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JEE Main 12 April 2019 Shift 1 Question Paper with Answers

12 April 2019 · April session · 85 questions

85 of the 90 questions from the JEE Main 12 April 2019 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

5 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
28
Chemistry
29
Mathematics
28

Physics — JEE Main 12 April 2019 Shift 1

Q1·PhysicsSingle correct
The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 Å is used, the minimum separation between two points, to be seen as distinct, will be :
  1. (A)0.48 μm
  2. (B)0.38 μm
  3. (C)0.24 μm
  4. (D)0.12 μm

Correct answer: (C)

Step-by-step solution →
Q2·PhysicsSingle correct
The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of 1 cms−1^{-1}−1. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 Ω, the current in the loop at that instant will be close to :
  1. (A)115 μA
  2. (B)170 μA
  3. (C)60 μA
  4. (D)150 μA

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as (σ0r)\left(\dfrac{\sigma_0}{r}\right)(rσ0​​), then the radius of gyration of the disc about its axis passing through the centre is :
  1. (A)a+b3\dfrac{a+b}{3}3a+b​
  2. (B)a2+b2+ab3\sqrt{\dfrac{a^{2}+b^{2}+ab}{3}}3a2+b2+ab​​
  3. (C)a+b2\dfrac{a+b}{2}2a+b​
  4. (D)a2+b2+ab2\sqrt{\dfrac{a^{2}+b^{2}+ab}{2}}2a2+b2+ab​​

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms−1^{-1}−1 with respect to the man. The speed of the man with respect to the surface is :
  1. (A)0.47 ms−1^{-1}−1
  2. (B)0.28 ms−1^{-1}−1
  3. (C)0.14 ms−1^{-1}−1
  4. (D)0.20 ms−1^{-1}−1

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1K_1K1​, K2K_2K2​ and K3K_3K3​. The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig. II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E1E_1E1​ refers to capacitor (I) and E2E_2E2​ to capacitor (II)) :
  1. (A)E1E2=K1K2K3(K1+K2+K3)(K2K3+K3K1+K1K2)\dfrac{E_1}{E_2}=\dfrac{K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}E2​E1​​=(K1​+K2​+K3​)(K2​K3​+K3​K1​+K1​K2​)K1​K2​K3​​
  2. (B)E1E2=9K1K2K3(K1+K2+K3)(K2K3+K3K1+K1K2)\dfrac{E_1}{E_2}=\dfrac{9K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}E2​E1​​=(K1​+K2​+K3​)(K2​K3​+K3​K1​+K1​K2​)9K1​K2​K3​​
  3. (C)E1E2=(K1+K2+K3)(K2K3+K3K1+K1K2)9K1K2K3\dfrac{E_1}{E_2}=\dfrac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{9K_1K_2K_3}E2​E1​​=9K1​K2​K3​(K1​+K2​+K3​)(K2​K3​+K3​K1​+K1​K2​)​
  4. (D)E1E2=(K1+K2+K3)(K2K3+K3K1+K1K2)K1K2K3\dfrac{E_1}{E_2}=\dfrac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{K_1K_2K_3}E2​E1​​=K1​K2​K3​(K1​+K2​+K3​)(K2​K3​+K3​K1​+K1​K2​)​

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R = 8.3 J/mol K)
  1. (A)17.4 J/mol K
  2. (B)15.7 J/mol K
  3. (C)19.7 J/mol K
  4. (D)21.6 J/mol K

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
The stopping potential V0V_0V0​ (in volt) as a function of frequency (ν\nuν) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be : (Given : Planck's constant (h) = 6.63 ×\times× 10−34^{-34}−34 Js, electron charge e = 1.6 ×\times× 10−19^{-19}−19 C)
  1. (A)1.82 eV
  2. (B)1.66 eV
  3. (C)2.12 eV
  4. (D)1.95 eV

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30º. If B1B_1B1​ and B2B_2B2​ are respectively the total magnetic field due to the earth at the two places, then the ratio B1/B2B_1/B_2B1​/B2​ is best given by :
  1. (A)3.6
  2. (B)1.8
  3. (C)2.2
  4. (D)0.7

Correct answer: (D)

Step-by-step solution →
Q9·PhysicsSingle correct
An excited He+^++ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength λ\lambdaλ, energy E=1240 eVλ(in nm)E=\dfrac{1240\ \text{eV}}{\lambda(\text{in nm})}E=λ(in nm)1240 eV​ :)
  1. (A)n = 4
  2. (B)n = 6
  3. (C)n = 5
  4. (D)n = 7

Correct answer: (C)

Step-by-step solution →
Q10·PhysicsSingle correct
When M1M_1M1​ gram of ice at −10-10−10ºC (specific heat = 0.5 cal g−1^{-1}−1°C−1^{-1}−1) is added to M2M_2M2​ gram of water at 50ºC, finally no ice is left and the water is at 0ºC. The value of latent heat of ice, in cal g−1^{-1}−1 is:
  1. (A)50M2M1−5\dfrac{50M_2}{M_1}-5M1​50M2​​−5
  2. (B)5M2M1−5\dfrac{5M_2}{M_1}-5M1​5M2​​−5
  3. (C)50M2M1\dfrac{50M_2}{M_1}M1​50M2​​
  4. (D)5M1M2−50\dfrac{5M_1}{M_2}-50M2​5M1​​−50

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1t_1t1​ and t2t_2t2​ are the values of the time taken by it to hit the target in two possible ways, the product t1t2t_1t_2t1​t2​ is:
  1. (A)2R / g
  2. (B)R / 4g
  3. (C)R / g
  4. (D)R/2g

