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JEE Main 12 April 2019 Shift 2 Question Paper with Answers

12 April 2019 · April session · 87 questions

87 of the 90 questions from the JEE Main 12 April 2019 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

3 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
29
Chemistry
30
Mathematics
28

Physics — JEE Main 12 April 2019 Shift 2

Q1·PhysicsSingle correct
Figure shown a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the unregulated input voltage varies between 10 V to 16 V, then what is the maximum Zener current?
  1. (A)2.5 mA
  2. (B)3.5 mA
  3. (C)7.5 mA
  4. (D)1.5 mA

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :
  1. (A)(37m,712m)\left(\dfrac{\sqrt{3}}{7} m, \dfrac{7}{12} m\right)(73​​m,127​m)
  2. (B)(712m,38m)\left(\dfrac{7}{12} m, \dfrac{\sqrt{3}}{8} m\right)(127​m,83​​m)
  3. (C)(34m,512m)\left(\dfrac{\sqrt{3}}{4} m, \dfrac{5}{12} m\right)(43​​m,125​m)
  4. (D)(712m,34m)\left(\dfrac{7}{12} m, \dfrac{\sqrt{3}}{4} m\right)(127​m,43​​m)

Correct answer: (D)

Step-by-step solution →
Q3·PhysicsSingle correct
The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9 : 4. The mass of the planet is 19\dfrac{1}{9}91​th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)
  1. (A)R3\dfrac{R}{3}3R​
  2. (B)R4\dfrac{R}{4}4R​
  3. (C)R9\dfrac{R}{9}9R​
  4. (D)R2\dfrac{R}{2}2R​

Correct answer: (D)

Step-by-step solution →
Q4·PhysicsSingle correct
A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30º with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is m = 0.2. The difference between the accelerations of the block, in case (B) and case (A) will be : (g = 10 ms−2^{-2}−2)
  1. (A)0.4 ms−2^{-2}−2
  2. (B)3.2 ms−2^{-2}−2
  3. (C)0 ms−2^{-2}−2
  4. (D)0.8 ms−2^{-2}−2

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
In the given circuit, the charge on 4 μF capacitor will be :
  1. (A)13.4 μC
  2. (B)24 μC
  3. (C)9.6 μC
  4. (D)5.4 μC

Correct answer: (B)

Step-by-step solution →
Q6·PhysicsSingle correct
A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?
  1. (A)40 J
  2. (B)30 J
  3. (C)35 J
  4. (D)25 J

Correct answer: (C)

Step-by-step solution →
Q7·PhysicsSingle correct
A Carnot engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperatures of the source and the sink are, respectively
  1. (A)62ºC, 124ºC
  2. (B)99ºC, 37ºC
  3. (C)37ºC, 99ºC
  4. (D)124ºC, 62ºC

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Consider an electron in a hydrogen atom, revolving in its second excited state (having radius 4.65 Å). The de-Broglie wavelength of this electron is :
  1. (A)12.9 Å
  2. (B)9.7 Å
  3. (C)6.6 Å
  4. (D)3.5 Å

Correct answer: (B)

Step-by-step solution →
Q9·PhysicsSingle correct
A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as 10−1210^{-12}10−12W/m2^{2}2]
  1. (A)30 cm
  2. (B)10 cm
  3. (C)40 cm
  4. (D)20 cm

Correct answer: (C)

Step-by-step solution →
Q10·PhysicsSingle correct
A system of three polarizers P1_{1}1​, P2_{2}2​, P3_{3}3​ is set up such that the pass axis of P3_{3}3​ is crossed with respect to that of P1_{1}1​. The pass axis of P2_{2}2​ is inclined at 60º to the pass axis of P3_{3}3​. When a beam of unpolarized light of intensity I0 is incident on P1_{1}1​, the intensity of light transmitted by the three polarizers is I. The ratio (I0_{0}0​/I) equals (nearly) :
  1. (A)10.67
  2. (B)1.80
  3. (C)5.33
  4. (D)16.00

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by r(r) = kr, where r is the distance from the centre. Two charges A and B, of −Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then :
  1. (A)a=3R21/4a = \dfrac{3R}{2^{1/4}}a=21/43R​
  2. (B)a=2−1/4Ra = 2^{-1/4}Ra=2−1/4R
  3. (C)a=8−1/4Ra = 8^{-1/4}Ra=8−1/4R
  4. (D)a=R/3a = R/\sqrt{3}a=R/3​

Correct answer: (C)

Step-by-step solution →
Q12·PhysicsSingle correct
An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field B⃗=(1.5×10−3T)k^\vec{B} = (1.5 \times 10^{-3} T)\hat{k}B=(1.5×10−3T)k^ at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is : (electron's charge = 1.6×10−191.6 \times 10^{-19}1.6×10−19 C, mass of electron = 9.1×10−319.1 \times 10^{-31}9.1×10−31 kg)
  1. (A)12.87 cm
  2. (B)2.25 cm
  3. (C)1.22 cm
  4. (D)11.65 cm

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1_{1}1​ and h2_{2}2​. Which of the following is correct?
  1. (A)R2^{2}2 = 4 h1_{1}1​h2_{2}2​
  2. (B)R2^{2}2 = 2 h1_{1}1​h2_{2}2​
  3. (C)R2^{2}2 = 16 h1_{1}1​h2_{2}2​
  4. (D)R2^{2}2 = h1_{1}1​h2_{2}2​

Correct answer: (C)

