Jarvis OS
PYQ papersPricingSign inGet started
  1. Home
  2. /JEE Main PYQs
  3. /2019
  4. /11 Jan Shift 1

JEE Main 11 January 2019 Shift 1 Question Paper with Answers

11 January 2019 · January session · 83 questions

83 of the 90 questions from the JEE Main 11 January 2019 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

7 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
29
Mathematics
29

Physics — JEE Main 11 January 2019 Shift 1

Q1·PhysicsSingle correct
A body is projected at t = 0 with a velocity 10 ms−1^{-1}−1 at an angle of 600^{0}0 with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms−2^{-2}−2, the radius of R is:
  1. (A)10.3 m
  2. (B)2.8 m
  3. (C)2.5 m
  4. (D)5.1 m

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Å. The radius of the atom in the excited state, in terms of Bohr radius a0a_0a0​, will be: (hc = 12500 eV- Å)
  1. (A)25a025a_025a0​
  2. (B)9a09a_09a0​
  3. (C)16a016a_016a0​
  4. (D)4a04a_04a0​

Correct answer: (C)

Step-by-step solution →
Q3·PhysicsSingle correct
In the given circuit the current through Zener Diode is close to:
  1. (A)0.0 mA
  2. (B)6.7 mA
  3. (C)4.0 mA
  4. (D)6.0 mA

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
There are two long co – axial solenoids of same length l. The inner and outer coils have radii r1_11​ and r2_22​ and number of turns per unit length n1_11​ and n2_22​ respectively. The ratio of mutual inductance to the self – inductance of the inner – coil is:
  1. (A)n1n2\frac{n_1}{n_2}n2​n1​​
  2. (B)n2n1⋅r1r2\frac{n_2}{n_1}\cdot\frac{r_1}{r_2}n1​n2​​⋅r2​r1​​
  3. (C)n2n1⋅r22r12\frac{n_2}{n_1}\cdot\frac{r_2^2}{r_1^2}n1​n2​​⋅r12​r22​​
  4. (D)n2n1\frac{n_2}{n_1}n1​n2​​

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A satellite is revolving in a circular orbit at a height h from the earth surface, such that h < < R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:
  1. (A)2gR\sqrt{2gR}2gR​
  2. (B)gR\sqrt{gR}gR​
  3. (C)gR2\sqrt{\frac{gR}{2}}2gR​​
  4. (D)gR(2−1)\sqrt{gR}(\sqrt{2}-1)gR​(2​−1)

Correct answer: (D)

Step-by-step solution →
Q6·PhysicsSingle correct
The force of interaction between two atoms is given by F=αβ exp(−x2αkt)F = \alpha\beta\, exp\left(-\dfrac{x^{2}}{\alpha kt}\right)F=αβexp(−αktx2​); where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is:
  1. (A)M⁰L²T⁻⁴
  2. (B)M²LT⁻⁴
  3. (C)MLT⁻²
  4. (D)M²L²T⁻²

Correct answer: (B)

Step-by-step solution →
Q7·PhysicsSingle correct
In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is 1/8th^{th}th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:
  1. (A)0.74
  2. (B)0.85
  3. (C)0.94
  4. (D)0.80

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Three charges Q, +q and +q are placed at the vertices of a right – angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is:
  1. (A)+q
  2. (B)−2q2+1\frac{-\sqrt{2}q}{\sqrt{2}+1}2​+1−2​q​
  3. (C)−q1+2\frac{-q}{1+\sqrt{2}}1+2​−q​
  4. (D)–2q

Correct answer: (B)

Step-by-step solution →
Q9·PhysicsSingle correct
The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if Dm_mm​ is the angle of minimum deviation?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
The equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the mid points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0_00​. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:
  1. (A)I = 1516\frac{15}{16}1615​I0_00​
  2. (B)I = 34\frac{3}{4}43​I0_00​
  3. (C)I = 916\frac{9}{16}169​I0_00​
  4. (D)I = I04\frac{I_0}{4}4I0​​

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
Ice at –200^{0}0C is added to 50 g of water at 400^{0}0C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/0^{0}0C) Heat of fusion of water at 0°C = 334 J/g)
  1. (A)50 g
  2. (B)100 g
  3. (C)60 g
  4. (D)40 g

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
A particle is moving along a circular path with a constant speed of 10 ms−1^{-1}−1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 600^{0}0 around the centre of the circle?
  1. (A)10310\sqrt{3}103​ m/s
  2. (B)0
  3. (C)10210\sqrt{2}102​ m/s
  4. (D)10 m/s

Correct answer: (D)

Step-by-step solution →
Q13·PhysicsSingle correct
An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be:
  1. (A)2.26×10−32.26 \times 10^{-3}2.26×10−3 m/s away from the lens
  2. (B)0.92×10−30.92 \times 10^{-3}0.92×10−3 m/s away from the lens
  3. (C)3.22×10−33.22 \times 10^{-3}3.22×10−3 m/s towards the lens
  4. (D)1.16×10−31.16 \times 10^{-3}1.16×10−3 m/s towards the lens

Correct answer: (D)