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
The transfer characteristic curve of a transistor, having input and output resistance 100 Ω and 100 kΩ respectively, is shown in the figure. The Voltage and Power gain, are respectively :
  1. (A)5×1045\times10^{4}5×104, 2.5×1062.5\times10^{6}2.5×106
  2. (B)5×1045\times10^{4}5×104, 5×1065\times10^{6}5×106
  3. (C)5×1045\times10^{4}5×104, 5×1055\times10^{5}5×105
  4. (D)2.5×1042.5\times10^{4}2.5×104, 2.5×1062.5\times10^{6}2.5×106

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole P⃗\vec{P}P as shown. In this case :
  1. (A)Surface charge density on the inner surface of the shell is zero everywhere.
  2. (B)Electric field outside the shell is the same as that of a point charge at the centre of the shell.
  3. (C)Surface charge density on the inner surface is uniform and equal to (Q/2)4πa2\dfrac{(Q/2)}{4\pi a^{2}}4πa2(Q/2)​
  4. (D)Surface charge density on the outer surface depends on ∣P⃗∣|\vec{P}|∣P∣

Correct answer: (B)

Step-by-step solution →
Q14·PhysicsSingle correct
Which of the following combinations has the dimension of electrical resistance (ϵ0\epsilon_0ϵ0​ is the permittivity of vacuum and μ0\mu_0μ0​ is the permeability of vacuum)?
  1. (A)ϵ0μ0\sqrt{\dfrac{\epsilon_0}{\mu_0}}μ0​ϵ0​​​
  2. (B)μ0ϵ0\dfrac{\mu_0}{\epsilon_0}ϵ0​μ0​​
  3. (C)ϵ0μ0\dfrac{\epsilon_0}{\mu_0}μ0​ϵ0​​
  4. (D)μ0ϵ0\sqrt{\dfrac{\mu_0}{\epsilon_0}}ϵ0​μ0​​​

Correct answer: (D)

Step-by-step solution →
Q15·PhysicsSingle correct
A galvanometer of resistance 100 Ω\OmegaΩ has 50 divisions on its scale and has sensitivity of 20 μ\muμA / division. It is to be converted to a voltmeter with three ranges, of 0–2 V, 0–10 V and 0–20 V. The appropriate circuit to do so is :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
In a double slit experiment, when a thin film of thickness t having refractive index μ\muμ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is (λ\lambdaλ is the wavelength of the light used) :
  1. (A)λ2(μ−1)\dfrac{\lambda}{2(\mu-1)}2(μ−1)λ​
  2. (B)λ(μ−1)\dfrac{\lambda}{(\mu-1)}(μ−1)λ​
  3. (C)λ(2μ−1)\dfrac{\lambda}{(2\mu-1)}(2μ−1)λ​
  4. (D)2λ(μ−1)\dfrac{2\lambda}{(\mu-1)}(μ−1)2λ​

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
A progressive wave travelling along the positive x-direction is represented by y(x, t) = A sin(kx −-− ω\omegaωt + ϕ\phiϕ). Its snapshot at t = 0 is given in the figure: For this wave, the phase ϕ\phiϕ is :
  1. (A)π\piπ
  2. (B)π2\dfrac{\pi}{2}2π​
  3. (C)−π2-\dfrac{\pi}{2}−2π​
  4. (D)0

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
A uniform rod of length ℓ\ellℓ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (D)

Step-by-step solution →
Q19·PhysicsSingle correct
A point dipole p⃗=−p0x^\vec{p} = -p_0\hat{x}p​=−p0​x^ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively : (Take V = 0 at infinity)
  1. (A)∣p⃗∣4πε0d2,−p⃗4πε0d3\dfrac{|\vec{p}|}{4\pi\varepsilon_0 d^{2}}, \dfrac{-\vec{p}}{4\pi\varepsilon_0 d^{3}}4πε0​d2∣p​∣​,4πε0​d3−p​​
  2. (B)0,p⃗4πε0d30, \dfrac{\vec{p}}{4\pi\varepsilon_0 d^{3}}0,4πε0​d3p​​
  3. (C)∣p⃗∣4πε0d2,p⃗4πε0d3\dfrac{|\vec{p}|}{4\pi\varepsilon_0 d^{2}}, \dfrac{\vec{p}}{4\pi\varepsilon_0 d^{3}}4πε0​d2∣p​∣​,4πε0​d3p​​
  4. (D)0,−p⃗4πε0d30, \dfrac{-\vec{p}}{4\pi\varepsilon_0 d^{3}}0,4πε0​d3−p​​

Correct answer: (D)

Step-by-step solution →
Q20·PhysicsSingle correct
An electromagnetic wave is represented by the electric field E⃗=E0n^sin⁡[ωt+(6y−8z)]\vec{E} = E_0\hat{n}\sin[\omega t + (6y - 8z)]E=E0​n^sin[ωt+(6y−8z)]. Taking unit vectors in x, y and z directions to be i^,j^,k^\hat{i}, \hat{j}, \hat{k}i^,j^​,k^, the direction of propogation s^\hat{s}s^, is :
  1. (A)S^=(−3j^+4k^5)\hat{S} = \left(\dfrac{-3\hat{j}+4\hat{k}}{5}\right)S^=(5−3j^​+4k^​)
  2. (B)S^=(4j^−3k^5)\hat{S} = \left(\dfrac{4\hat{j}-3\hat{k}}{5}\right)S^=(54j^​−3k^​)
  3. (C)S^=(−4k^+3j^5)\hat{S} = \left(\dfrac{-4\hat{k}+3\hat{j}}{5}\right)S^=(5−4k^+3j^​​)
  4. (D)S^=(−3i^−4j^5)\hat{S} = \left(\dfrac{-3\hat{i}-4\hat{j}}{5}\right)S^=(5−3i^−4j^​​)

Correct answer: (A)