Step-by-step solution →
Q14·PhysicsSingle correct
A particle is moving with speed v = vx\sqrt{x}x​ along positive x-axis. Calculate the speed of the particle at time t = t (assume that the particle is at origin at t = 0).
  1. (A)b2^{2}2τ
  2. (B)b2τ2\dfrac{b^{2}\tau}{2}2b2τ​
  3. (C)b2τ2\dfrac{b^{2}\tau}{\sqrt{2}}2​b2τ​
  4. (D)b2τ4\dfrac{b^{2}\tau}{4}4b2τ​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
One kg of water, at 20ºC, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/kg ºC), Latent heat of water = 2260 kJ/kg]
  1. (A)3 minutes
  2. (B)10 minutes
  3. (C)22 minutes
  4. (D)16 minutes

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :
  1. (A)9 : 8
  2. (B)1 : 8
  3. (C)8 : 1
  4. (D)3 : 8

Correct answer: (A)

Step-by-step solution →
Q17·PhysicsSingle correct
In an amplitude modulator circuit, the carrier wave is given by, C(t)=4sin⁡(20000πt)C(t) = 4\sin(20000\pi t)C(t)=4sin(20000πt) while modulating signal is given by, m(t)=2sin⁡(2000πt)m(t) = 2\sin(2000\pi t)m(t)=2sin(2000πt). The values of modulation index and lower side band frequency are:
  1. (A)0.5 and 9 kHz
  2. (B)0.3 and 9 kHz
  3. (C)0.5 and 10 kHz
  4. (D)0.4 and 10 kHz

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to :
  1. (A)9F/(πr2YT)9F/(\pi r^{2}YT)9F/(πr2YT)
  2. (B)F/(3πr2YT)F/(3\pi r^{2}YT)F/(3πr2YT)
  3. (C)3F/(πr2YT)3F/(\pi r^{2}YT)3F/(πr2YT)
  4. (D)6F/(πr2YT)6F/(\pi r^{2}YT)6F/(πr2YT)

Correct answer: (C)

Step-by-step solution →
Q19·PhysicsSingle correct
Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t=LRt = \dfrac{L}{R}t=RL​ is :
  1. (A)EL7.3R2\dfrac{EL}{7.3R^{2}}7.3R2EL​
  2. (B)EL2.7R2\dfrac{EL}{2.7R^{2}}2.7R2EL​
  3. (C)7.3ELR2\dfrac{7.3EL}{R^{2}}R27.3EL​
  4. (D)2.7ELR2\dfrac{2.7EL}{R^{2}}R22.7EL​

Correct answer: (B)

Step-by-step solution →
Q20·PhysicsSingle correct
Two sources of sound S1_{1}1​ and S2_{2}2​ produce sound waves of same frequency 660 Hz. A listener is moving from source S1_{1}1​ towards S2_{2}2​ with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals:
  1. (A)15.0 m/s
  2. (B)10.0 m/s
  3. (C)5.5 m/s
  4. (D)2.5 m/s

Correct answer: (D)

Step-by-step solution →
Q21·PhysicsSingle correct
Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) (μ\muμ0 = 4p ×\times× 10–7 N-A–2)
  1. (A)2.0 ×\times× 10−5^{-5}−5 T
  2. (B)3.0 ×\times× 10−5^{-5}−5 T
  3. (C)2.5 ×\times× 10−5^{-5}−5 T
  4. (D)1.5 ×\times× 10−5^{-5}−5 T

Correct answer: (D)

Step-by-step solution →
Q22·PhysicsSingle correct
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ1/λ2\lambda_{1}/\lambda_{2}λ1​/λ2​, of the photons emitted in this process is :
  1. (A)20/7
  2. (B)7/5
  3. (C)9/7
  4. (D)27/5

Correct answer: (A)

Step-by-step solution →
Q23·PhysicsSingle correct
A smooth wire of length 2πr2\pi r2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed w about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2\omega^{2}ω2 is equal to:
  1. (A)3 g2r\dfrac{\sqrt{3}\,g}{2r}2r3​g​
  2. (B)(g3)/r(g\sqrt{3})/r(g3​)/r
  3. (C)2g/r2g/r2g/r
  4. (D)2g/(r3)2g/(r\sqrt{3})2g/(r3​)

Correct answer: (D)

Step-by-step solution →
Q24·PhysicsSingle correct
A solid sphere, of radius R acquires a terminal velocity v1_{1}1​ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η\etaη. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2_{2}2​, when falling through the same fluid, the ratio (v1_{1}1​/v2_{2}2​) equals :
  1. (A)27
  2. (B)1/27
  3. (C)9
  4. (D)1/9

Correct answer: (C)

Step-by-step solution →
Q25·PhysicsSingle correct
The number density of molecules of a gas depends on their distance r from the origin as, n(r)=n0e−αr4n(r) = n_{0}e^{-\alpha r^{4}}n(r)=n0​e−αr4. Then the total number of molecules is proportional to :
  1. (A)n0α−3/4n_{0}\alpha^{-3/4}n0​α−3/4
  2. (B)n0α−3n_{0}\alpha^{-3}n0​α−3
  3. (C)n0α1/4n_{0}\alpha^{1/4}n0​α1/4
  4. (D)n0 α1/2\sqrt{n_{0}}\,\alpha^{1/2}n0​​α1/2

Correct answer: (A)

Step-by-step solution →
Q26·PhysicsSingle correct
A transparent cube of side d, made of a material of refractive index μ2\mu_{2}μ2​, is immersed in a liquid of refractive index μ1(μ1<μ2)\mu_{1}(\mu_{1} < \mu_{2})μ1​(μ1​<μ2​). A ray is incident on the face AB at an angle q(shown in the figure). Total internal reflection takes place at point E on the face BC. The q must satisfy :
  1. (A)θ>sin⁡−1μ1μ2\theta > \sin^{-1}\dfrac{\mu_{1}}{\mu_{2}}θ>sin−1μ2​μ1​​
  2. (B)θ>sin⁡−1μ22μ12−1\theta > \sin^{-1}\sqrt{\dfrac{\mu_{2}^{2}}{\mu_{1}^{2}}-1}θ>sin−1μ12​μ22​​−1​
  3. (C)θ<sin⁡−1μ1μ2\theta < \sin^{-1}\dfrac{\mu_{1}}{\mu_{2}}θ<sin−1μ2​μ1​​
  4. (D)θ<sin⁡−1μ22μ12−1\theta < \sin^{-1}\sqrt{\dfrac{\mu_{2}^{2}}{\mu_{1}^{2}}-1}θ<sin−1μ12​μ22​​−1​

