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JEE Main 10 January 2019 Shift 1 Question Paper with Answers

10 January 2019 · January session · 75 questions

75 of the 90 questions from the JEE Main 10 January 2019 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

15 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
24
Chemistry
29
Mathematics
22

Physics — JEE Main 10 January 2019 Shift 1

Q1·PhysicsSingle correct
In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5×10−127.5 \times 10^{-12}7.5×10−12 m, the minimum electron energy required is close to:
  1. (A)500 keV
  2. (B)100 keV
  3. (C)1 keV
  4. (D)25 keV

Correct answer: (D)

Step-by-step solution →
Q2·PhysicsSingle correct
A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε\varepsilonε and internal resistance r. A cell C having emf ε\varepsilonε/2 and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is:
  1. (A)1112\dfrac{11}{12}1211​L
  2. (B)1124\dfrac{11}{24}2411​L
  3. (C)1324\dfrac{13}{24}2413​L
  4. (D)512\dfrac{5}{12}125​L

Correct answer: (C)

Step-by-step solution →
Q3·PhysicsSingle correct
A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth =6.4×106= 6.4 \times 10^{6}=6.4×106 m).
  1. (A)65 km
  2. (B)48 km
  3. (C)80 km
  4. (D)40 km

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:
  1. (A)12\dfrac{1}{2}21​a(k^−i^)\left(\hat{k}-\hat{i}\right)(k^−i^)
  2. (B)12\dfrac{1}{2}21​a(i^−k^)\left(\hat{i}-\hat{k}\right)(i^−k^)
  3. (C)12\dfrac{1}{2}21​a(j^−i^)\left(\hat{j}-\hat{i}\right)(j^​−i^)
  4. (D)12\dfrac{1}{2}21​a(j^−k^)\left(\hat{j}-\hat{k}\right)(j^​−k^)

Correct answer: (C)

Step-by-step solution →
Q5·PhysicsSingle correct
A uniform metallic wire has a resistance of 18 Ω\OmegaΩ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is:
  1. (A)4 Ω\OmegaΩ
  2. (B)8 Ω\OmegaΩ
  3. (C)12 Ω\OmegaΩ
  4. (D)2 Ω\OmegaΩ

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time t is:
  1. (A)−mg2t28-\dfrac{mg^{2}t^{2}}{8}−8mg2t2​
  2. (B)mg2t28\dfrac{mg^{2}t^{2}}{8}8mg2t2​
  3. (C)0
  4. (D)3mg2t28\dfrac{3mg^{2}t^{2}}{8}83mg2t2​

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 140\dfrac{1}{40}401​ rad by using light of wavelength λ1\lambda_{1}λ1​. When the light of wavelength λ2\lambda_{2}λ2​ is used a bright fringe is seen at the same angle in the same set up. Given that λ1\lambda_{1}λ1​ and λ2\lambda_{2}λ2​ are in visible range (380 nm to 740 nm), their values are:
  1. (A)625 nm, 500 nm
  2. (B)380 nm, 525 nm
  3. (C)380 nm, 500 nm
  4. (D)400 nm, 500 nm

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
Two guns A and B can fire bullets at speed 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:
  1. (A)1 : 16
  2. (B)1 : 2
  3. (C)1 : 4
  4. (D)1 : 8

Correct answer: (A)

Step-by-step solution →
Q9·PhysicsSingle correct
The density of a material in SI units is 128 kg m−3^{-3}−3. In certain units in which the unit of length is 25 cm and the unit of mass 50 g, the numerical value of density of the material is:
  1. (A)40
  2. (B)16
  3. (C)640
  4. (D)410

Correct answer: (A)

Step-by-step solution →
Q10·PhysicsSingle correct
A heat source at T =103= 10^{3}=103 K is connected to another heat reservoir at T =102= 10^{2}=102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK−1^{-1}−1 m−1^{-1}−1, the energy flux through it in the steady state is:
  1. (A)90 Wm−2^{-2}−2
  2. (B)120 Wm−2^{-2}−2
  3. (C)65 Wm−2^{-2}−2
  4. (D)200 Wm−2^{-2}−2