Step-by-step solution →
Q21·PhysicsSingle correct
A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency ν\nuν. The value of ν\nuν is close to : (Speed of sound in water = 1500 ms−1^{-1}−1)
  1. (A)499 Hz
  2. (B)502 Hz
  3. (C)504 Hz
  4. (D)507 Hz

Correct answer: (B)

Step-by-step solution →
Q22·PhysicsSingle correct
The trajectory of a projectile near the surface of the earth is given as y = 2x −-− 9x2^{2}2. If it were launched at an angle θ0\theta_0θ0​ with speed v0_00​ then (g = 10 ms−2^{-2}−2) :
  1. (A)θ0=cos⁡−1(15)\theta_0 = \cos^{-1}\left(\dfrac{1}{\sqrt{5}}\right)θ0​=cos−1(5​1​) and v0_00​ = 53\dfrac{5}{3}35​ ms−1^{-1}−1
  2. (B)θ0=cos⁡−1(25)\theta_0 = \cos^{-1}\left(\dfrac{2}{\sqrt{5}}\right)θ0​=cos−1(5​2​) and v0_00​ = 35\dfrac{3}{5}53​ ms−1^{-1}−1
  3. (C)θ0=sin⁡−1(25)\theta_0 = \sin^{-1}\left(\dfrac{2}{\sqrt{5}}\right)θ0​=sin−1(5​2​) and v0_00​ = 35\dfrac{3}{5}53​ ms−1^{-1}−1
  4. (D)θ0=sin⁡−1(15)\theta_0 = \sin^{-1}\left(\dfrac{1}{\sqrt{5}}\right)θ0​=sin−1(5​1​) and v0_00​ = 53\dfrac{5}{3}35​ ms−1^{-1}−1

Correct answer: (A)

Step-by-step solution →
Q23·PhysicsSingle correct
A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40π\piπ rad s−1^{-1}−1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 ×\times× 10−9^{-9}−9 T, then the charge carried by the ring is close to (μ0=4π×10−7\mu_0 = 4\pi \times 10^{-7}μ0​=4π×10−7N/A2^{2}2).
  1. (A)2 ×\times× 10−6^{-6}−6 C
  2. (B)7 ×\times× 10−6^{-6}−6 C
  3. (C)4 ×\times× 10−5^{-5}−5 C
  4. (D)3 ×\times× 10−5^{-5}−5 C

Correct answer: (D)

Step-by-step solution →
Q24·PhysicsSingle correct
The truth table for the circuit given in the fig is :
  1. (A)A B Y: 0 0 1; 0 1 0; 1 0 0; 1 1 0
  2. (B)A B Y: 0 0 0; 0 1 0; 1 0 1; 1 1 1
  3. (C)A B Y: 0 0 1; 0 1 1; 1 0 1; 1 1 1
  4. (D)A B Y: 0 0 1; 0 1 1; 1 0 0; 1 1 0

Correct answer: (D)

Step-by-step solution →
Q25·PhysicsSingle correct
A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is −-−180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is :
  1. (A)120 J
  2. (B)100 J
  3. (C)140 J
  4. (D)130 J

Correct answer: (D)

Step-by-step solution →
Q26·PhysicsSingle correct
A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to : (Refractive index of water = 1.33)
  1. (A)13.4 cm
  2. (B)8.8 cm
  3. (C)6.7 cm
  4. (D)11.7 cm

Correct answer: (B)

Step-by-step solution →
Q27·PhysicsSingle correct
To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained: If V0_00​ is almost zero, identify the correct statement:
  1. (A)The potential difference across the battery is 1.5 V when it sends a current of 1000 mA.
  2. (B)The emf of the battery is 1.5 V and the value of R is 1.5 Ω\OmegaΩ
  3. (C)The emf of the battery is 1.5 V and its internal resistance is 1.5 Ω\OmegaΩ
  4. (D)The value of the resistance R is 1.5 Ω\OmegaΩ

Correct answer: (C)

Step-by-step solution →
Q28·PhysicsSingle correct
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0\theta_0θ0​. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance ℓ\ellℓ (ℓ\ellℓ << L), is close to :
  1. (A)Mgℓ(1+θ02)Mg\ell(1+\theta_0^{2})Mgℓ(1+θ02​)
  2. (B)Mgℓ(1−θ02)Mg\ell(1-\theta_0^{2})Mgℓ(1−θ02​)
  3. (C)MgℓMg\ellMgℓ
  4. (D)Mgℓ(1+θ022)Mg\ell\left(1+\dfrac{\theta_0^{2}}{2}\right)Mgℓ(1+2θ02​​)

Correct answer: (A)

Step-by-step solution →

Chemistry — JEE Main 12 April 2019 Shift 1

Q29·ChemistrySingle correct
The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol kg−1^{-1}−1) of the aqueous solution is
  1. (A)13.88×10−213.88 \times 10^{-2}13.88×10−2
  2. (B)13.88×10−113.88 \times 10^{-1}13.88×10−1
  3. (C)13.8813.8813.88
  4. (D)13.88×10−313.88 \times 10^{-3}13.88×10−3

Correct answer: (C)

Step-by-step solution →
Q30·ChemistrySingle correct
The major products of the following reaction are: (1) CHCl3_33​/aq. NaOH (2) HCHO, NaOH(conc.) (3) H3_33​O+^++
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q31·ChemistrySingle correct
The correct statement among the following is
  1. (A)(SiH3)3N(SiH_3)_3N(SiH3​)3​N is planar and less basic than (CH3)3N(CH_3)_3N(CH3​)3​N.
  2. (B)(SiH3)3N(SiH_3)_3N(SiH3​)3​N is planar and more basic than (CH3)3N(CH_3)_3N(CH3​)3​N.
  3. (C)(SiH3)3N(SiH_3)_3N(SiH3​)3​N is pyramidal and less basic than (CH3)3N(CH_3)_3N(CH3​)3​N.
  4. (D)(SiH3)3N(SiH_3)_3N(SiH3​)3​N is pyramidal and more basic than (CH3)3N(CH_3)_3N(CH3​)3​N.