Correct answer: (D)

Step-by-step solution →
Q27·PhysicsSingle correct
A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, ℓ1=30\ell_{1} = 30ℓ1​=30 cm and ℓ2=70\ell_{2} = 70ℓ2​=70 cm. Then n is equal to :
  1. (A)332 ms−1^{-1}−1
  2. (B)338 ms−1^{-1}−1
  3. (C)384 ms−1^{-1}−1
  4. (D)379 ms−1^{-1}−1

Correct answer: (C)

Step-by-step solution →
Q28·PhysicsSingle correct
A spring whose unstretched length is ℓ\ellℓ has a force constant k. The spring is cut into two pieces of unstretched lengths ℓ1\ell_{1}ℓ1​ and ℓ2\ell_{2}ℓ2​ where, ℓ1=nℓ2\ell_{1} = n\ell_{2}ℓ1​=nℓ2​ and n is an integer. The ratio k1_{1}1​/k2_{2}2​ of the corresponding force constants, k1_{1}1​ and k2_{2}2​ will be:
  1. (A)n
  2. (B)1/n21/n^{2}1/n2
  3. (C)n2n^{2}n2
  4. (D)1/n1/n1/n

Correct answer: (D)

Step-by-step solution →
Q29·PhysicsSingle correct
A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig_{g}g​ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I0_{0}0​ (I0_{0}0​ > Ig_{g}g​) by connecting a shunt resistance RA_{A}A​ to it and (ii) into a voltmeter of range 0 to V(V = GI0_{0}0​) by connecting a series resistance RV_{V}V​ to it. Then,
  1. (A)RARV=G2R_AR_V = G^{2}RA​RV​=G2 and RARV=Ig(I0−Ig)\dfrac{R_A}{R_V} = \dfrac{I_g}{(I_0-I_g)}RV​RA​​=(I0​−Ig​)Ig​​
  2. (B)RARV=G2R_AR_V = G^{2}RA​RV​=G2 and RARV=(IgI0−Ig)2\dfrac{R_A}{R_V} = \left(\dfrac{I_g}{I_0-I_g}\right)^{2}RV​RA​​=(I0​−Ig​Ig​​)2
  3. (C)RARV=G2(IgI0−Ig)R_AR_V = G^{2}\left(\dfrac{I_g}{I_0-I_g}\right)RA​RV​=G2(I0​−Ig​Ig​​) and RARV=(I0−IgIg)2\dfrac{R_A}{R_V} = \left(\dfrac{I_0-I_g}{I_g}\right)^{2}RV​RA​​=(Ig​I0​−Ig​​)2
  4. (D)RA−RV=G2(I0−IgIg)R_A - R_V = G^{2}\left(\dfrac{I_0-I_g}{I_g}\right)RA​−RV​=G2(Ig​I0​−Ig​​) and RARV=(Ig(I0−Ig))2\dfrac{R_A}{R_V} = \left(\dfrac{I_g}{(I_0-I_g)}\right)^{2}RV​RA​​=((I0​−Ig​)Ig​​)2

Correct answer: (B)

Step-by-step solution →

Chemistry — JEE Main 12 April 2019 Shift 2

Q30·ChemistrySingle correct
What will be the major product when m-cresol is reacted with propargyl bromide (HC ≡ C – CH2_22​Br) in presence of K2_22​CO3_33​ in acetone
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (C)

Step-by-step solution →
Q31·ChemistrySingle correct
Which one of the following is likely to give a precipitate with AgNO3_33​ solution?
  1. (A)CH2_22​ = CH – Cl
  2. (B)CHCl3_33​
  3. (C)(CH3_33​)3_33​CCl
  4. (D)CCl4_44​

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
The INCORRECT match in the following is:
  1. (A)ΔG∘<0,K>1\Delta G^{\circ} < 0, K > 1ΔG∘<0,K>1
  2. (B)ΔG∘<0,K<1\Delta G^{\circ} < 0, K < 1ΔG∘<0,K<1
  3. (C)ΔG∘=0,K=1\Delta G^{\circ} = 0, K = 1ΔG∘=0,K=1
  4. (D)ΔG∘>0,K<1\Delta G^{\circ} > 0, K < 1ΔG∘>0,K<1

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
The INCORRECT statement is:
  1. (A)LiNO3_33​ decomposes on heating to give LiNO2_22​ and O2_22​.
  2. (B)Lithium is least reactive with water among the alkali metals.
  3. (C)LiCl crystallises from aqueous solution as LiCl.2H2_22​O.
  4. (D)Lithium is the strongest reducing agent among the alkali metals.

