)

Step-by-step solution →
Q58·MathematicsSingle correct
If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11th^{th}th tern is
  1. (A)−25-25−25
  2. (B)252525
  3. (C)−36-36−36
  4. (D)−35-35−35

Correct answer: (A)

Step-by-step solution →
Q59·MathematicsSingle correct
The value of the integral ∫01xcot⁡−1(1−x2+x4)dx\displaystyle\int_{0}^{1} x\cot^{-1}\left(1-x^2+x^4\right)dx∫01​xcot−1(1−x2+x4)dx is
  1. (A)π4−12log⁡e2\dfrac{\pi}{4}-\dfrac{1}{2}\log_e 24π​−21​loge​2
  2. (B)π2−log⁡e2\dfrac{\pi}{2}-\log_e 22π​−loge​2
  3. (C)π2−12log⁡e2\dfrac{\pi}{2}-\dfrac{1}{2}\log_e 22π​−21​loge​2
  4. (D)π4−log⁡e2\dfrac{\pi}{4}-\log_e 24π​−loge​2

Correct answer: (A)

Step-by-step solution →
Q60·MathematicsSingle correct
The value of sin⁡10∘sin⁡30∘sin⁡50∘sin⁡70∘\sin10^{\circ}\sin30^{\circ}\sin50^{\circ}\sin70^{\circ}sin10∘sin30∘sin50∘sin70∘ is
  1. (A)136\dfrac{1}{36}361​
  2. (B)132\dfrac{1}{32}321​
  3. (C)118\dfrac{1}{18}181​
  4. (D)116\dfrac{1}{16}161​

Correct answer: (D)

Step-by-step solution →
Q61·MathematicsSingle correct
Let z∈Cz \in Cz∈C be such that ∣z∣<1|z|<1∣z∣<1. If w=5+3z5(1−z)w=\dfrac{5+3z}{5(1-z)}w=5(1−z)5+3z​, then
  1. (A)5 Im(w)<15\,\text{Im}(w)<15Im(w)<1
  2. (B)4 Im(w)>54\,\text{Im}(w)>54Im(w)>5
  3. (C)5 Re(w)>15\,\text{Re}(w)>15Re(w)>1
  4. (D)5 Re(w)>45\,\text{Re}(w)>45Re(w)>4

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
If some three consecutive in the binomial expansion of (x+1)n(x+1)^{n}(x+1)n in powers of x are in the ratio 2:15:702 : 15 : 702:15:70, then the average of these three coefficient is:
  1. (A)964964964
  2. (B)625625625
  3. (C)227227227
  4. (D)232232232

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
If cos⁡xdydx−ysin⁡x=6x,(0<x<π2)\cos x\dfrac{dy}{dx} - y\sin x = 6x, \left(0 < x < \dfrac{\pi}{2}\right)cosxdxdy​−ysinx=6x,(0<x<2π​) and y(π3)=0y\left(\dfrac{\pi}{3}\right) = 0y(3π​)=0, then y(π6)y\left(\dfrac{\pi}{6}\right)y(6π​) is equal to:
  1. (A)−π243-\dfrac{\pi^{2}}{4\sqrt{3}}−43​π2​
  2. (B)−π22-\dfrac{\pi^{2}}{2}−2π2​
  3. (C)π223\dfrac{\pi^{2}}{2\sqrt{3}}23​π2​
  4. (D)−π223-\dfrac{\pi^{2}}{2\sqrt{3}}−23​π2​

Correct answer: (D)

Step-by-step solution →
Q64·MathematicsSingle correct
If the two lines x+(a−1)y=1x + (a-1)y = 1x+(a−1)y=1 and 2x+a2y=1 (a∈R−{0,1})2x + a^{2}y = 1\ (a \in R - \{0,1\})2x+a2y=1 (a∈R−{0,1}) are perpendicular, then the distance of their point of intersection from the origin is:
  1. (A)25\dfrac{2}{5}52​
  2. (B)25\dfrac{\sqrt{2}}{5}52​​
  3. (C)25\dfrac{2}{\sqrt{5}}5​2​
  4. (D)25\sqrt{\dfrac{2}{5}}52​​

Correct answer: (D)

Step-by-step solution →
Q65·MathematicsSingle correct
A water tank has the shape of an inverted right circular cone, whose semi vertical angle is tan⁡−1(12)\tan^{-1}\left(\dfrac{1}{2}\right)tan−1(21​). Water is poured in at a constant rage of 5 cubic meter per minute. Then the rate (in m/min) at which the level of water is rising at the instant when the depth of water in the tank is 10 m is:
  1. (A)2π\dfrac{2}{\pi}π2​
  2. (B)15π\dfrac{1}{5\pi}5π1​
  3. (C)110π\dfrac{1}{10\pi}10π1​
  4. (D)115π\dfrac{1}{15\pi}15π1​