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
A parallel plate capacitor is of area 6 cm2^{2}2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1_{1}1​ = 10, K2_{2}2​ = 12 and K3_{3}3​ = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:
  1. (A)4
  2. (B)14
  3. (C)12
  4. (D)36

Correct answer: (C)

Step-by-step solution →
Q12·PhysicsSingle correct
A charge Q is distributed over three concentric spherical shell of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be:
  1. (A)Q12πϵ0ab+bc+caabc\dfrac{Q}{12\pi\epsilon_{0}}\dfrac{ab+bc+ca}{abc}12πϵ0​Q​abcab+bc+ca​
  2. (B)Q(a2+b2+c2)4πϵ0(a3+b3+c3)\dfrac{Q\left(a^{2}+b^{2}+c^{2}\right)}{4\pi\epsilon_{0}\left(a^{3}+b^{3}+c^{3}\right)}4πϵ0​(a3+b3+c3)Q(a2+b2+c2)​
  3. (C)Q4πϵ0(a+b+c)\dfrac{Q}{4\pi\epsilon_{0}\left(a+b+c\right)}4πϵ0​(a+b+c)Q​
  4. (D)Q(a+b+C)4πϵ0(a2+b2+c2)\dfrac{Q\left(a+b+C\right)}{4\pi\epsilon_{0}\left(a^{2}+b^{2}+c^{2}\right)}4πϵ0​(a2+b2+c2)Q(a+b+C)​

Correct answer: (D)

Step-by-step solution →
Q13·PhysicsSingle correct
A satellite is moving with a constant speed vvv in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:
  1. (A)2mv22mv^{2}2mv2
  2. (B)mv2mv^{2}mv2
  3. (C)12mv2\frac{1}{2}mv^{2}21​mv2
  4. (D)32mv2\frac{3}{2}mv^{2}23​mv2

Correct answer: (B)

Step-by-step solution →
Q14·PhysicsSingle correct
Water flows into a large tank with flat bottom at the rate of 10−410^{-4}10−4 m3^{3}3s−1^{-1}−1. Water is also leaking out of a hole of area 1 cm2^{2}2 at its bottom. If the height of the water in the tank remains steady, then this height is:
  1. (A)5.1 cm
  2. (B)1.7 cm
  3. (C)4 cm
  4. (D)2.9 cm

Correct answer: (A)

Step-by-step solution →
Q15·PhysicsSingle correct
A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to:
  1. (A)10.0 cm
  2. (B)33.3 cm
  3. (C)16.6 cm
  4. (D)20.0 cm

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1f_{1}f1​. If the speed of the train is reduced to 17 m/s, the frequency registered is f2f_{2}f2​. If speed of sound is 340 m/s, then the ratio f1/f2f_{1}/f_{2}f1​/f2​ is:
  1. (A)18/17
  2. (B)19/18
  3. (C)20/19
  4. (D)21/20

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
To get output '1' at R, for the given logic gate circuit the input values must be:
  1. (A)X = 0, Y = 1
  2. (B)X = 1, Y = 1
  3. (C)X = 1, Y = 0
  4. (D)X = 0, Y = 0

Correct answer: (C)

Step-by-step solution →
Q18·PhysicsSingle correct
If the magnetic field of a plane electromagnetic wave is given by (The speed of light = 3×1083\times10^{8}3×108 m/s) B=100×10−6sin⁡[2π×2×1015(t−xc)]B=100\times10^{-6}\sin\left[2\pi\times2\times10^{15}\left(t-\frac{x}{c}\right)\right]B=100×10−6sin[2π×2×1015(t−cx​)] then the maximum electric field associated with it is:
  1. (A)6×1046\times10^{4}6×104 N/C
  2. (B)3×1043\times10^{4}3×104 N/C
  3. (C)4×1044\times10^{4}4×104 N/C
  4. (D)4.5×1044.5\times10^{4}4.5×104 N/C

Correct answer: (B)

Step-by-step solution →
Q19·PhysicsSingle correct
Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to:
  1. (A)200
  2. (B)150
  3. (C)400
  4. (D)360

Correct answer: (A)

Step-by-step solution →
Q20·PhysicsSingle correct
A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is:
  1. (A)12 mV
  2. (B)6 mV
  3. (C)1 mV
  4. (D)2 mV

Correct answer: (A)