Correct answer: (A)

Step-by-step solution →
Q32·ChemistrySingle correct
The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is (Phen = the ligand shown, and ignore pairing energy)
  1. (A)[Ni(phen)3]2+[Ni(phen)_3]^{2+}[Ni(phen)3​]2+
  2. (B)[Zn(phen)3]2+[Zn(phen)_3]^{2+}[Zn(phen)3​]2+
  3. (C)[Co(phen)3]2+[Co(phen)_3]^{2+}[Co(phen)3​]2+
  4. (D)[Fe(phen)3]2+[Fe(phen)_3]^{2+}[Fe(phen)3​]2+

Correct answer: (D)

Step-by-step solution →
Q33·ChemistrySingle correct
The correct set of species responsible for the photochemical smog is :
  1. (A)NO, NO2_22​, O3_33​ and hydrocarbons
  2. (B)CO2_22​, NO2_22​ SO2_22​ and hydrocarbons
  3. (C)N2_22​, NO2_22​ and hydrocarbons
  4. (D)N2_22​, O2_22​, O3_33​ and hydrocarbons

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
The major product(s) obtained in the following reaction is/are: (i) KOt^ttBu (ii) O3_33​/Me2_22​S
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
The major product of the following addition reaction is: H3_33​C – CH=CH2_22​ →Cl2/H2O\xrightarrow{Cl_2/H_2O}Cl2​/H2​O​
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
The correct sequence of thermal stability of the following carbonates is :
  1. (A)BaCO3<SrCO3<CaCO3<MgCO3BaCO_3 < SrCO_3 < CaCO_3 < MgCO_3BaCO3​<SrCO3​<CaCO3​<MgCO3​
  2. (B)BaCO3<CaCO3<SrCO3<MgCO3BaCO_3 < CaCO_3 < SrCO_3 < MgCO_3BaCO3​<CaCO3​<SrCO3​<MgCO3​
  3. (C)MgCO3<CaCO3<SrCO3<BaCO3MgCO_3 < CaCO_3 < SrCO_3 < BaCO_3MgCO3​<CaCO3​<SrCO3​<BaCO3​
  4. (D)MgCO3<SrCO3<CaCO3<BaCO3MgCO_3 < SrCO_3 < CaCO_3 < BaCO_3MgCO3​<SrCO3​<CaCO3​<BaCO3​

Correct answer: (C)

Step-by-step solution →
Q37·ChemistrySingle correct
The group number, number of valence electrons and valency of an element with atomic number 15, respectively, are:
  1. (A)15, 5 and 3
  2. (B)15, 6 and 2
  3. (C)16, 5 and 2
  4. (D)16, 6 and 3

Correct answer: (A)

Step-by-step solution →
Q38·ChemistrySingle correct
Peptization is a :
  1. (A)process of converting soluble particles to form colloidal solution
  2. (B)process of converting precipitate into colloidal solution
  3. (C)process of converting a colloidal solution into precipitate
  4. (D)process of bringing colloidal molecule into solution

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
The metal that gives hydrogen gas upon treatment with both acid as well as base is:
  1. (A)iron
  2. (B)magnesium
  3. (C)zinc
  4. (D)mercury

Correct answer: (C)

Step-by-step solution →
Q40·ChemistrySingle correct
The electrons are more likely to be found:
  1. (A)in the region a and b
  2. (B)in the region a and c
  3. (C)only in the region a
  4. (D)only in the region c

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
An example of a disproportionation reaction is :
  1. (A)2KMnO4→K2MnO4+MnO2+O22KMnO_4 \rightarrow K_2MnO_4 + MnO_2 + O_22KMnO4​→K2​MnO4​+MnO2​+O2​
  2. (B)2NaBr+Cl2→2naCl+Br22NaBr + Cl_2 \rightarrow 2naCl + Br_22NaBr+Cl2​→2naCl+Br2​
  3. (C)2CuBr→CuBr2+Cu2CuBr \rightarrow CuBr_2 + Cu2CuBr→CuBr2​+Cu
  4. (D)2MnO4−+10I−+16H+→2Mn2++5I2+8H2O2MnO_4^- + 10I^- + 16H^+ \rightarrow 2Mn^{2+} + 5I_2 + 8H_2O2MnO4−​+10I−+16H+→2Mn2++5I2​+8H2​O

Correct answer: (C)

Step-by-step solution →
Q42·ChemistrySingle correct
5 moles of AB2_22​ weigh 125×10−3125 \times 10^{-3}125×10−3 kg and 10 moles of A2_22​B2_22​ weigh 300×10−3300 \times 10^{-3}300×10−3 kg. The molar mass of A(MA_AA​) and molar mass of B(MB_BB​) in kg mol−1^{-1}−1 are :
  1. (A)MA=50×10−3M_A = 50 \times 10^{-3}MA​=50×10−3 and MB=25×10−3M_B = 25 \times 10^{-3}MB​=25×10−3
  2. (B)MA=10×10−3M_A = 10 \times 10^{-3}MA​=10×10−3 and MB=5×10−3M_B = 5 \times 10^{-3}MB​=5×10−3
  3. (C)MA=5×10−3M_A = 5 \times 10^{-3}MA​=5×10−3 and MB=10×10−3M_B = 10 \times 10^{-3}MB​=10×10−3
  4. (D)MA=25×10−3M_A = 25 \times 10^{-3}MA​=25×10−3 and MB=50×10−3M_B = 50 \times 10^{-3}MB​=50×10−3

Correct answer: (C)