Correct answer: (A)

Step-by-step solution →
Q35·ChemistrySingle correct
The C–C bond length is maximum in
  1. (A)graphite
  2. (B)C70_{70}70​
  3. (C)diamond
  4. (D)C60_{60}60​

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
Consider the following reactions : 'A' is:
  1. (A)CH2_22​ = CH2_22​
  2. (B)CH3_33​ – C ≡ CH
  3. (C)CH ≡ CH
  4. (D)CH3_33​ – C ≡ C – CH3_33​

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
In which one of the following equilibria, Kp_pp​ ≠ Kc_cc​?
  1. (A)2NO(g) ⇌ N2_22​(g) + O2_22​(g)
  2. (B)2C(s) + O2_22​(g) ⇌ 2CO(g)
  3. (C)NO2_22​(g) + SO2_22​(g) ⇌ NO(g) + SO3_33​(g)
  4. (D)2HI(g) ⇌ H2_22​(g) + I2_22​(g)

Correct answer: (B)

Step-by-step solution →
Q38·ChemistrySingle correct
The coordination numbers of Co and Al in [Co(Cl)(en)2_22​]Cl and K3_33​[Al(C2_22​O4_44​)3_33​], respectively, are (en = ethane-1,2-diamine)
  1. (A)6 and 6
  2. (B)5 and 3
  3. (C)3 and 3
  4. (D)5 and 6

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
Which of the given statements is INCORRECT about glycogen?
  1. (A)It is present in some yeast and fungi
  2. (B)It is present in animal cells
  3. (C)Only α-linkages are present in the molecule
  4. (D)It is a straight chain polymer similar to amylase

Correct answer: (D)

Step-by-step solution →
Q40·ChemistrySingle correct
The primary pollutant that leads to photochemical smog is:
  1. (A)acrolein
  2. (B)nitrogen oxides
  3. (C)ozone
  4. (D)sulphur dioxide

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively :
  1. (A)1 : 2 : 4
  2. (B)4 : 2 : 3
  3. (C)4 : 2 : 1
  4. (D)8 : 1 : 6

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
Thermal decomposition of a Mn compound (X) at 513 K results in compound Y, MnO2_22​ and a gaseous product. MnO2_22​ reacts with NaCl and concentrated H2_22​SO4_44​ to give a pungent gas Z. X, Y and Z, respectively.
  1. (A)K2_22​MnO4_44​, KMnO4_44​ and SO2_22​
  2. (B)K3_33​MnO4_44​, K2_22​MnO4_44​ and Cl2_22​
  3. (C)K2_22​MnO4_44​, KMnO4_44​ and Cl2_22​
  4. (D)KMnO4_44​, K2_22​MnO4_44​ and Cl2_22​

Correct answer: (D)

Step-by-step solution →
Q43·ChemistrySingle correct
An ' Assertion' and a 'Reason' are given below. Choose the correct answer from the following options. Assertion (A): Vinyl halides do not undergo nucleophilic substitution easily. Reason (R): Even though the intermediate carbocation is stabilized by loosely held p-electrons, the cleavage is difficult because of strong bonding.
  1. (A)Both (A) and (R) are correct statements but (R) is not the correct explanation of (A)
  2. (B)Both (A) and (R) are wrong statements
  3. (C)Both (A) and (R) are correct statements and (R) is the correct explanation of (A)
  4. (D)(A) is a correct statement but (R) is a wrong statement.

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
The molar solubility of Cd(OH)2_22​ is 1.84 ×\times× 10−5^{-5}−5 M in water. The expected solubility of Cd(OH)2_22​ in a buffer solution of pH = 12 is :
  1. (A)6.23 ×\times× 10−11^{-11}−11 M
  2. (B)1.84 ×\times× 10−9^{-9}−9 M
  3. (C)2.491.84×10−9\frac{2.49}{1.84} \times 10^{-9}1.842.49​×10−9 M
  4. (D)2.49 ×\times× 10−10^{-10}−10 M

Correct answer: (D)

Step-by-step solution →
Q45·ChemistrySingle correct
The compound used in the treatment of lead poisoning is:
  1. (A)EDTA
  2. (B)Cis-platin
  3. (C)D-penicillamine
  4. (D)desferrioxime B

Correct answer: (A)

Step-by-step solution →
Q46·ChemistrySingle correct
The pair that has similar atomic radii is:
  1. (A)Ti and Hf
  2. (B)Mn and Re
  3. (C)Sc and Ni
  4. (D)Mo and W

Correct answer: (D)

Step-by-step solution →
Q47·ChemistrySingle correct
25 g of an unknown hydrocarbon upon burning produces 88 g of CO2_{2}2​ and 9 g of H2_{2}2​O. This unknown hydrocarbon contains.
  1. (A)24g of carbon and 1 g of hydrogen
  2. (B)22g of carbon and 3 g of hydrogen
  3. (C)18g of carbon and 7 g of hydrogen
  4. (D)20g of carbon and 5 g of hydrogen

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
The decreasing order of electrical conductivity of the following aqueous solutions is: 0.1 M Formic acid (a) 0.1 M Acetic acid (b) 0.1 M Benzoic acid (c)
  1. (A)a > c > b
  2. (B)c > a > b
  3. (C)c > b > a
  4. (D)a > b > c

Correct answer: (A)

Step-by-step solution →
Q49·ChemistrySingle correct
Among the following, the energy of 2s orbital is lowest in:
  1. (A)K
  2. (B)Na
  3. (C)H
  4. (D)Li

Correct answer: (A)

Step-by-step solution →
Q50·ChemistrySingle correct
In the following skew conformation of ethane, H'\u2013C\u2013C\u2013H" dihedral angle is :
  1. (A)58°
  2. (B)120°
  3. (C)149°
  4. (D)151°

Correct answer: (C)

Step-by-step solution →
Q51·ChemistrySingle correct
The correct statement is:
  1. (A)leaching of bauxite using concentrated NaOH solution gives sodium aluminate and sodium silicate
  2. (B)the Hall-Heroult process is used for the production of aluminium and iron
  3. (C)the blistered appearance of copper during the metallurgical process is due to the evolution of CO2_{2}2​
  4. (D)pig iron is obtained from cast iron

Correct answer: (A)