Step-by-step solution →
Q21·PhysicsSingle correct
Two electric dipoles A, B with respective dipole moments dA⃗=−4qai^\vec{d_{A}}=-4qa\hat{i}dA​​=−4qai^ and dB⃗=2qai^\vec{d_{B}}=2qa\hat{i}dB​​=2qai^ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is:
  1. (A)R2+1\frac{R}{\sqrt{2}+1}2​+1R​
  2. (B)2R2+1\frac{\sqrt{2}R}{\sqrt{2}+1}2​+12​R​
  3. (C)R2−1\frac{R}{\sqrt{2}-1}2​−1R​
  4. (D)2R2−1\frac{\sqrt{2}R}{\sqrt{2}-1}2​−12​R​

Correct answer: (B)

Step-by-step solution →
Q22·PhysicsSingle correct
In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R1R_{1}R1​ and R2R_{2}R2​ respectively, are:
  1. (A)1, 2
  2. (B)2, 2
  3. (C)0.5, 0
  4. (D)0, 1

Correct answer: (C)

Step-by-step solution →
Q23·PhysicsSingle correct
A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is:
  1. (A)20 mA
  2. (B)100 mA
  3. (C)0.4 mA
  4. (D)63 mA

Correct answer: (A)

Step-by-step solution →
Q24·PhysicsSingle correct
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms−1^{-1}−1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is: (g = 10 ms−2^{-2}−2)
  1. (A)20 m
  2. (B)30 m
  3. (C)40 m
  4. (D)10 m

Correct answer: (C)

Step-by-step solution →

Chemistry — JEE Main 10 January 2019 Shift 1

Q25·ChemistrySingle correct
The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO2_{2}2​)] is
  1. (A)16
  2. (B)8
  3. (C)4
  4. (D)12

Correct answer: (D)

Step-by-step solution →
Q26·ChemistrySingle correct
A process that has ΔH=200\Delta H = 200ΔH=200 J mol−1^{-1}−1 and ΔS=40\Delta S = 40ΔS=40 JK−1^{-1}−1 mol−1^{-1}−1. Out of the values given below, choose the minimum temperature above which the process will be spontaneous:
  1. (A)20 K
  2. (B)12 K
  3. (C)5 K
  4. (D)4 K

Correct answer: (C)

Step-by-step solution →
Q27·ChemistrySingle correct
The values of Kp_{p}p​/Kc_{c}c​ for the following reactions at 300 K are respectively: (At 300 K, Rt = 24.62 dm3^{3}3 atm mol−1^{-1}−1) N2_{2}2​(g) + O2_{2}2​(g) = 2NO(g) N2_{2}2​O4_{4}4​(g) = 2NO2_{2}2​(g) N2_{2}2​(g) + 3H2_{2}2​(g) = 2NH3_{3}3​(g)
  1. (A)1, 24.62 dm3^{3}3 atm mol−1^{-1}−1, 606.0 dm6^{6}6 atm2^{2}2 mol−2^{-2}−2
  2. (B)1, 24.62 dm3^{3}3 atm mol−1^{-1}−1, 1.65 ×\times× 10−3^{-3}−3 dm−6^{-6}−6 atm−2^{-2}−2 mol2^{2}2
  3. (C)1, 4.1 ×\times× 10−2^{-2}−2 dm−3^{-3}−3 atm−1^{-1}−1 mol, 606.0 dm6^{6}6 atm2^{2}2 mol−2^{-2}−2
  4. (D)24.62 dm3^{3}3 atm mol−1^{-1}−1, 606.0 dm6^{6}6 atm2^{2}2 atm2^{2}2 mol−2^{-2}−2, 1.65 ×\times× 10−3^{-3}−3 dm−6^{-6}−6 atm−2^{-2}−2 mol2^{2}2

Correct answer: (B)

Step-by-step solution →
Q28·ChemistrySingle correct
The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively are
  1. (A)3 and 1
  2. (B)3 and 2
  3. (C)2 and 1
  4. (D)2 and 0

Correct answer: (A)

Step-by-step solution →
Q29·ChemistrySingle correct
Water filled in two glasses A and B have BOD values of 10 and 20 respectively. The correct statement regarding them is
  1. (A)B is more polluted than A
  2. (B)A is suitable for drinking, whereas B is not
  3. (C)both A and B are suitable for drinking
  4. (D)A is more polluted than B