Step-by-step solution →
Q14·PhysicsSingle correct
A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is:
  1. (A)15 RT
  2. (B)12 RT
  3. (C)4 RT
  4. (D)20 RT

Correct answer: (A)

Step-by-step solution →
Q15·PhysicsSingle correct
Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be.
  1. (A)60 W
  2. (B)240 W
  3. (C)120 W
  4. (D)30 W

Correct answer: (B)

Step-by-step solution →
Q16·PhysicsSingle correct
The resistance of the meter bridge AB in given figure is 4 Ω4\ \Omega4 Ω. With a cell of emf ε\varepsilonε = 005 V and rheostat resistance Rh=2 ΩR_h = 2\ \OmegaRh​=2 Ω the null point is obtained at some point J. When the cell is replaced by another one of emf ε=ε2\varepsilon = \varepsilon_2ε=ε2​ the same null point J is found for Rh=6 ΩR_h = 6\ \OmegaRh​=6 Ω. The emf ε2\varepsilon_2ε2​ is:
  1. (A)0.4V
  2. (B)0.3V
  3. (C)0.6V
  4. (D)0.5V

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
An electromagnetic wave of intensity 50 Wm−2^{-2}−2 enters in a medium of refractive index' n' without any loss . The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively. Given by:
  1. (A)(1n,1n)\left(\dfrac{1}{\sqrt{n}}, \dfrac{1}{\sqrt{n}}\right)(n​1​,n​1​)
  2. (B)(n,n)\left(\sqrt{n}, \sqrt{n}\right)(n​,n​)
  3. (C)(n,1n)\left(\sqrt{n}, \dfrac{1}{\sqrt{n}}\right)(n​,n​1​)
  4. (D)(1n,n)\left(\dfrac{1}{\sqrt{n}}, \sqrt{n}\right)(n​1​,n​)

Correct answer: (D)

Step-by-step solution →
Q18·PhysicsSingle correct
In the figure shown below, the charge on the left plate of the μ\muμF capacitor is −30μ-30\mu−30μC. The charge on the right place of the 6 μ\muμF capacitor is:
  1. (A)−12μ-12\mu−12μC
  2. (B)+12μ+12\mu+12μC
  3. (C)−18μ-18\mu−18μC
  4. (D)+18μ+18\mu+18μC

Correct answer: (D)

Step-by-step solution →
Q19·PhysicsSingle correct
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is TVxTV^{x}TVx = constant, then x is:
  1. (A)3/5
  2. (B)2/5
  3. (C)2/3
  4. (D)5/3

Correct answer: (B)

Step-by-step solution →
Q20·PhysicsSingle correct
A liquid of density ρ\rhoρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:
  1. (A)14ρv2\dfrac{1}{4}\rho v^{2}41​ρv2
  2. (B)34ρv2\dfrac{3}{4}\rho v^{2}43​ρv2
  3. (C)12ρv2\dfrac{1}{2}\rho v^{2}21​ρv2
  4. (D)ρv2\rho v^{2}ρv2

Correct answer: (B)

Step-by-step solution →
Q21·PhysicsSingle correct
If the deBroglie wavelength of an electron is equal to 10−310^{-3}10−3 times the wavelength of a photon of frequency 6×10146 \times 10^{14}6×1014 Hz, then the speed of electron is equal to: (Speed of light = 3 x 10 = 8 = m/s ; Planck's constant = 6.63×10−346.63 \times 10^{-34}6.63×10−34 J.s ; Mass of electron = 9.1×10−319.1 \times 10^{-31}9.1×10−31 kg)
  1. (A)1.1×1061.1 \times 10^{6}1.1×106 m/s
  2. (B)1.7×1061.7 \times 10^{6}1.7×106 m/s
  3. (C)1.8×1061.8 \times 10^{6}1.8×106 m/s
  4. (D)1.45×1061.45 \times 10^{6}1.45×106 m/s

Correct answer: (D)

Step-by-step solution →
Q22·PhysicsSingle correct
The give graph shown variation (with distance r from centre) of:
  1. (A)Electric field of a uniformly charged sphere
  2. (B)Potential of a uniformly charged spherical shell
  3. (C)Potential of a uniformly charged sphere
  4. (D)Electric field of a uniformly charged spherical shell

Correct answer: (B)

Step-by-step solution →
Q23·PhysicsSingle correct
Equation of travelling wave on a stretched string of linear density 5 g/m is y=0.03sin⁡(450t−9x)y = 0.03\sin(450t - 9x)y=0.03sin(450t−9x) where distance and time are measured in SI united. The tension in the string is:
  1. (A)10 N
  2. (B)7.5 N
  3. (C)12.5 N
  4. (D)5 N

Correct answer: (C)

Step-by-step solution →
Q24·PhysicsSingle correct
In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6×10−191.6 \times 10^{-19}1.6×10−19 C Mass of the electron = 9.1×10−319.1 \times 10^{-31}9.1×10−31 kg]
  1. (A)7.5×10−37.5 \times 10^{-3}7.5×10−3 m
  2. (B)7.5×10−27.5 \times 10^{-2}7.5×10−2 m
  3. (C)7.5 m
  4. (D)7.5×10−47.5 \times 10^{-4}7.5×10−4 m

Correct answer: (D)