Step-by-step solution →
Q43·ChemistrySingle correct
The basic structural unit of feldspar, zeolites, mica and asbestos is :
  1. (A){SiRR−O}n\left\{\overset{R}{\underset{R}{\text{Si}}}-\text{O}\right\}_n{RSi​R​−O}n​ (R = Me)
  2. (B)(SiO3)2−(SiO_3)^{2-}(SiO3​)2−
  3. (C)SiO2SiO_2SiO2​
  4. (D)(SiO4)4−(SiO_4)^{4-}(SiO4​)4−

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
Enthalpy of sublimation of iodine is 24 cal g−1^{-1}−1 at 200°C. If specific heat of I2_22​(s) and I2_22​ (vap) are 0.055 and 0.031 cal g−1^{-1}−1K−1^{-1}−1 respectively, then enthalpy of sublimation of iodine at 250°C in cal g−1^{-1}−1 is :
  1. (A)2.85
  2. (B)11.4
  3. (C)5.7
  4. (D)22.8

Correct answer: (D)

Step-by-step solution →
Q45·ChemistrySingle correct
Which of the following is a thermosetting polymer?
  1. (A)PVC
  2. (B)Bakelite
  3. (C)Buna-N
  4. (D)Nylon 6

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is:
  1. (A)a2\dfrac{a}{2}2a​
  2. (B)2a\sqrt{2}a2​a
  3. (C)32a\dfrac{3}{2}a23​a
  4. (D)a

Correct answer: (A)

Step-by-step solution →
Q47·ChemistrySingle correct
An organic compound 'A' is oxidized with Na2_22​O2_22​ followed by boiling with HNO3_33​. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is :
  1. (A)Phosphorus
  2. (B)Sulphur
  3. (C)Nitrogen
  4. (D)Fluorine

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
The idea of froth floatation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:
  1. (A)washer woman and concentration
  2. (B)fisher woman and concentration
  3. (C)fisher man and reduction
  4. (D)washer man and reduction

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
In the following reaction; xA ⟶\longrightarrow⟶ yB log⁡10[−d[A]dt]=log⁡10[d[B]dt]+0.3010\log_{10}\left[-\dfrac{d[A]}{dt}\right]=\log_{10}\left[\dfrac{d[B]}{dt}\right]+0.3010log10​[−dtd[A]​]=log10​[dtd[B]​]+0.3010 'A' and 'B' respectively can be :
  1. (A)C2_22​H2_22​ and C6_66​H6_66​
  2. (B)n-Butane and Iso-butane
  3. (C)N2_22​O4_44​ and NO2_22​
  4. (D)C2_22​H4_44​ and C4_44​H8_88​

Correct answer: (D)

Step-by-step solution →
Q50·ChemistrySingle correct
Glucose and Galactose are having identical configuration in all the positions except position.
  1. (A)C-4
  2. (B)C-3
  3. (C)C-5
  4. (D)C-2

Correct answer: (A)

Step-by-step solution →
Q51·ChemistrySingle correct
Which of the following statements is not true about RNA?
  1. (A)It has always double stranded α-helix structure
  2. (B)It is present in the nucleus of the cell
  3. (C)It controls the synthesis of protein
  4. (D)It usually does not replicate

Correct answer: (A)

Step-by-step solution →
Q52·ChemistrySingle correct
What is the molar solubility of Al(OH)3_33​ in 0.2 M NaOH solution? Given that, solubility product of Al(OH)3_33​ = 2.4 ×\times× 10−24^{-24}−24 :
  1. (A)3×\times×10−19^{-19}−19
  2. (B)12×\times×10−21^{-21}−21
  3. (C)12×\times×10−23^{-23}−23
  4. (D)3×\times×10−22^{-22}−22

Correct answer: (D)

Step-by-step solution →
Q53·ChemistrySingle correct
Given : Co3+^{3+}3+e−^{-}− ⟶\longrightarrow⟶ Co2+^{2+}2+; E° = 1.81 V Pb4^{4}4 +2e−^{-}− ⟶\longrightarrow⟶ Pb2+^{2+}2+; E° = +1.67 V Ce4+^{4+}4+ + e−^{-}− ⟶\longrightarrow⟶ Ce3+^{3+}3+; E° +1.61 V Bi3+^{3+}3+ + 3e−^{-}− ⟶\longrightarrow⟶ Bi ; E° = +0.20 V Oxidizing power of the species will increase in the order
  1. (A)Ce4+^{4+}4+ < Pb4+^{4+}4+ < Bi3+^{3+}3+ < Co3+^{3+}3+
  2. (B)Co3+^{3+}3+ < Pb4+^{4+}4+ < Ce4+^{4+}4+ < Bi3+^{3+}3+
  3. (C)Bi3+^{3+}3+ < Ce4+^{4+}4+ < Pb4+^{4+}4+ < Co3+^{3+}3+
  4. (D)Co3+^{3+}3+ < Ce4+^{4+}4+ < Bi3+^{3+}3+ < Pb4+^{4+}4+

Correct answer: (C)

Step-by-step solution →
Q54·ChemistrySingle correct
But-2-ene on reaction with alkaline KMnO4_44​ at elevated temperature followed by acidification will give :
  1. (A)One molecule of CH3_33​CHO and one molecule of CH3_33​COOH
  2. (B)2 molecules of CH3_33​CHO
  3. (C)2 molecules of CH3_33​COOH
  4. (D)CH3_33​-CH(OH)-CH(OH)-CH3_33​

Correct answer: (C)

Step-by-step solution →
Q55·ChemistrySingle correct
The major product of the following reaction is : (1) CrO3_33​ (2) SOCl2_22​/Δ\DeltaΔ (3) Δ\DeltaΔ
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q56·ChemistrySingle correct
Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q57·ChemistrySingle correct
An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1bar. The work done in kJ is:
  1. (A)−9.0-9.0−9.0
  2. (B)−0.9-0.9−0.9
  3. (C)−2.0-2.0−2.0
  4. (D)+10.0+10.0+10.0