Correct answer: (A)

Step-by-step solution →
Q30·ChemistrySingle correct
Which primitive unit cell has unequal edge length (a ≠ b ≠ c) and all axial angles different from 90°?
  1. (A)Triclinic
  2. (B)Hexagonal
  3. (C)Monoclinic
  4. (D)Tetragonal

Correct answer: (A)

Step-by-step solution →
Q31·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 →
Q32·ChemistrySingle correct
Consider the given plots for a reaction obeying Arrhenius equation (0°C < T < 300°C) : (k and Ea_{a}a​ are rate constant and activation energy respectively) Choose the correct option:
  1. (A)I is right but II is wrong
  2. (B)Both I and Ii are correct
  3. (C)I is wrong but II is right
  4. (D)Both I and II are wrong

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Wilkinson catalyst is
  1. (A)[(Ph3_{3}3​P)3_{3}3​IrCl]
  2. (B)[Et3_{3}3​P)3_{3}3​RhCl]
  3. (C)[(Ph3_{3}3​P)3_{3}3​RhCl]
  4. (D)[(Et3_{3}3​P)3_{3}3​IrCl]

Correct answer: (C)

Step-by-step solution →
Q34·ChemistrySingle correct
If dichloromethane(DCM) and water(H2_{2}2​O) are used for differential extraction, which one of the following statements is correct?
  1. (A)DCM and H2_{2}2​O would stay as lower and upper layer respectively in the S.F
  2. (B)DCM and H2_{2}2​O will make turbid/colloidal mixture
  3. (C)DCM and H2_{2}2​O would stay as upper and lower layer respectively in the separating funnel(S.F)
  4. (D)DCM and H2_{2}2​O will be miscible clearly

Correct answer: (A)

Step-by-step solution →
Q35·ChemistrySingle correct
Which diccarboxylic acid in presence of a dehydrating agent is least reactive to give anhydride?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
The decreasing order of ease of alkaline hydrolysis for the following ester is
  1. (A)III > II > IV > I
  2. (B)III > II > I > IV
  3. (C)IV > II > III > I
  4. (D)II > III > I > IV

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
Which of the following is not an example of heterogeneous catalytic reaction?
  1. (A)Ostwald's process
  2. (B)Combustion of coal
  3. (C)Hydrogenation of vegetable oils
  4. (D)Haber's process

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
The effect of lanthanoid contraction in the lanthanoid series of elements by the large means
  1. (A)increase in both atomic and ionic radii
  2. (B)decrease in atomic radii and increase in ionic radii
  3. (C)decrease in both atomic and ionic radii
  4. (D)increase in atomic radii and decrease in ionic radii

Correct answer: (C)

Step-by-step solution →
Q40·ChemistrySingle correct
Which hydrogen in compound(E) is easily replaceable during bromination reaction in presence of light?
  1. (A)α\alphaα - hydrogen
  2. (B)γ\gammaγ - hydrogen
  3. (C)δ\deltaδ - hydrogen
  4. (D)β\betaβ - hydrogen

Correct answer: (B)

Step-by-step solution →
Q41·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 →
Q42·ChemistrySingle correct
The correct structure of product 'P' in the following reaction is
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
The type of hybridisation and number of lone pair(s) of electrons of Xe in XeOF4_{4}4​ respectively are
  1. (A)sp3^{3}3d2^{2}2 and 1
  2. (B)sp3^{3}3d and 2
  3. (C)sp3^{3}3d2^{2}2 and 2
  4. (D)sp3^{3}3d and 1

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
The electronegativity of aluminium is similar to
  1. (A)carbon
  2. (B)beryllium
  3. (C)boron
  4. (D)lithium

Correct answer: (B)