Step-by-step solution →
Q25·PhysicsSingle correct
In a Wheatstone bridge (see figure) Resistance P and Q are approximately equal. When R = 400 Ω\OmegaΩ, the bridge is balanced. On interchanging P and Q, the value of R, for balance is 405 Ω\OmegaΩ. The value of X is close to:
  1. (A)401.5 ohm
  2. (B)404.5 ohm
  3. (C)403.5 ohm
  4. (D)402.5 ohm

Correct answer: (D)

Step-by-step solution →

Chemistry — JEE Main 11 January 2019 Shift 1

Q26·ChemistrySingle correct
Among the following compounds, which one is found in RNA?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q27·ChemistrySingle correct
The correct match between items I and II is:
Item – I (Mixture)Item – II (Separation method)
a.H2OH_2OH2​O : Sugarp.Sublimation
b.H2OH_2OH2​O : Anilineq.Recrystallization
c.H2OH_2OH2​O : Toluener.Stem distillation
s.Differential extraction
  1. (A)a - d, b – r, c – p
  2. (B)a – q, b – r, c – s
  3. (C)a – r, b – p, c – s
  4. (D)a – q, b – r, c – p

Correct answer: (B)

Step-by-step solution →
Q28·ChemistrySingle correct
Which compounds out of the following is/are not aromatic?
  1. (A)b, c and d
  2. (B)c and d
  3. (C)b
  4. (D)a and c

Correct answer: (A)

Step-by-step solution →
Q29·ChemistrySingle correct
A solid having density of 9×1039 × 10^{3}9×103 kg m−3^{-3}−3 forms face centred cubic crystale of edge length 2002200\sqrt{2}2002​ pm. What is the molar mass of the solid? [Avogadro constant ≅ 6 × 102310^{23}1023 and mol−1^{-1}−1, π ≅ 3]
  1. (A)0.0432 kg mol−1^{-1}−1
  2. (B)0.0216 kg mol−1^{-1}−1
  3. (C)0.0305 kg mol−1^{-1}−1
  4. (D)0.4320 kg mol−1^{-1}−1

Correct answer: (C)

Step-by-step solution →
Q30·ChemistrySingle correct
For the cell Zn(s)∣Zn2+(aq)∣∣Mx+(aq)∣M(s)Zn(s)|Zn^{2+}(aq)||M^{x+}(aq)|M(s)Zn(s)∣Zn2+(aq)∣∣Mx+(aq)∣M(s), different half cells and their standard electrode potentials are given below: If EZn2+/Zn0=−0.76E^{0}_{Zn^{2+}/Zn} = -0.76EZn2+/Zn0​=−0.76 V, which cathode will given a maximum value of Ecell0E^{0}_{cell}Ecell0​ per electron transferred?
Mx+(aq)/M(s)M^{x+}(aq)/M(s)Mx+(aq)/M(s)Au3+(aq)/Au(s)Au^{3+}(aq)/Au(s)Au3+(aq)/Au(s)Ag+(aq)/Ag(s)Ag^{+}(aq)/Ag(s)Ag+(aq)/Ag(s)Fe3+(aq)/Fe2+(aq)Fe^{3+}(aq)/Fe^{2+}(aq)Fe3+(aq)/Fe2+(aq)Fe2+(aq)/Fe(s)Fe^{2+}(aq)/Fe(s)Fe2+(aq)/Fe(s)
EMx+/M∘E^{\circ}_{M^{x+}/M}EMx+/M∘​/(V)1.400.800.77-0.44
  1. (A)Ag+/AgAg^{+}/AgAg+/Ag
  2. (B)Fe3+/Fe2+Fe^{3+}/Fe^{2+}Fe3+/Fe2+
  3. (C)Au3+/AuAu^{3+}/AuAu3+/Au
  4. (D)Fe2+/FeFe^{2+}/FeFe2+/Fe

Correct answer: (A)

Step-by-step solution →
Q31·ChemistrySingle correct
The correct match between item I and item II is:
Item – IItem – II
a.Norethindronep.Anti – biotic
b.Ofloxacinq.Anti – fertility
c.Equanilr.Hypertention
s.Analgesics
  1. (A)a – q, b – r, c – s
  2. (B)a – q, b – p, c – r
  3. (C)a – r, b – p, c – s
  4. (D)a – r, b – p, c – r

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
The polymer obtained from the following reactions is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q33·ChemistrySingle correct
NaH is an example of:
  1. (A)electron rich hydride
  2. (B)metallic hydride
  3. (C)saline hydride
  4. (D)molecular hydride

Correct answer: (C)

Step-by-step solution →
Q34·ChemistrySingle correct
The element the usually does NOT show variable oxidation states is:
  1. (A)Cu
  2. (B)Ti
  3. (C)Sc
  4. (D)V

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
An example of solid sol is:
  1. (A)Paint
  2. (B)Gem stones
  3. (C)Butter
  4. (D)Hair cream

Correct answer: (B)

Step-by-step solution →
Q36·ChemistrySingle correct
The concentration of dissolved oxygen (DO) is cold water can go upto:
  1. (A)14 ppm
  2. (B)8 ppm
  3. (C)10 ppm
  4. (D)16 ppm