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of 15∘15^{\circ}15∘ with ground. Then the distance (in m) between the poles, is
  1. (A)52(2+3)\dfrac{5}{2}\left(2+\sqrt{3}\right)25​(2+3​)
  2. (B)5(3+1)5\left(\sqrt{3}+1\right)5(3​+1)
  3. (C)5(2+3)5\left(2+\sqrt{3}\right)5(2+3​)
  4. (D)10(3−1)10\left(\sqrt{3}-1\right)10(3​−1)

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
The vertices B and C of a △ABC\triangle ABC△ABC lie on the line, x+23=y−10=z4\dfrac{x+2}{3}=\dfrac{y-1}{0}=\dfrac{z}{4}3x+2​=0y−1​=4z​ such that BC = 5 units. Then the area (in sq. units) of this triangle, given that the point A (1,−1,2)(1,-1,2)(1,−1,2) is:
  1. (A)2342\sqrt{34}234​
  2. (B)34\sqrt{34}34​
  3. (C)666
  4. (D)5175\sqrt{17}517​

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
The area in sq. units) of the smaller of the two circles that touch the parabola, y2=4xy^2=4xy2=4x at the points (1,2)(1,2)(1,2) and the axis is
  1. (A)4π(2−2)4\pi\left(2-\sqrt{2}\right)4π(2−2​)
  2. (B)8π(3−22)8\pi\left(3-2\sqrt{2}\right)8π(3−22​)
  3. (C)4π(3+2)4\pi\left(3+\sqrt{2}\right)4π(3+2​)
  4. (D)8π(2−2)8\pi\left(2-\sqrt{2}\right)8π(2−2​)

Correct answer: (B)

Step-by-step solution →
Q69·MathematicsSingle correct
If the function f(x)={a∣π−x∣+1,x≤5b∣π−x∣+3,x>5f\left(x\right)=\begin{cases} a\left|\pi-x\right|+1, & x\leq 5 \\ b\left|\pi-x\right|+3, & x>5 \end{cases}f(x)={a∣π−x∣+1,b∣π−x∣+3,​x≤5x>5​ is continuous at x=5x=5x=5, then the value of a−ba-ba−b is
  1. (A)25−π\dfrac{2}{5-\pi}5−π2​
  2. (B)2π−5\dfrac{2}{\pi-5}π−52​
  3. (C)2π+5\dfrac{2}{\pi+5}π+52​
  4. (D)−2π+5\dfrac{-2}{\pi+5}π+5−2​

Correct answer: (A)

Step-by-step solution →
Q70·MathematicsSingle correct
If f(x)=[x]−[x4],x∈Rf\left(x\right)=\left[x\right]-\left[\dfrac{x}{4}\right],x\in Rf(x)=[x]−[4x​],x∈R, where [x] denotes the greatest integer function, then:
  1. (A)Both lim⁡x→4−f(x)\lim\limits_{x\to4-}f\left(x\right)x→4−lim​f(x) and lim⁡x→4+f(x)\lim\limits_{x\to4+}f\left(x\right)x→4+lim​f(x) exist but are not equal
  2. (B)lim⁡x→4−f(x)\lim\limits_{x\to4-}f\left(x\right)x→4−lim​f(x) exists but lim⁡x→4+f(x)\lim\limits_{x\to4+}f\left(x\right)x→4+lim​f(x) does not exist
  3. (C)lim⁡x→4+f(x)\lim\limits_{x\to4+}f\left(x\right)x→4+lim​f(x) exists but lim⁡x→4−f(x)\lim\limits_{x\to4-}f\left(x\right)x→4−lim​f(x) does not exist
  4. (D)f is continuous at x = 4

Correct answer: (D)

Step-by-step solution →
Q71·MathematicsSingle correct
If m is chosen in the quadratic equation (m2+1)x2−3x+(m2+1)2=0\left(m^{2}+1\right)x^{2}-3x+\left(m^{2}+1\right)^{2}=0(m2+1)x2−3x+(m2+1)2=0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:
  1. (A)838\sqrt{3}83​
  2. (B)434\sqrt{3}43​
  3. (C)10510\sqrt{5}105​
  4. (D)858\sqrt{5}85​

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
Two newspaper A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is:
  1. (A)12.8
  2. (B)13.5
  3. (C)13.9
  4. (D)13

Correct answer: (C)

Step-by-step solution →
Q73·MathematicsSingle correct
Let P be the plane, which contains the line of intersection of the planes, x+y+z−6=0x+y+z-6=0x+y+z−6=0 and 2x+3y+z+5=02x+3y+z+5=02x+3y+z+5=0 and it is perpendicular to the xy - plane. Then the distance of the point (0,0,256)(0,0,256)(0,0,256) from P is equal to:
  1. (A)63563\sqrt{5}635​
  2. (B)2055205\sqrt{5}2055​
  3. (C)175\dfrac{17}{\sqrt{5}}5​17​
  4. (D)115\dfrac{11}{\sqrt{5}}5​11​

Correct answer: (D)