Step-by-step solution →
Q45·ChemistrySingle correct
Consider the following Zn2+^{2+}2+ + 2e−^{-}− ⟶\longrightarrow⟶ Zn(s); Eo^{o}o = −0.76-0.76−0.76 V Ca2+^{2+}2+ + 2e−^{-}− ⟶\longrightarrow⟶ Ca(s); Eo^{o}o = −2.87-2.87−2.87 V Mg2+^{2+}2+ + 2e−^{-}− ⟶\longrightarrow⟶ Mg(s); Eo^{o}o = −2.36-2.36−2.36 V Ni2+^{2+}2+ + 2e−^{-}− ⟶\longrightarrow⟶ Ni(s); Eo^{o}o = −0.25-0.25−0.25 V The reducing power of the metals increases in the order
  1. (A)Ca < Zn < Mg < Ni
  2. (B)Ni < Zn < Mg < Ca
  3. (C)Zn < Mg < Ni < Ca
  4. (D)Ca < Mg < Zn < Ni

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
The chemical nature of hydrogen peroxide is
  1. (A)oxidising agent in acidic medium, but not in basic medium
  2. (B)reducing agent in basic medium but not in acidic medium
  3. (C)oxidising and reducing agent in acidic medium but not in basic medium
  4. (D)oxidising and reducing agent in both acidic and basic medium

Correct answer: (D)

Step-by-step solution →
Q47·ChemistrySingle correct
A mixture of 100 m mol of Ca(OH)2_{2}2​ and 2 g of sodium sulphate was dissolved in water and the volume was made upto 100 mL. The mass of calcium sulphate formed and the concentration of OH−^{-}− in resulting solution, respectively are (Molar mass of Ca(OH)2_{2}2​, Na2_{2}2​SO4_{4}4​ and CaSO4_{4}4​ are 74, 143 and 136 g mol−1^{-1}−1 respectively; Ksp_{sp}sp​ of Ca(OH)2_{2}2​ is 5.5 ×\times× 10−6^{-6}−6)
  1. (A)1.9 g, 0.28 mol L−1^{-1}−1
  2. (B)13.6 g, 0.28 mol L−1^{-1}−1
  3. (C)1.9g, 0.14 mol L−1^{-1}−1
  4. (D)13.6 g, 0.14 mol L−1^{-1}−1

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
Liquids A and B form and ideal solution in the entire composition range. At 350 K, the vapour pressures of pure A and pure B are 7 ×\times× 103^{3}3 Pa and 12 ×\times× 103^{3}3 Pa, respectively. The composition of the vapour in equilibrium with a solution containing 40 mole percent of A at this temperature is
  1. (A)xA_{A}A​ = 0.37; xB_{B}B​ = 0.63
  2. (B)xA_{A}A​ = 0.28; xB_{B}B​ = 0.72
  3. (C)xA_{A}A​ = 0.4; xB_{B}B​ = 0.6
  4. (D)xA_{A}A​ = 0.76; xB_{B}B​ = 0.24

Correct answer: (B)

Step-by-step solution →
Q49·ChemistrySingle correct
The major product 'X' formed in the following reaction is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q50·ChemistrySingle correct
The metal used for making X-ray tube window is
  1. (A)Mg
  2. (B)Na
  3. (C)Be
  4. (D)Ca

Correct answer: (C)

Step-by-step solution →
Q51·ChemistrySingle correct
The increasing order of pKa values of the following compounds is
  1. (A)C < B < A < D
  2. (B)B < C < D < A
  3. (C)D < A < C < B
  4. (D)B < C < A < D

Correct answer: (D)

Step-by-step solution →
Q52·ChemistrySingle correct
Hall-Herolut's process is given by
  1. (A)Cu2+^{2+}2+(aq) + H2_{2}2​(g) ⟶\longrightarrow⟶ Cu(s) + 2H+^{+}+(aq)
  2. (B)Cr2_{2}2​O3_{3}3​ + 2Al ⟶\longrightarrow⟶ Al2_{2}2​O3_{3}3​ + 2Cr
  3. (C)2Al2_{2}2​O3_{3}3​ + 3C ⟶\longrightarrow⟶ 4Al + 3CO2_{2}2​
  4. (D)ZnO + C →Coke, 1673 K\xrightarrow{\text{Coke, 1673 K}}Coke, 1673 K​ Zn + CO

Correct answer: (C)

Step-by-step solution →
Q53·ChemistrySingle correct
Two pi and half sigma bonds are present in
  1. (A)O2+_{2}^{+}2+​
  2. (B)N2_{2}2​
  3. (C)O2_{2}2​
  4. (D)N2+_{2}^{+}2+​