Correct answer: (C)

Step-by-step solution →
Q37·ChemistrySingle correct
The correct statements among (a) to (d) regarding H2H_2H2​ as a fuel are: (a) it produces less pollutants than petrol (b) A cylinder of compressed dihydrogen weighs ~30 times more than a petrol tank producing the same amount of energy. (c) Dihydrogen is stored in tanks of metal alloys like NaNi5NaNi_5NaNi5​ (d) On combustion, values of energy released per gram of liquid dihydrogen and LPG are 50 and 142 kJ, respectively.
  1. (A)(b) and (d) only
  2. (B)(a) and (d) only
  3. (C)(b), (c) and (d) only
  4. (D)(a), (b) and (c) only

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
The major product of the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
The freezing point of diluted milk sample is found to be −0.2∘C-0.2^{\circ}C−0.2∘C, while it should have been 0.5∘C0.5^{\circ}C0.5∘C for pure milk. How much water been added to pure milk to make the diluted sample?
  1. (A)1 cup of water to 2 cups of pure milk
  2. (B)3 cups of water to 2 cups of pure milk
  3. (C)1 cup of water to 3 cups of pure milk
  4. (D)2 cups of water to 3 cups of pure milk

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
If a reaction follows the Arrhenius equation, the plot ln k v 1/(RT)1/(RT)1/(RT) gives straight line with a gradient (−y)(-y)(−y) unit. The energy required to activate the reactant is:
  1. (A)y/R unit
  2. (B)y unit
  3. (C)yR unit
  4. (D)–y unit

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
A 10 g effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO2CO_2CO2​ at T = 298.15 K and p = 1 bar. If molar volume of CO2CO_2CO2​ is 25.0 L under such condition, what is the percentage of sodium bicarbonate in each tablet? [Molar mass of NaHCO3NaHCO_3NaHCO3​ = 84 g mol−1^{-1}−1]
  1. (A)0.84
  2. (B)33.6
  3. (C)16.8
  4. (D)8.4

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
The amphoteric hydroxide is:
  1. (A)Be(OH)2Be(OH)_2Be(OH)2​
  2. (B)Ca(OH)2Ca(OH)_2Ca(OH)2​
  3. (C)Mg(OH)2Mg(OH)_2Mg(OH)2​
  4. (D)Sr(OH)2Sr(OH)_2Sr(OH)2​

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
Peroxyacetyl nitrate (PAN), an eye irritant is produced by:
  1. (A)classical smog
  2. (B)acid rain
  3. (C)organic waste
  4. (D)photochemical smog

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
The major product of the following reactions is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
An organic compound is estimated through Dumus method and was found to evolve 6 mole of CO2CO_2CO2​, 4 moles of H2OH_2OH2​O and 1 mole of nitrogen gas. The formula of the compound is:
  1. (A)C12H8NC_{12}H_8NC12​H8​N
  2. (B)C12H8N2C_{12}H_8N_2C12​H8​N2​
  3. (C)C6H8N2C_6H_8N_2C6​H8​N2​
  4. (D)C6H8NC_6H_8NC6​H8​N

Correct answer: (C)

Step-by-step solution →
Q46·ChemistrySingle correct
Consider the reaction N2(g)+3H2(g)⇌2NH3(g)N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)N2​(g)+3H2​(g)⇌2NH3​(g) The equilibrium constant of the above reaction is K3K_3K3​. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that PNH3≪PtotalP_{NH_3} \ll P_{total}PNH3​​≪Ptotal​ at equilibrium)
  1. (A)33/2Kp1/2P216\dfrac{3^{3/2}K_p^{1/2}P^2}{16}1633/2Kp1/2​P2​
  2. (B)Kp1/2P216\dfrac{K_p^{1/2}P^2}{16}16Kp1/2​P2​
  3. (C)Kp1/2P24\dfrac{K_p^{1/2}P^2}{4}4Kp1/2​P2​
  4. (D)33/2Kp1/2P24\dfrac{3^{3/2}K_p^{1/2}P^2}{4}433/2Kp1/2​P2​

Correct answer: (A)

Step-by-step solution →
Q47·ChemistrySingle correct
Two blocks of the same metal having same mass and at temperature T1T_1T1​ and T2T_2T2​ respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, ΔS\Delta SΔS, for this process is:
  1. (A)Cpln⁡[(T1+T2)24T1T2]C_p \ln\left[\dfrac{(T_1+T_2)^2}{4T_1T_2}\right]Cp​ln[4T1​T2​(T1​+T2​)2​]
  2. (B)2Cpln⁡[(T1+T2)1/2T1T2]2C_p \ln\left[\dfrac{(T_1+T_2)^{1/2}}{T_1T_2}\right]2Cp​ln[T1​T2​(T1​+T2​)1/2​]
  3. (C)2Cpln⁡[(T1+T2)4T1T2]2C_p \ln\left[\dfrac{(T_1+T_2)}{4T_1T_2}\right]2Cp​ln[4T1​T2​(T1​+T2​)​]
  4. (D)2Cpln⁡[(T1+T2)2T1T2]2C_p \ln\left[\dfrac{(T_1+T_2)}{2T_1T_2}\right]2Cp​ln[2T1​T2​(T1​+T2​)​]