Step-by-step solution →
Q52·ChemistrySingle correct
NO2_{2}2​ required for a reaction is produced by the decomposition of N2_{2}2​O5_{5}5​ in CCl4_{4}4​ as per the equation 2N2O5(g)→4NO2(g)+O2(g)2N_{2}O_{5}(g) \rightarrow 4NO_{2}(g) + O_{2}(g)2N2​O5​(g)→4NO2​(g)+O2​(g) The initial concentration of N2_{2}2​O5_{5}5​ is 3.00 mol L−1^{-1}−1 and it is 2.75 mol L−1^{-1}−1 after 30 minutes. The rate of formation of NO2_{2}2​ is :
  1. (A)1.667 ×\times× 10−2^{-2}−2 mol L−1^{-1}−1 min−1^{-1}−1
  2. (B)4.167 ×\times× 10−3^{-3}−3 mol L−1^{-1}−1 min−1^{-1}−1
  3. (C)8.333 ×\times× 10−3^{-3}−3 mol L−1^{-1}−1 min−1^{-1}−1
  4. (D)2.083 ×\times× 10−3^{-3}−3 mol L−1^{-1}−1 min−1^{-1}−1

Correct answer: (A)

Step-by-step solution →
Q53·ChemistrySingle correct
The correct name of the following polymer is:
  1. (A)Polyisoprene
  2. (B)Polytert-butylene
  3. (C)Polyisobutane
  4. (D)Polyisobutylene

Correct answer: (D)

Step-by-step solution →
Q54·ChemistrySingle correct
Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives X as the major product. Reaction of X with Hg(OAc)2_{2}2​/H2_{2}2​O followed by NaBH4_{4}4​ gives Y as the major product. Y is:
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q55·ChemistrySingle correct
The IUPAC name of the following compound is :
  1. (A)3, 5-dimethyl-4-propylhept-1-en-6-yne
  2. (B)3-methyl-4-(1-methylprop-2-ynyl)-1-heptene
  3. (C)3-methyl-4-(3-methylprop-1-enyl)-1-heptyne
  4. (D)3, 5-dimethyl-4-propylhept-6-en-1-yne

Correct answer: (A)

Step-by-step solution →
Q56·ChemistrySingle correct
Among the following, the INCORRECT statement about colloids is :
  1. (A)The range of diameters of colloidal particles is between 1 and 1000 nm
  2. (B)The osmotic pressure of a colloidal solution is of higher order than the true solution at the same concentration
  3. (C)They can scatter light
  4. (D)They are larger than small molecules and have high molar mass

Correct answer: (B)

Step-by-step solution →
Q57·ChemistrySingle correct
In comparison to boron, berylium has:
  1. (A)greater nuclear charge and greater first ionisation enthalpy
  2. (B)lesser nuclear charge and lesser first ionisation enthalpy
  3. (C)greater nuclear charge and lesser first ionisation enthalpy
  4. (D)lesser nuclear charge and greater first ionisation enthalpy

Correct answer: (D)

Step-by-step solution →
Q58·ChemistrySingle correct
A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol−1^{-1}−1) and 1.8 g of glucose (molar mass = 180 g mol−1^{-1}−1) in 100 mL of water at 27°C. The osmotic pressure of the solution is : (R = 0.08206 L atm K−1^{-1}−1 mol−1^{-1}−1)
  1. (A)8.2 atm
  2. (B)1.64 atm
  3. (C)4.92 atm
  4. (D)2.46 atm

Correct answer: (C)

Step-by-step solution →
Q59·ChemistrySingle correct
The temporary hardness of a water sample is due to compound X. Boiling this sample converts X to compound Y. X and Y, respectively, are :
  1. (A)Mg(HCO3_{3}3​)2_{2}2​ and MgCO3_{3}3​
  2. (B)Ca(HCO3_{3}3​)2_{2}2​ and CaO
  3. (C)Mg(HCO3_{3}3​)2_{2}2​ and Mg(OH)2_{2}2​
  4. (D)Ca(HCO3_{3}3​)2_{2}2​ and Ca(OH)2_{2}2​

Correct answer: (C)

Step-by-step solution →

Mathematics — JEE Main 12 April 2019 Shift 2

Q60·MathematicsSingle correct
The general solution of the differential equation (y2−x3)dx−xy dy=0(y^{2}-x^{3})dx - xy\,dy = 0(y2−x3)dx−xydy=0 (x≠0)(x \neq 0)(x=0) is : (where c is a constant of integration)
  1. (A)y2+2x3+cx2=0y^{2}+2x^{3}+cx^{2}=0y2+2x3+cx2=0
  2. (B)y2−2x3+cx2=0y^{2}-2x^{3}+cx^{2}=0y2−2x3+cx2=0
  3. (C)y2+2x2+cx3=0y^{2}+2x^{2}+cx^{3}=0y2+2x2+cx3=0
  4. (D)y2−2x2+cx3=0y^{2}-2x^{2}+cx^{3}=0y2−2x2+cx3=0

Correct answer: (A)

Step-by-step solution →
Q61·MathematicsSingle correct
Let α∈R\alpha \in Rα∈R and the three vectors a⃗=αi^+j^+3k^\vec{a} = \alpha\hat{i} + \hat{j} + 3\hat{k}a=αi^+j^​+3k^, b⃗=2i^+j^−αk^\vec{b} = 2\hat{i} + \hat{j} - \alpha\hat{k}b=2i^+j^​−αk^ and c⃗=αi^−2j^+3k^\vec{c} = \alpha\hat{i} - 2\hat{j} + 3\hat{k}c=αi^−2j^​+3k^. Then the set S=(α:a⃗,b⃗ and c⃗ are coplanar)S = (\alpha : \vec{a}, \vec{b} \text{ and } \vec{c} \text{ are coplanar})S=(α:a,b and c are coplanar)
  1. (A)Contains exactly two numbers only one of which is positive
  2. (B)is empty
  3. (C)Contains exactly two positive numbers
  4. (D)is singleton