Correct answer: (D)

Step-by-step solution →

Mathematics — JEE Main 10 January 2019 Shift 1

Q54·MathematicsSingle correct
The shortest distance between the point (32,0)\left(\frac{3}{2},0\right)(23​,0) and the curve y=x,(x>0)y=\sqrt{x},(x>0)y=x​,(x>0), is:
  1. (A)52\frac{\sqrt{5}}{2}25​​
  2. (B)32\frac{\sqrt{3}}{2}23​​
  3. (C)32\frac{3}{2}23​
  4. (D)54\frac{5}{4}45​

Correct answer: (A)

Step-by-step solution →
Q55·MathematicsSingle correct
The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is:
  1. (A)10 : 3
  2. (B)4 : 9
  3. (C)5 : 8
  4. (D)6 : 7

Correct answer: (B)

Step-by-step solution →
Q56·MathematicsSingle correct
If 5, 5r, 5r2^{2}2 are the lengths of the sides of a triangle, then r cannot be equal to:
  1. (A)34\frac{3}{4}43​
  2. (B)54\frac{5}{4}45​
  3. (C)74\frac{7}{4}47​
  4. (D)32\frac{3}{2}23​

Correct answer: (C)

Step-by-step solution →
Q57·MathematicsSingle correct
If ∑i=120(20Ci−120Ci+20Ci−1)3=k21\sum_{i=1}^{20}\left(\frac{^{20}C_{i-1}}{^{20}C_i+^{20}C_{i-1}}\right)^{3}=\frac{k}{21}∑i=120​(20Ci​+20Ci−1​20Ci−1​​)3=21k​, then k equals:
  1. (A)400
  2. (B)50
  3. (C)200
  4. (D)100

Correct answer: (D)

Step-by-step solution →
Q58·MathematicsSingle correct
The sum of all values of θ∈(0,π2)\theta\in\left(0,\frac{\pi}{2}\right)θ∈(0,2π​) satisfying sin⁡22θ+cos⁡42θ=34\sin^{2}2\theta+\cos^{4}2\theta=\frac{3}{4}sin22θ+cos42θ=43​ is:
  1. (A)π\piπ
  2. (B)5π4\frac{5\pi}{4}45π​
  3. (C)π2\frac{\pi}{2}2π​
  4. (D)3π8\frac{3\pi}{8}83π​

Correct answer: (C)

Step-by-step solution →
Q59·MathematicsSingle correct
If dydx+3cos⁡2xy=1cos⁡2x,x∈(−π3,π3)\frac{dy}{dx}+\frac{3}{\cos^{2}x}y=\frac{1}{\cos^{2}x},x\in\left(\frac{-\pi}{3},\frac{\pi}{3}\right)dxdy​+cos2x3​y=cos2x1​,x∈(3−π​,3π​) and y(π4)=43y\left(\frac{\pi}{4}\right)=\frac{4}{3}y(4π​)=34​, then y(−π4)y\left(-\frac{\pi}{4}\right)y(−4π​) equals:
  1. (A)13+e6\frac{1}{3}+e^{6}31​+e6
  2. (B)13\frac{1}{3}31​
  3. (C)−43-\frac{4}{3}−34​
  4. (D)13+e3\frac{1}{3}+e^{3}31​+e3

Correct answer: (A)

Step-by-step solution →
Q60·MathematicsSingle correct
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:
  1. (A)102
  2. (B)42
  3. (C)1
  4. (D)38

Correct answer: (D)

Step-by-step solution →
Q61·MathematicsSingle correct
If the third term in the binomial expansion of (1+xlog⁡2x)5\left(1+x^{\log_{2}x}\right)^{5}(1+xlog2​x)5 equals 2560, then a possible value of x is:
  1. (A)14\frac{1}{4}41​
  2. (B)424\sqrt{2}42​
  3. (C)18\frac{1}{8}81​
  4. (D)222\sqrt{2}22​

Correct answer: (A)