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
Match the metal column I with the coordination compounds/enzymes column II
Column I (Metals)Column II (Coordination compounds/enzymes)
a.Coi.Wilkinson catalyst
b.Znii.Chlorophyll
c.Rhiii.Vitamin B12
d.Mgiv.Carbonic anhydrase
  1. (A)a – iii, b – iv, c – i, d - ii
  2. (B)a – i, b – ii, c – iii, d – iv
  3. (C)a – ii, b – i, c – iv, d – iii
  4. (D)a – iv, b – iii, c – i, d – ii

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
For the chemical reaction X⇌YX \rightleftharpoons YX⇌Y, the standard reaction Gibbs energy depends on temperature T (in K) as ΔrG0(in kJ mol−1)=120−38T\Delta_rG^0(\text{in kJ mol}^{-1}) = 120 - \dfrac{3}{8}TΔr​G0(in kJ mol−1)=120−83​T The major component of the reaction mixture at T is:
  1. (A)Y if T = 300 K
  2. (B)Y if T = 280 K
  3. (C)X if T = 350 K
  4. (D)X if T = 315 K

Correct answer: (D)

Step-by-step solution →
Q50·ChemistrySingle correct
Match the ores (column A) with the metals (column B)
Column A (Ores)Column B (Metals)
I.Sideritea.Zinc
II.Kaoliniteb.Copper
III.Malachitec.Iron
IV.Calamined.Aluminium
  1. (A)I - a, II - b, III - c, IV - d
  2. (B)I - c, II - d, III - b, IV - a
  3. (C)I - c, II - d, III - a, IV - b
  4. (D)I - b, II - c, III - d, IV - a

Correct answer: (B)

Step-by-step solution →
Q51·ChemistrySingle correct
Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H - atom is suitable for this purpose? [RH=1×105 cm−1,h=6.6×10−34 Js,c=3×108 ms−1][R_H = 1\times10^5\ cm^{-1}, h = 6.6\times10^{-34}\ Js, c = 3\times10^8\ ms^{-1}][RH​=1×105 cm−1,h=6.6×10−34 Js,c=3×108 ms−1]
  1. (A)Paschen, ∞→3\infty \rightarrow 3∞→3
  2. (B)Paschen, 5→35 \rightarrow 35→3
  3. (C)Balmer, ∞→2\infty \rightarrow 2∞→2
  4. (D)Lyman, ∞→1\infty \rightarrow 1∞→1

Correct answer: (A)

Step-by-step solution →
Q52·ChemistrySingle correct
The chloride that CANNOT get hydrolysed is
  1. (A)PbCl4PbCl_4PbCl4​
  2. (B)CCl4CCl_4CCl4​
  3. (C)SnCl4SnCl_4SnCl4​
  4. (D)SiCl4SiCl_4SiCl4​

Correct answer: (B)

Step-by-step solution →
Q53·ChemistrySingle correct
The correct order of the atomic radii of C, Cs, Al and S is:
  1. (A)C < S < Al < Cs
  2. (B)S < C < Cs < Al
  3. (C)S < C < Al, Cs
  4. (D)C < S < Cs < Al

Correct answer: (A)

Step-by-step solution →
Q54·ChemistrySingle correct
The major product of the following reaction is
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →

Mathematics — JEE Main 11 January 2019 Shift 1

Q55·MathematicsSingle correct
If the system of linear equations 2x+2y+3z=a2x + 2y + 3z = a2x+2y+3z=a 3x−y+5z=b3x - y + 5z = b3x−y+5z=b x−3y+2z=cx - 3y + 2z = cx−3y+2z=c Where a, b, c are non zero real numbers, has more than one solution, then:
  1. (A)b−c+a=0b-c+a=0b−c+a=0
  2. (B)b−c−a=0b-c-a=0b−c−a=0
  3. (C)a+b+c=0a+b+c=0a+b+c=0
  4. (D)b+c−a=0b+c-a=0b+c−a=0

Correct answer: (B)

Step-by-step solution →
Q56·MathematicsSingle correct
Let fk(x)=1k(sin⁡kx+cos⁡kx)f_{k}(x)=\frac{1}{k}(\sin^{k}x+\cos^{k}x)fk​(x)=k1​(sinkx+coskx) for k = 1, 2, 3, … Then for all x ∈ R, the value of f4(x)−f6(x)f_{4}(x)-f_{6}(x)f4​(x)−f6​(x) is equal to:
  1. (A)112\frac{1}{12}121​
  2. (B)14\frac{1}{4}41​
  3. (C)−112\frac{-1}{12}12−1​
  4. (D)512\frac{5}{12}125​

Correct answer: (A)

Step-by-step solution →
Q57·MathematicsSingle correct
A square is inscribed in the circle x2+y2−6x+8y−103=0x^{2}+y^{2}-6x+8y-103=0x2+y2−6x+8y−103=0 with its sides parallel to the coordinate axes. Then the distance of the vertex of the square which is nearest to the origin is:
  1. (A)666
  2. (B)137\sqrt{137}137​
  3. (C)41\sqrt{41}41​
  4. (D)131313

Correct answer: (C)