Step-by-step solution →
Q74·MathematicsSingle correct
If P⇒(q∨r)P\Rightarrow\left(q\vee r\right)P⇒(q∨r) is false, then the truth values of p, q, r are respectively
  1. (A)F, T, T
  2. (B)T, F, F
  3. (C)T, T, F
  4. (D)F, F, F

Correct answer: (B)

Step-by-step solution →
Q75·MathematicsSingle correct
The domain of the definition of the function f(x)=14−x2+log⁡(x3−x)f\left(x\right)=\dfrac{1}{4-x^{2}}+\log\left(x^{3}-x\right)f(x)=4−x21​+log(x3−x) is
  1. (A)(1,2)∪(2,∞)\left(1,2\right)\cup\left(2,\infty\right)(1,2)∪(2,∞)
  2. (B)(−1,0)∪(1,2)∪(3,∞)\left(-1,0\right)\cup\left(1,2\right)\cup\left(3,\infty\right)(−1,0)∪(1,2)∪(3,∞)
  3. (C)(−1,0)∪(1,2)∪(2,∞)\left(-1,0\right)\cup\left(1,2\right)\cup\left(2,\infty\right)(−1,0)∪(1,2)∪(2,∞)
  4. (D)(−2,−1)∪(−1,0)∪(2,∞)\left(-2,-1\right)\cup\left(-1,0\right)\cup\left(2,\infty\right)(−2,−1)∪(−1,0)∪(2,∞)

Correct answer: (C)

Step-by-step solution →
Q76·MathematicsSingle correct
The sum of the series 1+2×3+3×5+4×7+....1+2\times3+3\times5+4\times7+....1+2×3+3×5+4×7+.... upto 11th11^{th}11th term is
  1. (A)915
  2. (B)946
  3. (C)945
  4. (D)916

Correct answer: (B)

Step-by-step solution →
Q77·MathematicsSingle correct
The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then yx\dfrac{y}{x}xy​ is equal to
  1. (A)73\dfrac{7}{3}37​
  2. (B)94\dfrac{9}{4}49​
  3. (C)72\dfrac{7}{2}27​
  4. (D)83\dfrac{8}{3}38​

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsSingle correct
The area (in sq. units) of the region A={(x,y):y22≤x≤y+4}A=\left\{\left(x,y\right):\dfrac{y^{2}}{2}\leq x\leq y+4\right\}A={(x,y):2y2​≤x≤y+4} is:
  1. (A)533\dfrac{53}{3}353​
  2. (B)18
  3. (C)30
  4. (D)16

Correct answer: (B)

Step-by-step solution →
Q79·MathematicsSingle correct
If a unit vector r⃗\vec{r}r makes angles π3\dfrac{\pi}{3}3π​ with i^\hat{i}i^, π4\dfrac{\pi}{4}4π​ with j^\hat{j}j^​ and θ∈(0,π)\theta\in\left(0,\pi\right)θ∈(0,π) with k^\hat{k}k^, then a value of θ\thetaθ is
  1. (A)5π12\dfrac{5\pi}{12}125π​
  2. (B)5π6\dfrac{5\pi}{6}65π​
  3. (C)2π3\dfrac{2\pi}{3}32π​
  4. (D)π4\dfrac{\pi}{4}4π​

Correct answer: (C)

Step-by-step solution →
Q80·MathematicsSingle correct
A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+73y=x+73y=x+7. If the two adjacent vertices of the rectangle are (−8,5)\left(-8,5\right)(−8,5) and (6,5)\left(6,5\right)(6,5) then the area of the rectangle (in sq. units) is
  1. (A)72
  2. (B)84
  3. (C)98
  4. (D)56

Correct answer: (B)

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
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Chemical Bonding and Molecular Structure 151/186
  • 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
  • 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
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Parabola 101/186
  • Statistics 118/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Environmental Chemistry 83/186
  • Polymers 64/186
  • Chemistry in Everyday Life 60/186
  • States of Matter: Gases and Liquids 52/186
  • Reaction Mechanism 29/186
  • Mathematical Reasoning 26/186
  • Communication Systems 11/186
← 9 Apr Shift 1 2019All papers10 Apr Shift 1 2019 →

Attempt this paper under exam timing.

Take the 9 April 2019 Shift 2 paper as a timed mock and Jarvis marks it, then tells you which errors were conceptual gaps, which were silly mistakes, and which pattern you have now repeated. Step-by-step solutions for every question included.

Attempt this paper freeSee pricing

Free plan, no time limit · No credit card needed

Jarvis OS

AI-powered JEE preparation.

Question papers

JEE Main PYQsJEE Advanced PYQsPhysics PYQsChemistry PYQsMaths PYQs

Product

TourPricingSign inCreate account

Legal

Privacy PolicyTerms of ServiceRefund & CancellationShipping & DeliveryContact Us

Operated by

Venyou Craft Private Limited

info@jarvisos.net

© 2026 Jarvis OS