Correct answer: (B)

Step-by-step solution →
Q62·MathematicsSingle correct
Let α∈(0,π/2)\alpha \in (0, \pi/2)α∈(0,π/2) be fixed. If the integral ∫tan⁡x+tan⁡αtan⁡x−tan⁡αdx=A(x)cos⁡2α+B(x)sin⁡2α+C\displaystyle\int \frac{\tan x + \tan \alpha}{\tan x - \tan \alpha}dx = A(x)\cos 2\alpha + B(x)\sin 2\alpha + C∫tanx−tanαtanx+tanα​dx=A(x)cos2α+B(x)sin2α+C, where C is a constant of integration, then the functions A(x) and B(x) are respectively:
  1. (A)x+αx+\alphax+α and log⁡e∣sin⁡(x−α)∣\log_{e}\left|\sin(x-\alpha)\right|loge​∣sin(x−α)∣
  2. (B)x−αx-\alphax−α and log⁡e∣cos⁡(x−α)∣\log_{e}\left|\cos(x-\alpha)\right|loge​∣cos(x−α)∣
  3. (C)x−αx-\alphax−α and log⁡e∣sin⁡(x−α)∣\log_{e}\left|\sin(x-\alpha)\right|loge​∣sin(x−α)∣
  4. (D)x+αx+\alphax+α and log⁡e∣sin⁡(x+α)∣\log_{e}\left|\sin(x+\alpha)\right|loge​∣sin(x+α)∣

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
Let S be the set of all α∈R\alpha \in Rα∈R such that the equation, cos⁡2x+αsin⁡x=2α−7\cos 2x + \alpha \sin x = 2\alpha - 7cos2x+αsinx=2α−7 has a solution. Then S is equal to :
  1. (A)[3,7][3,7][3,7]
  2. (B)RRR
  3. (C)[2,6][2,6][2,6]
  4. (D)[1,4][1,4][1,4]

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
Let f(x)=5−∣x−2∣f(x) = 5 - |x-2|f(x)=5−∣x−2∣ and g(x)=∣x+1∣g(x) = |x+1|g(x)=∣x+1∣, x∈Rx \in Rx∈R. If f(x)f(x)f(x) attains maximum value at α\alphaα and g(x)g(x)g(x) attains minimum value at β\betaβ, then lim⁡x→−αβ(x−1)(x2−5x+6)x2−6x+8\displaystyle\lim_{x \to -\alpha\beta} \frac{(x-1)(x^{2}-5x+6)}{x^{2}-6x+8}x→−αβlim​x2−6x+8(x−1)(x2−5x+6)​ is equal to :
  1. (A)32\dfrac{3}{2}23​
  2. (B)−32\dfrac{-3}{2}2−3​
  3. (C)12\dfrac{1}{2}21​
  4. (D)−12\dfrac{-1}{2}2−1​

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
Let z∈Cz \in Cz∈C with Im(z)=10\text{Im}(z) = 10Im(z)=10 and it satisfies 2z−n2z+n=2i−1\dfrac{2z-n}{2z+n} = 2i - 12z+n2z−n​=2i−1 for some natural number n. Then :
  1. (A)n = 40 and Re(z) = 10
  2. (B)n = 20 and Re(z) = 10
  3. (C)n = 40 and Re(z) = −10-10−10
  4. (D)n = 20 and Re(z) = −10-10−10

Correct answer: (C)

Step-by-step solution →
Q66·MathematicsSingle correct
The term independent of x in the expansion of (160−x881)⋅(2x2−3x2)6\left(\dfrac{1}{60} - \dfrac{x^{8}}{81}\right)\cdot\left(2x^{2} - \dfrac{3}{x^{2}}\right)^{6}(601​−81x8​)⋅(2x2−x23​)6 is equal to:
  1. (A)36
  2. (B)−36-36−36
  3. (C)−108-108−108
  4. (D)−72-72−72

Correct answer: (B)

Step-by-step solution →
Q67·MathematicsSingle correct
If the area (in sq. units) bounded by the parabola y2=4λxy^{2} = 4\lambda xy2=4λx and the line y=λxy = \lambda xy=λx, λ>0\lambda > 0λ>0, is 19\dfrac{1}{9}91​, then λ\lambdaλ is equal to :
  1. (A)48
  2. (B)434\sqrt{3}43​
  3. (C)262\sqrt{6}26​
  4. (D)24

Correct answer: (D)

Step-by-step solution →
Q68·MathematicsSingle correct
If [x] denotes the greatest integer ≤\leq≤ x, then the system of linear equations [sin θ\thetaθ] x + [−cos⁡θ-\cos\theta−cosθ] y = 0 [cot θ\thetaθ] x + y = 0
  1. (A)have infinitely many solutions if θ∈(π2,2π3)\theta \in \left(\dfrac{\pi}{2}, \dfrac{2\pi}{3}\right)θ∈(2π​,32π​) and has a unique solution if θ∈(π,7π6)\theta \in \left(\pi, \dfrac{7\pi}{6}\right)θ∈(π,67π​)
  2. (B)have infinitely many solutions if θ∈(π2,2π3)∪(π,7π6)\theta \in \left(\dfrac{\pi}{2}, \dfrac{2\pi}{3}\right) \cup \left(\pi, \dfrac{7\pi}{6}\right)θ∈(2π​,32π​)∪(π,67π​)
  3. (C)has a unique solution if θ∈(π2,2π3)\theta \in \left(\dfrac{\pi}{2}, \dfrac{2\pi}{3}\right)θ∈(2π​,32π​) and have infinitely many solutions if θ∈(π,7π6)\theta \in \left(\pi, \dfrac{7\pi}{6}\right)θ∈(π,67π​)
  4. (D)has a unique solution if θ∈(π2,2π3)∪(π,7π6)\theta \in \left(\dfrac{\pi}{2}, \dfrac{2\pi}{3}\right) \cup \left(\pi, \dfrac{7\pi}{6}\right)θ∈(2π​,32π​)∪(π,67π​)