Step-by-step solution →
Q58·MathematicsSingle correct
If q is false and p∧q↔rp \wedge q \leftrightarrow rp∧q↔r is true, then which one of the following statements is a tautology?
  1. (A)(p∨r)→(p∧r)(p \vee r) \rightarrow (p \wedge r)(p∨r)→(p∧r)
  2. (B)(p∧r)→(p∨r)(p \wedge r) \rightarrow (p \vee r)(p∧r)→(p∨r)
  3. (C)p∧rp \wedge rp∧r
  4. (D)p∨rp \vee rp∨r

Correct answer: (B)

Step-by-step solution →
Q59·MathematicsSingle correct
The area (in sq. units) of the region bounded by the curve x2=4yx^{2}=4yx2=4y and the straight line x=4y−2x=4y-2x=4y−2 is:
  1. (A)5/45/45/4
  2. (B)9/89/89/8
  3. (C)7/87/87/8
  4. (D)3/43/43/4

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
The value of the integral ∫−22sin⁡2x[xπ]+12 dx\int_{-2}^{2}\dfrac{\sin^{2}x}{\left[\dfrac{x}{\pi}\right]+\dfrac{1}{2}}\,dx∫−22​[πx​]+21​sin2x​dx (where [x] denotes the greatest integer less than or equal to x) is:
  1. (A)0
  2. (B)sin⁡4\sin 4sin4
  3. (C)4
  4. (D)4−sin⁡44-\sin 44−sin4

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
The outcome of each of 30 items was observed; 10 items gave an outcome 12−d\dfrac{1}{2}-d21​−d each, 10 items gave outcome 12\dfrac{1}{2}21​ each and the remaining 10 items gave outcome 12+d\dfrac{1}{2}+d21​+d each. If the variance of this outcome data is 43\dfrac{4}{3}34​ then ∣d∣|d|∣d∣ equals:
  1. (A)23\dfrac{2}{3}32​
  2. (B)2
  3. (C)52\dfrac{\sqrt{5}}{2}25​​
  4. (D)2\sqrt{2}2​

Correct answer: (D)

Step-by-step solution →
Q62·MathematicsSingle correct
The plane containing the line x−32=y+2−1=z−13\dfrac{x-3}{2}=\dfrac{y+2}{-1}=\dfrac{z-1}{3}2x−3​=−1y+2​=3z−1​ and also containing its projection on the plane 2x+3y−z=52x+3y-z=52x+3y−z=5, contains which one of the following points?
  1. (A)(2,2,0)(2,2,0)(2,2,0)
  2. (B)(−2,2,2)(-2,2,2)(−2,2,2)
  3. (C)(0,−2,2)(0,-2,2)(0,−2,2)
  4. (D)(2,0,−2)(2,0,-2)(2,0,−2)

Correct answer: (D)

Step-by-step solution →
Q63·MathematicsSingle correct
Two integers are selected at random from the set {1, 2, …, 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:
  1. (A)710\frac{7}{10}107​
  2. (B)12\frac{1}{2}21​
  3. (C)25\frac{2}{5}52​
  4. (D)35\frac{3}{5}53​

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Two circles with equal radii intersecting at the points (0, 1) and (0, −1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:
  1. (A)111
  2. (B)222
  3. (C)222\sqrt{2}22​
  4. (D)2\sqrt{2}2​

Correct answer: (B)

Step-by-step solution →
Q65·MathematicsSingle correct
The value of r for which 20Cr 20C0+20Cr−1 20C1+20Cr−2 20C2+…+20C0 20Cr^{20}C_{r}\,^{20}C_{0}+^{20}C_{r-1}\,^{20}C_{1}+^{20}C_{r-2}\,^{20}C_{2}+\ldots+^{20}C_{0}\,^{20}C_{r}20Cr​20C0​+20Cr−1​20C1​+20Cr−2​20C2​+…+20C0​20Cr​ is maximum is:
  1. (A)151515
  2. (B)202020
  3. (C)111111
  4. (D)101010

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
If tangents are drawn to the ellipse x2+2y2=2x^{2}+2y^{2}=2x2+2y2=2 at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve:
  1. (A)14x2+12y2=1\frac{1}{4x^{2}}+\frac{1}{2y^{2}}=14x21​+2y21​=1
  2. (B)x24+y22=1\frac{x^{2}}{4}+\frac{y^{2}}{2}=14x2​+2y2​=1
  3. (C)12x2+14y2=1\frac{1}{2x^{2}}+\frac{1}{4y^{2}}=12x21​+4y21​=1
  4. (D)x22+y24=1\frac{x^{2}}{2}+\frac{y^{2}}{4}=12x2​+4y2​=1

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
Let f(x)={−1,−2≤x<0x2−1,0≤x≤2f(x)=\begin{cases}-1, & -2\le x<0\\ x^{2}-1, & 0\le x\le 2\end{cases}f(x)={−1,x2−1,​−2≤x<00≤x≤2​ and g(x)=∣f(x)∣+f(∣x∣)g(x)=|f(x)|+f(|x|)g(x)=∣f(x)∣+f(∣x∣), Then, in the interval (−2,2)(-2,2)(−2,2), g is:
  1. (A)differentiable at all points
  2. (B)not continuous
  3. (C)not differentiable at two points
  4. (D)not differentiable at one point