Correct answer: (B)

Step-by-step solution →

Mathematics — JEE Main 12 April 2019 Shift 1

Q58·MathematicsSingle correct
Let P be the point of intersection of the common tangents to the parabola y2=12xy^{2}=12xy2=12x and the hyperbola 8x2−y2=88x^{2}-y^{2}=88x2−y2=8. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio:
  1. (A)2:1
  2. (B)13:11
  3. (C)5:4
  4. (D)14:13

Correct answer: (C)

Step-by-step solution →
Q59·MathematicsSingle correct
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :
  1. (A)310\frac{3}{10}103​
  2. (B)15\frac{1}{5}51​
  3. (C)110\frac{1}{10}101​
  4. (D)320\frac{3}{20}203​

Correct answer: (C)

Step-by-step solution →
Q60·MathematicsSingle correct
Let f : R →\rightarrow→ R be a continuously differentiable function such that f(2) = 6 and f′(2)=148f'(2) = \frac{1}{48}f′(2)=481​. If ∫6f(x)4t3 dt=(x−2)g(x)\int_{6}^{f(x)} 4t^{3}\, dt = (x-2)g(x)∫6f(x)​4t3dt=(x−2)g(x), then lim⁡x→2g(x)\lim_{x \to 2} g(x)limx→2​g(x) is equal to :
  1. (A)24
  2. (B)18
  3. (C)12
  4. (D)36

Correct answer: (B)

Step-by-step solution →
Q61·MathematicsSingle correct
The integral ∫2x3−1x4+x dx\int \frac{2x^{3}-1}{x^{4}+x}\, dx∫x4+x2x3−1​dx is equal to : (Here C is a constant of integration)
  1. (A)12log⁡e∣x3+1x2∣+C\frac{1}{2}\log_{e}\left|\frac{x^{3}+1}{x^{2}}\right|+C21​loge​​x2x3+1​​+C
  2. (B)12log⁡e∣x3+1∣2∣x3∣+C\frac{1}{2}\log_{e}\frac{|x^{3}+1|^{2}}{|x^{3}|}+C21​loge​∣x3∣∣x3+1∣2​+C
  3. (C)log⁡e∣∣x3+1∣x∣+C\log_{e}\left|\frac{|x^{3}+1|}{x}\right|+Cloge​​x∣x3+1∣​​+C
  4. (D)log⁡e∣x3+1∣x2+C\log_{e}\frac{|x^{3}+1|}{x^{2}}+Cloge​x2∣x3+1∣​+C

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
The coefficient of x18x^{18}x18 in the product (1+x)(1−x)10(1+x+x2)9(1+x)(1-x)^{10}(1+x+x^{2})^{9}(1+x)(1−x)10(1+x+x2)9 is :
  1. (A)84
  2. (B)126
  3. (C)−126-126−126
  4. (D)−84-84−84

Correct answer: (A)

Step-by-step solution →
Q63·MathematicsSingle correct
The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :
  1. (A)2202^{20}220
  2. (B)220+12^{20}+1220+1
  3. (C)2212^{21}221
  4. (D)220−12^{20}-1220−1

Correct answer: (A)

Step-by-step solution →
Q64·MathematicsSingle correct
Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X≤2)=k216P(X \le 2) = \frac{k}{2^{16}}P(X≤2)=216k​, then k is equal to :
  1. (A)17
  2. (B)137
  3. (C)1
  4. (D)121

Correct answer: (B)

Step-by-step solution →
Q65·MathematicsSingle correct
The equation ∣z−i∣=∣z−1∣,i=−1|z-i|=|z-1|, i=\sqrt{-1}∣z−i∣=∣z−1∣,i=−1​, represents :
  1. (A)a circle of radius 12\frac{1}{2}21​
  2. (B)the line through the origin with slope 1
  3. (C)a circle of radius 1
  4. (D)the line through the origin with slope −1-1−1

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
If m is the minimum value of k for which the function f(x)=xkx−x2f(x)=x\sqrt{kx-x^{2}}f(x)=xkx−x2​ is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to :
  1. (A)(5,36)(5, 3\sqrt{6})(5,36​)
  2. (B)(4,32)(4, 3\sqrt{2})(4,32​)
  3. (C)(3,33)(3, 3\sqrt{3})(3,33​)
  4. (D)(4,33)(4, 3\sqrt{3})(4,33​)

Correct answer: (D)

Step-by-step solution →
Q67·MathematicsSingle correct
If the data x1,x2,....,x10x_{1}, x_{2}, ...., x_{10}x1​,x2​,....,x10​ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000; then the standard deviation of this data is :
  1. (A)222\sqrt{2}22​
  2. (B)2
  3. (C)4
  4. (D)2\sqrt{2}2​

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
If the area (in sq. units) of the region {(x,y):y2≤4x,x+y≤1,x≥0,y≥0}\{(x,y): y^{2} \le 4x, x+y \le 1, x \ge 0, y \ge 0\}{(x,y):y2≤4x,x+y≤1,x≥0,y≥0} is a2+ba\sqrt{2}+ba2​+b, then a −-− b is equal to :
  1. (A)103\frac{10}{3}310​
  2. (B)6
  3. (C)83\frac{8}{3}38​
  4. (D)−23-\frac{2}{3}−32​

Correct answer: (B)