Step-by-step solution →
Q62·MathematicsSingle correct
If the parabolas y2=4b(x−c)y^{2}=4b(x-c)y2=4b(x−c) and y2=8axy^{2}=8axy2=8ax have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c)?
  1. (A)(12,2,3)\left(\frac{1}{2},2,3\right)(21​,2,3)
  2. (B)(1, 1, 3)
  3. (C)(12,2,0)\left(\frac{1}{2},2,0\right)(21​,2,0)
  4. (D)(1, 1, 0)

Correct answer: (B)

Step-by-step solution →
Q63·MathematicsSingle correct
If the system of equations x+y+z=5x+y+z=5x+y+z=5, x+2y+3z=9x+2y+3z=9x+2y+3z=9, x+3y+αz=βx+3y+\alpha z=\betax+3y+αz=β has infinitely many solutions, then β−α\beta-\alphaβ−α equals:
  1. (A)21
  2. (B)8
  3. (C)18
  4. (D)5

Correct answer: (B)

Step-by-step solution →
Q64·MathematicsSingle correct
Let I=∫ab(x4−2x2) dxI = \displaystyle\int_{a}^{b} (x^4 - 2x^2)\,dxI=∫ab​(x4−2x2)dx. If I is minimum then the ordered pair (a, b) is:
  1. (A)(0,2)(0, \sqrt{2})(0,2​)
  2. (B)(−2,0)(-\sqrt{2}, 0)(−2​,0)
  3. (C)(2,−2)(\sqrt{2}, -\sqrt{2})(2​,−2​)
  4. (D)(−2,2)(-\sqrt{2}, \sqrt{2})(−2​,2​)

Correct answer: (D)

Step-by-step solution →
Q65·MathematicsSingle correct
A point P moves on the line 2x−3y+4=02x - 3y + 4 = 02x−3y+4=0. If Q(1, 4) and R(3, −2-2−2) are fixed points, then the locus of the centroid of △\triangle△PQR is a line:
  1. (A)with slope 32\dfrac{3}{2}23​
  2. (B)parallel to x-axis
  3. (C)with slope 23\dfrac{2}{3}32​
  4. (D)parallel to y-axis

Correct answer: (C)

Step-by-step solution →
Q66·MathematicsSingle correct
Let f(x)={max⁡{∣x∣,x2},∣x∣≤28−2∣x∣,2<∣x∣≤4f(x) = \begin{cases} \max\{|x|, x^2\}, & |x| \leq 2 \\ 8 - 2|x|, & 2 < |x| \leq 4 \end{cases}f(x)={max{∣x∣,x2},8−2∣x∣,​∣x∣≤22<∣x∣≤4​. Let S be the set of points in the interval (−4, 4) at which f is not differentiable. Then S:
  1. (A)is an empty set
  2. (B)equals {−2,−1,0,1,2}\{-2, -1, 0, 1, 2\}{−2,−1,0,1,2}
  3. (C)equals {−2,−1,1,2}\{-2, -1, 1, 2\}{−2,−1,1,2}
  4. (D)equals {−2,2}\{-2, 2\}{−2,2}

Correct answer: (B)

Step-by-step solution →
Q67·MathematicsSingle correct
If a circle C passing through the point (4, 0) touches the circle x2+y2+4x−6y=12x^2 + y^2 + 4x - 6y = 12x2+y2+4x−6y=12 externally at the point (1, −1), then the radius of C is:
  1. (A)252\sqrt{5}25​
  2. (B)4
  3. (C)5
  4. (D)57\sqrt{57}57​

Correct answer: (C)

Step-by-step solution →
Q68·MathematicsSingle correct
Let f:R→Rf : R \to Rf:R→R be a function such that f(x)=x3+x2f′(1)+xf′′(2)+f′′′(3)f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)f(x)=x3+x2f′(1)+xf′′(2)+f′′′(3), x∈Rx \in Rx∈R. Then f(2)f(2)f(2) equals:
  1. (A)-4
  2. (B)30
  3. (C)-2
  4. (D)8

Correct answer: (C)