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 45\dfrac{4}{5}54​, then the probability that he is unable to solve less than two problems is :
  1. (A)16425(15)48\dfrac{164}{25}\left(\dfrac{1}{5}\right)^{48}25164​(51​)48
  2. (B)2015(15)49\dfrac{201}{5}\left(\dfrac{1}{5}\right)^{49}5201​(51​)49
  3. (C)545(45)49\dfrac{54}{5}\left(\dfrac{4}{5}\right)^{49}554​(54​)49
  4. (D)31625(45)48\dfrac{316}{25}\left(\dfrac{4}{5}\right)^{48}25316​(54​)48

Correct answer: (C)

Step-by-step solution →
Q70·MathematicsSingle correct
If a1,a2,a3,……a_{1}, a_{2}, a_{3}, \ldots\ldotsa1​,a2​,a3​,…… are in A.P. such that a1+a7+a16=40a_{1} + a_{7} + a_{16} = 40a1​+a7​+a16​=40, then the sum of the first 15 terms of this A.P. is:
  1. (A)200
  2. (B)280
  3. (C)150
  4. (D)120

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
An ellipse, with foci at (0, 2) and (0, −2-2−2) and minor axis of length 4, passes through which of the following points?
  1. (A)(2,2)\left(2, \sqrt{2}\right)(2,2​)
  2. (B)(2,22)\left(2, 2\sqrt{2}\right)(2,22​)
  3. (C)(1,22)\left(1, 2\sqrt{2}\right)(1,22​)
  4. (D)(2,2)\left(\sqrt{2}, 2\right)(2​,2)

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines r⃗=(i^+j^)+λ(i^+2j^−k^)\vec{r} = (\hat{i}+\hat{j}) + \lambda(\hat{i}+2\hat{j}-\hat{k})r=(i^+j^​)+λ(i^+2j^​−k^) and r⃗=(i^+j^)+μ(−i^+j^−2k^)\vec{r} = (\hat{i}+\hat{j}) + \mu(-\hat{i}+\hat{j}-2\hat{k})r=(i^+j^​)+μ(−i^+j^​−2k^) is:
  1. (A)13\dfrac{1}{3}31​
  2. (B)3\sqrt{3}3​
  3. (C)13\dfrac{1}{\sqrt{3}}3​1​
  4. (D)3

Correct answer: (B)

Step-by-step solution →
Q73·MathematicsSingle correct
Let A, B and C be sets such that ϕ≠A∩B⊆C\phi \neq A \cap B \subseteq Cϕ=A∩B⊆C. Then which of the following statements is not true?
  1. (A)If (A−C)⊆B(A-C) \subseteq B(A−C)⊆B, then A⊆BA \subseteq BA⊆B
  2. (B)If (A−B)⊆C(A-B) \subseteq C(A−B)⊆C, then A⊆CA \subseteq CA⊆C
  3. (C)(C∪A)∩(C∪B)=C(C \cup A) \cap (C \cup B) = C(C∪A)∩(C∪B)=C
  4. (D)B∩C≠ϕB \cap C \neq \phiB∩C=ϕ

Correct answer: (A)

Step-by-step solution →
Q74·MathematicsSingle correct
If α\alphaα, β\betaβ and γ\gammaγ are three consecutive terms of a non-constant G.P. such that the equations αx2+2βx+γ=0\alpha x^{2} + 2\beta x + \gamma = 0αx2+2βx+γ=0 and x2+x−1=0x^{2} + x - 1 = 0x2+x−1=0 have a common root, then α(β+γ)\alpha(\beta+\gamma)α(β+γ) is equal to :
  1. (A)αγ\alpha\gammaαγ
  2. (B)0
  3. (C)αβ\alpha\betaαβ
  4. (D)βγ\beta\gammaβγ

Correct answer: (D)

Step-by-step solution →
Q75·MathematicsSingle correct
The tangents to the curve y=(x−2)2−1y = (x-2)^{2} -1y=(x−2)2−1 at its points of intersection with the line x−y=3x - y = 3x−y=3, intersect at the point :
  1. (A)(53,1)\left(\dfrac{5}{3},1\right)(35​,1)
  2. (B)(−52,−1)\left(-\dfrac{5}{2},-1\right)(−25​,−1)
  3. (C)(−52,1)\left(-\dfrac{5}{2},1\right)(−25​,1)
  4. (D)(52,−1)\left(\dfrac{5}{2},-1\right)(25​,−1)

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be 45°45°45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30°30°30°, then the distance (in m) of the foot of the tower from the point A is:
  1. (A)15(1+3)15\left(1+\sqrt{3}\right)15(1+3​)
  2. (B)15(3−3)15\left(3-\sqrt{3}\right)15(3−3​)
  3. (C)15(3+3)15\left(3+\sqrt{3}\right)15(3+3​)
  4. (D)15(5−3)15\left(5-\sqrt{3}\right)15(5−3​)

Correct answer: (C)

Step-by-step solution →
Q77·MathematicsSingle correct
A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (−1, 1) and (2,3). Then the centroid of this triangle is :
  1. (A)(1,73)\left(1,\dfrac{7}{3}\right)(1,37​)
  2. (B)(13,1)\left(\dfrac{1}{3},1\right)(31​,1)
  3. (C)(13,2)\left(\dfrac{1}{3},2\right)(31​,2)
  4. (D)(13,53)\left(\dfrac{1}{3},\dfrac{5}{3}\right)(31​,35​)

Correct answer: (C)