Step-by-step solution →
Q69·MathematicsSingle correct
Consider the differential equation, y2dx+(x−1y)dy=0y^{2}dx+\left(x-\frac{1}{y}\right)dy=0y2dx+(x−y1​)dy=0. If value of y is 1 when x = 1, then the value of x for which y = 2, is :
  1. (A)32−e\frac{3}{2}-\sqrt{e}23​−e​
  2. (B)12+1e\frac{1}{2}+\frac{1}{\sqrt{e}}21​+e​1​
  3. (C)32−1e\frac{3}{2}-\frac{1}{\sqrt{e}}23​−e​1​
  4. (D)52+1e\frac{5}{2}+\frac{1}{\sqrt{e}}25​+e​1​

Correct answer: (C)

Step-by-step solution →
Q70·MathematicsSingle correct
If α\alphaα and β\betaβ are the roots of the equation 375x2−25x−2=0375x^{2}-25x-2=0375x2−25x−2=0, then lim⁡n→∞∑r=1nαr+lim⁡n→∞∑r=1nβr\lim_{n \to \infty}\sum_{r=1}^{n}\alpha^{r} + \lim_{n \to \infty}\sum_{r=1}^{n}\beta^{r}limn→∞​∑r=1n​αr+limn→∞​∑r=1n​βr is equal to :
  1. (A)112\frac{1}{12}121​
  2. (B)29358\frac{29}{358}35829​
  3. (C)7116\frac{7}{116}1167​
  4. (D)21346\frac{21}{346}34621​

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/ sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :
  1. (A)25
  2. (B)253\frac{25}{3}325​
  3. (C)25325\sqrt{3}253​
  4. (D)253\frac{25}{\sqrt{3}}3​25​

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
The number of solutions of the equation 1+sin⁡4x=cos⁡23x,x∈[−5π2,5π2]1+\sin^{4}x=\cos^{2}3x, x \in \left[-\frac{5\pi}{2}, \frac{5\pi}{2}\right]1+sin4x=cos23x,x∈[−25π​,25π​] is :
  1. (A)3
  2. (B)4
  3. (C)5
  4. (D)7

Correct answer: (C)

Step-by-step solution →
Q73·MathematicsSingle correct
If ey+xy=ee^{y} + xy = eey+xy=e, the ordered pair (dydx,d2ydx2)\left(\dfrac{dy}{dx}, \dfrac{d^{2}y}{dx^{2}}\right)(dxdy​,dx2d2y​) at x = 0 is equal to :
  1. (A)(1e,−1e2)\left(\dfrac{1}{e}, -\dfrac{1}{e^{2}}\right)(e1​,−e21​)
  2. (B)(1e,1e2)\left(\dfrac{1}{e}, \dfrac{1}{e^{2}}\right)(e1​,e21​)
  3. (C)(−1e,1e2)\left(-\dfrac{1}{e}, \dfrac{1}{e^{2}}\right)(−e1​,e21​)
  4. (D)(−1e,−1e2)\left(-\dfrac{1}{e}, -\dfrac{1}{e^{2}}\right)(−e1​,−e21​)

Correct answer: (C)

Step-by-step solution →
Q74·MathematicsSingle correct
The value of sin⁡−1(1213)−sin⁡−1(35)\sin^{-1}\left(\dfrac{12}{13}\right) - \sin^{-1}\left(\dfrac{3}{5}\right)sin−1(1312​)−sin−1(53​) is equal to :
  1. (A)π−cos⁡−1(3365)\pi - \cos^{-1}\left(\dfrac{33}{65}\right)π−cos−1(6533​)
  2. (B)π−sin⁡−1(6365)\pi - \sin^{-1}\left(\dfrac{63}{65}\right)π−sin−1(6563​)
  3. (C)π2−cos⁡−1(965)\dfrac{\pi}{2} - \cos^{-1}\left(\dfrac{9}{65}\right)2π​−cos−1(659​)
  4. (D)π2−sin⁡−1(5665)\dfrac{\pi}{2} - \sin^{-1}\left(\dfrac{56}{65}\right)2π​−sin−1(6556​)

Correct answer: (D)

Step-by-step solution →
Q75·MathematicsSingle correct
If the normal to the ellipse 3x2+4y2=123x^{2} + 4y^{2} = 123x2+4y2=12 at a point P on it is parallel to the line, 2x+y=42x + y = 42x+y=4 and the tangent to the ellipse at P passes through Q(4, 4) then PQ is equal to :
  1. (A)1572\dfrac{\sqrt{157}}{2}2157​​
  2. (B)552\dfrac{5\sqrt{5}}{2}255​​
  3. (C)2212\dfrac{\sqrt{221}}{2}2221​​
  4. (D)612\dfrac{\sqrt{61}}{2}261​​

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
Let a⃗=3i^+2j^+2k^\vec{a} = 3\hat{i} + 2\hat{j} + 2\hat{k}a=3i^+2j^​+2k^ and b⃗=i^+2j^−2k^\vec{b} = \hat{i} + 2\hat{j} - 2\hat{k}b=i^+2j^​−2k^ be two vectors. If a vector perpendicular to both the vectors a⃗+b⃗\vec{a} + \vec{b}a+b and a⃗−b⃗\vec{a} - \vec{b}a−b has the magnitude 12 then one such vector is:
  1. (A)4(2i^−2j^−k^)4\left(2\hat{i} - 2\hat{j} - \hat{k}\right)4(2i^−2j^​−k^)
  2. (B)4(2i^−2j^+k^)4\left(2\hat{i} - 2\hat{j} + \hat{k}\right)4(2i^−2j^​+k^)
  3. (C)4(2i^+2j^+k^)4\left(2\hat{i} + 2\hat{j} + \hat{k}\right)4(2i^+2j^​+k^)
  4. (D)4(2i^+2j^−k^)4\left(2\hat{i} + 2\hat{j} - \hat{k}\right)4(2i^+2j^​−k^)

Correct answer: (A)