Correct answer: (D)

Step-by-step solution →
Q68·MathematicsSingle correct
If xlog⁡e(log⁡ex)−x2+y2=4 (y>0)x\log_{e}(\log_{e}x)-x^{2}+y^{2}=4\,(y>0)xloge​(loge​x)−x2+y2=4(y>0), then dydx\frac{dy}{dx}dxdy​ at x = e is equal to:
  1. (A)(1+2e)24+e2\frac{(1+2e)}{2\sqrt{4+e^{2}}}24+e2​(1+2e)​
  2. (B)(2e−1)24+e2\frac{(2e-1)}{2\sqrt{4+e^{2}}}24+e2​(2e−1)​
  3. (C)(1+2e)4+e2\frac{(1+2e)}{\sqrt{4+e^{2}}}4+e2​(1+2e)​
  4. (D)e4+e2\frac{e}{\sqrt{4+e^{2}}}4+e2​e​

Correct answer: (B)

Step-by-step solution →
Q69·MathematicsSingle correct
If ∫1−x2x4dx=A(x)(1−x2)m+C\int\frac{\sqrt{1-x^{2}}}{x^{4}}dx=A(x)(\sqrt{1-x^{2}})^{m}+C∫x41−x2​​dx=A(x)(1−x2​)m+C, for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))m(A(x))^{m}(A(x))m equals:
  1. (A)−127x9\frac{-1}{27x^{9}}27x9−1​
  2. (B)−13x3\frac{-1}{3x^{3}}3x3−1​
  3. (C)127x6\frac{1}{27x^{6}}27x61​
  4. (D)19x4\frac{1}{9x^{4}}9x41​

Correct answer: (A)

Step-by-step solution →
Q70·MathematicsSingle correct
Let [x] denote the greatest integer less than or equal to x. Then: lim⁡x→0tan⁡(πsin⁡2x)+(∣x∣−sin⁡(x[x]))2x2\lim_{x\to 0}\frac{\tan\left(\pi\sin^{2}x\right)+\left(|x|-\sin\left(x[x]\right)\right)^{2}}{x^{2}}limx→0​x2tan(πsin2x)+(∣x∣−sin(x[x]))2​
  1. (A)does not exist
  2. (B)equals π
  3. (C)equal π + 1
  4. (D)equals 0

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
The maximum value of the function f(x)=3x3−18x2+27x−40f(x)=3x^{3}-18x^{2}+27x-40f(x)=3x3−18x2+27x−40 on the set S = {x∈R:x2+30≤11x}\{x\in R : x^{2}+30\le 11x\}{x∈R:x2+30≤11x} is
  1. (A)-122
  2. (B)-222
  3. (C)122
  4. (D)222

Correct answer: (C)

Step-by-step solution →
Q72·MathematicsSingle correct
Let f:R→Rf:R\rightarrow Rf:R→R be defined by f(x)=x1+x2f(x)=\dfrac{x}{1+x^{2}}f(x)=1+x2x​, x∈Rx\in Rx∈R. Then the range of f is:
  1. (A)[−12,12]\left[-\dfrac{1}{2},\dfrac{1}{2}\right][−21​,21​]
  2. (B)R−[−1,1]R-[-1,1]R−[−1,1]
  3. (C)R−[−12,12]R-\left[-\dfrac{1}{2},\dfrac{1}{2}\right]R−[−21​,21​]
  4. (D)(−1,1)−{0}(-1,1)-\{0\}(−1,1)−{0}

Correct answer: (A)

Step-by-step solution →
Q73·MathematicsSingle correct
The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 2719\frac{27}{19}1927​. Then the common ratio of this series is:
  1. (A)13\frac{1}{3}31​
  2. (B)23\frac{2}{3}32​
  3. (C)29\frac{2}{9}92​
  4. (D)49\frac{4}{9}94​

Correct answer: (B)

Step-by-step solution →
Q74·MathematicsSingle correct
The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is:
  1. (A)52\frac{\sqrt{5}}{2}25​​
  2. (B)252\sqrt{5}25​
  3. (C)54\frac{\sqrt{5}}{4}45​​
  4. (D)454\sqrt{5}45​

Correct answer: (A)

Step-by-step solution →
Q75·MathematicsSingle correct
In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x2−c2=yx^{2}-c^{2}=yx2−c2=y, where c is the length of the third side of the triangle, then the circumradius of the triangle is:
  1. (A)32y\frac{3}{2}y23​y
  2. (B)c3\frac{c}{\sqrt{3}}3​c​
  3. (C)c3\frac{c}{3}3c​
  4. (D)y3\frac{y}{\sqrt{3}}3​y​

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
Equation of a common tangent to the parabola y2=4xy^{2}=4xy2=4x and the hyperbola xy=2xy=2xy=2 is:
  1. (A)x+y+1=0x+y+1=0x+y+1=0
  2. (B)x−2y+4=0x-2y+4=0x−2y+4=0
  3. (C)x+2y+4=0x+2y+4=0x+2y+4=0
  4. (D)4x+2y+1=04x+2y+1=04x+2y+1=0