Step-by-step solution →
Q78·MathematicsSingle correct
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs.12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
  1. (A)14\dfrac{1}{4}41​ loss
  2. (B)2 gain
  3. (C)12\dfrac{1}{2}21​ gain
  4. (D)12\dfrac{1}{2}21​ loss

Correct answer: (D)

Step-by-step solution →
Q79·MathematicsSingle correct
The derivative of tan⁡−1(sin⁡x−cos⁡xsin⁡x+cos⁡x)\tan^{-1}\left(\dfrac{\sin x - \cos x}{\sin x + \cos x}\right)tan−1(sinx+cosxsinx−cosx​), with respect to x2\dfrac{x}{2}2x​, where (x∈(0,π2))\left(x \in \left(0,\dfrac{\pi}{2}\right)\right)(x∈(0,2π​)) is:
  1. (A)2
  2. (B)12\dfrac{1}{2}21​
  3. (C)1
  4. (D)23\dfrac{2}{3}32​

Correct answer: (A)

Step-by-step solution →
Q80·MathematicsSingle correct
A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :
  1. (A)(3, 5)
  2. (B)(1, 5)
  3. (C)(3, 10)
  4. (D)(2, 3)

Correct answer: (C)

Step-by-step solution →
Q81·MathematicsSingle correct
The equation of a common tangent to the curves, y2=16xy^{2} = 16xy2=16x and xy=−4xy = -4xy=−4 is :
  1. (A)x−2y+16=0x - 2y + 16 = 0x−2y+16=0
  2. (B)2x−y+2=02x - y + 2 = 02x−y+2=0
  3. (C)x+y+4=0x + y + 4 = 0x+y+4=0
  4. (D)x−y+4=0x - y + 4 = 0x−y+4=0

Correct answer: (D)

Step-by-step solution →
Q82·MathematicsSingle correct
A plane which bisects the angle between the two given planes 2x−y+2z−4=02x - y + 2z - 4 = 02x−y+2z−4=0 and x+2y+2z−2=0x + 2y + 2z - 2 = 0x+2y+2z−2=0, passes through the point:
  1. (A)(1, 4, −1)
  2. (B)(2, −4, 1)
  3. (C)(2, 4, 1)
  4. (D)(1, −4, 1)

Correct answer: (B)

Step-by-step solution →
Q83·MathematicsSingle correct
A value of α\alphaα such that ∫αα+1dx(x+α)(x+α+1)=log⁡e(98)\displaystyle\int_{\alpha}^{\alpha+1} \dfrac{dx}{(x+\alpha)(x+\alpha+1)} = \log_{e}\left(\dfrac{9}{8}\right)∫αα+1​(x+α)(x+α+1)dx​=loge​(89​) is:
  1. (A)−12-\dfrac{1}{2}−21​
  2. (B)−2-2−2
  3. (C)12\dfrac{1}{2}21​
  4. (D)2

Correct answer: (B)

Step-by-step solution →
Q84·MathematicsSingle correct
A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to:
  1. (A)24
  2. (B)28
  3. (C)27
  4. (D)25

Correct answer: (D)

Step-by-step solution →
Q85·MathematicsSingle correct
A value of θ∈(0,π/3)\theta \in (0, \pi/3)θ∈(0,π/3), for which ∣1+cos⁡2θsin⁡2θ4cos⁡6θcos⁡2θ1+sin⁡2θ4cos⁡6θcos⁡2θsin⁡2θ1+4cos⁡6θ∣=0\begin{vmatrix} 1+\cos^{2}\theta & \sin^{2}\theta & 4\cos 6\theta \\ \cos^{2}\theta & 1+\sin^{2}\theta & 4\cos 6\theta \\ \cos^{2}\theta & \sin^{2}\theta & 1+4\cos 6\theta \end{vmatrix} = 0​1+cos2θcos2θcos2θ​sin2θ1+sin2θsin2θ​4cos6θ4cos6θ1+4cos6θ​​=0, is:
  1. (A)π18\dfrac{\pi}{18}18π​
  2. (B)π9\dfrac{\pi}{9}9π​
  3. (C)7π36\dfrac{7\pi}{36}367π​
  4. (D)7π24\dfrac{7\pi}{24}247π​

Correct answer: (B)

Step-by-step solution →
Q86·MathematicsSingle correct
lim⁡x→0x+2sin⁡xx2+2sin⁡x+1−sin⁡2x−x+1\displaystyle\lim_{x\to 0} \dfrac{x + 2\sin x}{\sqrt{x^{2}+2\sin x+1} - \sqrt{\sin^{2}x - x + 1}}x→0lim​x2+2sinx+1​−sin2x−x+1​x+2sinx​ is:
  1. (A)2
  2. (B)6
  3. (C)3
  4. (D)1

Correct answer: (A)

Step-by-step solution →
Q87·MathematicsSingle correct
The Boolean expression ∼(p⇒(∼q))\sim(p \Rightarrow (\sim q))∼(p⇒(∼q)) is equivalent to:
  1. (A)(∼p)⇒q(\sim p) \Rightarrow q(∼p)⇒q
  2. (B)p∨qp \vee qp∨q
  3. (C)p∧qp \wedge qp∧q
  4. (D)q⇒∼pq \Rightarrow \sim pq⇒∼p

Correct answer: (C)

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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
  • 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
  • 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
  • Laws of Motion 130/186
  • Chemical Thermodynamics 165/186
  • Hydrocarbons 126/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • 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
  • Oscillations 117/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • 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
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Solid State 63/186
  • Diazonium Salts and Reactions 53/186
  • Isomerism 51/186
  • IUPAC Nomenclature 37/186
  • Mathematical Reasoning 26/186
  • Communication Systems 11/186
← 12 Apr Shift 1 2019All papers7 Jan Shift 1 2020 →

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