Step-by-step solution →
Q77·MathematicsSingle correct
The equation y=sin⁡xsin⁡(x+2)−sin⁡2(x+1)y = \sin x \sin(x + 2) - \sin^{2}(x+1)y=sinxsin(x+2)−sin2(x+1) represents a straight line lying in :
  1. (A)first, third and fourth quadrants
  2. (B)first, second and fourth quadrants
  3. (C)third and fourth quadrants only
  4. (D)second and third quadrants only

Correct answer: (C)

Step-by-step solution →
Q78·MathematicsSingle correct
For x∈(0,32)x \in \left(0, \dfrac{3}{2}\right)x∈(0,23​), let f(x)=xf(x) = \sqrt{x}f(x)=x​, g(x)=tan⁡xg(x) = \tan xg(x)=tanx and h(x)=1−x21+x2h(x) = \dfrac{1-x^{2}}{1+x^{2}}h(x)=1+x21−x2​. If ϕ(x)=((h∘f)∘g)(x)\phi(x) = ((h \circ f) \circ g)(x)ϕ(x)=((h∘f)∘g)(x), then ϕ(π3)\phi\left(\dfrac{\pi}{3}\right)ϕ(3π​) is equal to :
  1. (A)tan⁡11π12\tan \dfrac{11\pi}{12}tan1211π​
  2. (B)tan⁡π12\tan \dfrac{\pi}{12}tan12π​
  3. (C)tan⁡5π12\tan \dfrac{5\pi}{12}tan125π​
  4. (D)tan⁡7π12\tan \dfrac{7\pi}{12}tan127π​

Correct answer: (A)

Step-by-step solution →
Q79·MathematicsSingle correct
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :
  1. (A)132\dfrac{13}{2}213​
  2. (B)12013\dfrac{120}{13}13120​
  3. (C)135\dfrac{13}{5}513​
  4. (D)6013\dfrac{60}{13}1360​

Correct answer: (B)

Step-by-step solution →
Q80·MathematicsSingle correct
If ∫0π/2cot⁡xcot⁡x+cosec x dx=m(π+n)\displaystyle\int_{0}^{\pi/2} \dfrac{\cot x}{\cot x + \text{cosec}\,x}\,dx = m(\pi + n)∫0π/2​cotx+cosecxcotx​dx=m(π+n), then m⋅\cdot⋅n is equal to
  1. (A)1
  2. (B)12\dfrac{1}{2}21​
  3. (C)−12-\dfrac{1}{2}−21​
  4. (D)−1-1−1

Correct answer: (D)

Step-by-step solution →
Q81·MathematicsSingle correct
Let Sn_{n}n​ denote the sum of the first n terms of an A.P.. If S4_{4}4​ = 16 and S6_{6}6​ = −48-48−48, then S10_{10}10​ is equal to :
  1. (A)−410-410−410
  2. (B)−260-260−260
  3. (C)−320-320−320
  4. (D)−380-380−380

Correct answer: (C)

Step-by-step solution →
Q82·MathematicsSingle correct
If B = [52α1021α3−1]\begin{bmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{bmatrix}​50α​2α23​11−1​​ is the inverse of a 3×33 \times 33×3 matrix A, then the sum of all values of α\alphaα for which det(A) + 1 = 0, is :
  1. (A)0
  2. (B)−1-1−1
  3. (C)1
  4. (D)2

Correct answer: (C)

Step-by-step solution →
Q83·MathematicsSingle correct
If A is a symmetric matrix and B is a skew-symmetrix matrix such that A + B = [235−1]\begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}[25​3−1​], then AB is equal to :
  1. (A)[4−21−4]\begin{bmatrix} 4 & -2 \\ 1 & -4 \end{bmatrix}[41​−2−4​]
  2. (B)[4−2−1−4]\begin{bmatrix} 4 & -2 \\ -1 & -4 \end{bmatrix}[4−1​−2−4​]
  3. (C)[−4214]\begin{bmatrix} -4 & 2 \\ 1 & 4 \end{bmatrix}[−41​24​]
  4. (D)[−4−2−14]\begin{bmatrix} -4 & -2 \\ -1 & 4 \end{bmatrix}[−4−1​−24​]

Correct answer: (B)

Step-by-step solution →
Q84·MathematicsSingle correct
If the truth value of the statement p→(∼q∨r)p \rightarrow (\sim q \vee r)p→(∼q∨r) is false (F), then the truth values of the statement p, q, r are respectively :
  1. (A)T, T, F
  2. (B)F, T, T
  3. (C)T, F, T
  4. (D)T, F, F

Correct answer: (A)

Step-by-step solution →
Q85·MathematicsSingle correct
For x∈Rx \in Rx∈R, let [x][x][x] denote the greatest integer ≤x\le x≤x, then the sum of the series [−13]+[−13−1100]+[−13−2100]+⋯+[−13−99100]\left[-\dfrac{1}{3}\right] + \left[-\dfrac{1}{3} - \dfrac{1}{100}\right] + \left[-\dfrac{1}{3} - \dfrac{2}{100}\right] + \cdots + \left[-\dfrac{1}{3} - \dfrac{99}{100}\right][−31​]+[−31​−1001​]+[−31​−1002​]+⋯+[−31​−10099​]
  1. (A)−135-135−135
  2. (B)−153-153−153
  3. (C)−133-133−133
  4. (D)−131-131−131

Correct answer: (C)

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
  • 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
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Laws of Motion 130/186
  • 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
  • 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
  • Work, Energy and Power 132/186
  • 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
  • Purification and Characterisation of Organic Compounds 116/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Hyperbola 77/186
  • Experimental Skills 68/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Carboxylic Acids and Derivatives 54/186
  • Solid State 63/186
  • Magnetism and Matter 50/186
  • Mathematical Reasoning 26/186
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