Correct answer: (C)

Step-by-step solution →
Q77·MathematicsSingle correct
The sum of the real values of x for which the middle term in the binomial expansion of (x33+3x)8\left(\frac{x^{3}}{3}+\frac{3}{x}\right)^{8}(3x3​+x3​)8 equals 5670 is:
  1. (A)0
  2. (B)6
  3. (C)4
  4. (D)8

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsSingle correct
Let a1,a2,…,a10a_{1}, a_{2}, \ldots, a_{10}a1​,a2​,…,a10​ be a G.P. If a3a1=25\frac{a_{3}}{a_{1}}=25a1​a3​​=25, then a9a5\frac{a_{9}}{a_{5}}a5​a9​​ equals:
  1. (A)545^{4}54
  2. (B)4(52)4(5^{2})4(52)
  3. (C)535^{3}53
  4. (D)2(52)2(5^{2})2(52)

Correct answer: (A)

Step-by-step solution →
Q79·MathematicsSingle correct
Let A=(02qrpq−rp−qr)A=\begin{pmatrix}0 & 2q & r\\ p & q & -r\\ p & -q & r\end{pmatrix}A=​0pp​2qq−q​r−rr​​. If AAT=I3AA^{T}=I_{3}AAT=I3​, ∣P∣|P|∣P∣ then ∣p∣|p|∣p∣ is:
  1. (A)15\dfrac{1}{\sqrt{5}}5​1​
  2. (B)13\dfrac{1}{\sqrt{3}}3​1​
  3. (C)12\dfrac{1}{\sqrt{2}}2​1​
  4. (D)16\dfrac{1}{\sqrt{6}}6​1​

Correct answer: (C)

Step-by-step solution →
Q80·MathematicsSingle correct
If y (x) is the solution of the differential equation dydx+(2x+1x)y=e−2x,x>0\frac{dy}{dx}+\left(\frac{2x+1}{x}\right)y=e^{-2x}, x>0dxdy​+(x2x+1​)y=e−2x,x>0 where y(1)=12e−2y(1)=\frac{1}{2}e^{-2}y(1)=21​e−2, then:
  1. (A)y(log⁡e2)=log⁡e4y\left(\log_{e}2\right)=\log_{e}4y(loge​2)=loge​4
  2. (B)y(log⁡e2)=log⁡e24y\left(\log_{e}2\right)=\frac{\log_{e}2}{4}y(loge​2)=4loge​2​
  3. (C)y(x) is decreasing in (12,1)\left(\frac{1}{2},1\right)(21​,1)
  4. (D)y(x) is decreasing in (0, 1)

Correct answer: (C)

Step-by-step solution →
Q81·MathematicsSingle correct
Let a⃗=i^+2j^+4k^,b⃗=i^+λj^+4k^\vec{a}=\hat{i}+2\hat{j}+4\hat{k}, \vec{b}=\hat{i}+\lambda\hat{j}+4\hat{k}a=i^+2j^​+4k^,b=i^+λj^​+4k^ and c⃗=2i^+4j^+(λ2−1)k^\vec{c}=2\hat{i}+4\hat{j}+\left(\lambda^{2}-1\right)\hat{k}c=2i^+4j^​+(λ2−1)k^ be coplanar vectors. Then the non − zero vector a⃗×c⃗\vec{a}\times\vec{c}a×c is:
  1. (A)−10i^−5j^-10\hat{i}-5\hat{j}−10i^−5j^​
  2. (B)−14i^−5j^-14\hat{i}-5\hat{j}−14i^−5j^​
  3. (C)−14i^+5j^-14\hat{i}+5\hat{j}−14i^+5j^​
  4. (D)−10i^+5j^-10\hat{i}+5\hat{j}−10i^+5j^​

Correct answer: (D)

Step-by-step solution →
Q82·MathematicsSingle correct
If one real root of the quadratic equation 81x2+kx+256=081x^{2}+kx+256=081x2+kx+256=0 is cube of the other root, then a value of k is:
  1. (A)− 81
  2. (B)100
  3. (C)144
  4. (D)− 300

Correct answer: (D)

Step-by-step solution →
Q83·MathematicsSingle correct
Let (−2−13i)3=x+iy27\left(-2-\dfrac{1}{3}i\right)^{3}=\dfrac{x+iy}{27}(−2−31​i)3=27x+iy​ (i=−1)(i=\sqrt{-1})(i=−1​), where x and y are real numbers, then y−xy-xy−x equals:
  1. (A)91
  2. (B)-85
  3. (C)85
  4. (D)-91

Correct answer: (A)

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
  • Electromagnetic Waves 144/186
  • Application of Derivatives 139/186
  • Limits and Continuity 149/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Hydrocarbons 126/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • 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
  • Some Basic Concepts in Chemistry 129/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Alcohols and Ethers 106/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Experimental Skills 68/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Solid State 63/186
  • Chemistry in Everyday Life 60/186
  • Mathematical Reasoning 26/186
  • Aromaticity 22/186
← 10 Jan Shift 1 2019All papers11 Jan Shift 2 2019 →

Attempt this paper under exam timing.

Take the 11 January 2019 Shift 1 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