Step-by-step solution →
Q69·MathematicsSingle correct
Let a⃗=2i^+λ1j^+3k^\vec{a} = 2\hat{i} + \lambda_1\hat{j} + 3\hat{k}a=2i^+λ1​j^​+3k^, b⃗=4i^+(3−λ2)j^+6k^\vec{b} = 4\hat{i} + (3 - \lambda_2)\hat{j} + 6\hat{k}b=4i^+(3−λ2​)j^​+6k^ and c⃗=3i^+6j^+(λ3−1)k^\vec{c} = 3\hat{i} + 6\hat{j} + (\lambda_3 - 1)\hat{k}c=3i^+6j^​+(λ3​−1)k^ be three vectors such that b⃗=2a⃗\vec{b} = 2\vec{a}b=2a and a⃗\vec{a}a is perpendicular to c⃗\vec{c}c. Then a possible value of (λ1,λ2,λ3)(\lambda_1, \lambda_2, \lambda_3)(λ1​,λ2​,λ3​) is:
  1. (A)(1, 3, 1)
  2. (B)(−12,4,0)\left(-\dfrac{1}{2}, 4, 0\right)(−21​,4,0)
  3. (C)(12,4,−2)\left(\dfrac{1}{2}, 4, -2\right)(21​,4,−2)
  4. (D)(1, 5, 1)

Correct answer: (B)

Step-by-step solution →
Q70·MathematicsSingle correct
Let A be a point on the line r⃗=(1−3μ)i^+(μ−1)j^+(2+5μ)k^\vec{r} = (1 - 3\mu)\hat{i} + (\mu - 1)\hat{j} + (2 + 5\mu)\hat{k}r=(1−3μ)i^+(μ−1)j^​+(2+5μ)k^ and B(3, 2, 6) be a point in the space. Then the value of μ\muμ for which the vector AB→\overrightarrow{AB}AB is parallel to the plane x−4y+3z=1x - 4y + 3z = 1x−4y+3z=1 is:
  1. (A)14\dfrac{1}{4}41​
  2. (B)18\dfrac{1}{8}81​
  3. (C)12\dfrac{1}{2}21​
  4. (D)−14-\dfrac{1}{4}−41​

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is:
  1. (A)3221\dfrac{3}{2}\sqrt{21}23​21​
  2. (B)2321\dfrac{2}{3}\sqrt{21}32​21​
  3. (C)2212\sqrt{21}221​
  4. (D)7217\sqrt{21}721​

Correct answer: (B)

Step-by-step solution →
Q72·MathematicsSingle correct
The equation of a tangent to the hyperbola 4x2−5y2=204x^2 - 5y^2 = 204x2−5y2=20 parallel to the line x−y=2x - y = 2x−y=2 is:
  1. (A)x − y + 1 = 0
  2. (B)x − y + 7 = 0
  3. (C)x − y + 9 = 0
  4. (D)x − y − 3 = 0

Correct answer: (A)

Step-by-step solution →
Q73·MathematicsSingle correct
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is:
  1. (A)1256
  2. (B)1465
  3. (C)1365
  4. (D)1356

Correct answer: (D)

Step-by-step solution →
Q74·MathematicsSingle correct
If the area enclosed between the curves y=kx2y = kx^2y=kx2 and x=ky2x = ky^2x=ky2, (k>0k > 0k>0), is 1 square unit. Then k is:
  1. (A)32\dfrac{\sqrt{3}}{2}23​​
  2. (B)13\dfrac{1}{\sqrt{3}}3​1​
  3. (C)3\sqrt{3}3​
  4. (D)23\dfrac{2}{\sqrt{3}}3​2​

Correct answer: (B)

Step-by-step solution →
Q75·MathematicsSingle correct
Consider the statement: \"P(n): n2−n+41n^2 - n + 41n2−n+41 is prime.\" Then which one of the following is true?
  1. (A)Both P(3) and P(5) are true
  2. (B)P(3) is false but P(5) is true
  3. (C)Both P(3) and P(5) are false
  4. (D)P(5) is false but P(3) is true

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
  • Definite Integration 168/186
  • Redox Reactions and Electrochemistry 177/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • 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
  • Hydrocarbons 126/186
  • 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
  • Work, Energy and Power 132/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Alcohols and Ethers 106/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Statistics 118/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Hyperbola 77/186
  • Experimental Skills 68/186
  • Electric Potential 63/186
  • Carboxylic Acids and Derivatives 54/186
  • Solid State 63/186
  • Mathematical Reasoning 26/186
  • Communication Systems 11/186
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