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JEE Main 9 January 2019 Shift 1 Question Paper with Answers

9 January 2019 · January session · 84 questions

84 of the 90 questions from the JEE Main 9 January 2019 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

6 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
28
Mathematics
28

Physics — JEE Main 9 January 2019 Shift 1

Q1·PhysicsSingle correct
A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:
  1. (A)1.1 cm away fro the lens
  2. (B)0
  3. (C)0.55 cm towards the lens
  4. (D)0.55 cm away from the lens

Correct answer: (D)

Step-by-step solution →
Q2·PhysicsSingle correct
A resistance is shown in the figure. Its value and tolerance are given respectively by:
  1. (A)270 Ω\OmegaΩ, 10%
  2. (B)27 kΩ\OmegaΩ, 10%
  3. (C)27 kΩ\OmegaΩ, 20%
  4. (D)270 Ω\OmegaΩ, 5%

Correct answer: (B)

Step-by-step solution →
Q3·PhysicsSingle correct
Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2^{2}2, is v. If the electron density in copper is 9×10289 \times 10^{28}9×1028 /m3^{3}3 the value of v in mm/s is close to (Take charge of electron to be = 1.6×10−191.6 \times 10^{-19}1.6×10−19 C)
  1. (A)0.02
  2. (B)3
  3. (C)2
  4. (D)0.2

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is θ\thetaθ, then:
  1. (A)tan⁡θ=123\tan \theta = \dfrac{1}{2\sqrt{3}}tanθ=23​1​
  2. (B)tan⁡θ=12\tan \theta = \dfrac{1}{2}tanθ=21​
  3. (C)tan⁡θ=23\tan \theta = \dfrac{2}{\sqrt{3}}tanθ=3​2​
  4. (D)tan⁡θ=13\tan \theta = \dfrac{1}{3}tanθ=31​

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
A particle is moving with a velocity v⃗=K(yi^+xj^)\vec{v} = K(y\hat{i} + x\hat{j})v=K(yi^+xj^​), where K is a constant. The general equation for its path is:
  1. (A)y=x2y = x^{2}y=x2 + constant
  2. (B)y2=xy^{2} = xy2=x + constant
  3. (C)y2=x2y^{2} = x^{2}y2=x2 + constant
  4. (D)xy = constant

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds [Vrms(helium)Vrms(argon)]\left[\dfrac{V_{rms}(helium)}{V_{rms}(argon)}\right][Vrms​(argon)Vrms​(helium)​], is close to:
  1. (A)3.16
  2. (B)0.32
  3. (C)0.45
  4. (D)2.24

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:
  1. (A)1.0×10−71.0 \times 10^{-7}1.0×10−7 T
  2. (B)1.5×10−71.5 \times 10^{-7}1.5×10−7 T
  3. (C)1.5×10−51.5 \times 10^{-5}1.5×10−5 T
  4. (D)1.0×10−51.0 \times 10^{-5}1.0×10−5 T

Correct answer: (D)

Step-by-step solution →
Q8·PhysicsSingle correct
A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is
  1. (A)2Fmk\dfrac{2F}{\sqrt{mk}}mk​2F​
  2. (B)Fπmk\dfrac{F}{\pi\sqrt{mk}}πmk​F​
  3. (C)πFmk\dfrac{\pi F}{\sqrt{mk}}mk​πF​
  4. (D)Fmk\dfrac{F}{\sqrt{mk}}mk​F​

Correct answer: (D)

Step-by-step solution →
Q9·PhysicsSingle correct
For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:
  1. (A)R5\dfrac{R}{\sqrt{5}}5​R​
  2. (B)R2\dfrac{R}{\sqrt{2}}2​R​
  3. (C)R
  4. (D)R2R\sqrt{2}R2​

Correct answer: (B)

Step-by-step solution →
Q10·PhysicsSingle correct
Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:
  1. (A)16 : 9
  2. (B)25 : 9
  3. (C)4 : 1
  4. (D)5 : 3

Correct answer: (B)

Step-by-step solution →
Q11·PhysicsSingle correct
Surface of certain metal is first illuminated with light of wavelength λ1\lambda_{1}λ1​ = 350 nm and then, the light of wavelength λ2\lambda_{2}λ2​ = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to: (Energy of photon = 1240λ(in nm)\dfrac{1240}{\lambda(\text{in nm})}λ(in nm)1240​eV)
  1. (A)1.8
  2. (B)2.5
  3. (C)5.6
  4. (D)1.4

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length 3L2\dfrac{3L}{2}23L​, is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to:
  1. (A)45°C
  2. (B)75°C
  3. (C)60°C
  4. (D)35°C

Correct answer: (A)

Step-by-step solution →
Q13·PhysicsSingle correct
A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work down by the system is 10 J. the heat flow into the system in path ADB is
  1. (A)40 J
  2. (B)80 J
  3. (C)100 J
  4. (D)20 J

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ\muμ. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ\muμ is
  1. (A)53\sqrt{\dfrac{5}{3}}35​​
  2. (B)35\dfrac{3}{\sqrt{5}}5​3​
  3. (C)53\dfrac{5}{\sqrt{3}}3​5​
  4. (D)43\dfrac{4}{3}34​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 101910^{19}1019 m−3^{-3}−3 and their mobility is 1.6 m2^{2}2/(V.s) then the resistivity of the semiconductor(since it is an n-type semiconductor contribution of holes is ignored) is close to:
  1. (A)2 Ω\OmegaΩm
  2. (B)4 Ω\OmegaΩm
  3. (C)0.4 Ω\OmegaΩm
  4. (D)0.2 Ω\OmegaΩm

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, E⃗=6.3j^\vec{E} = 6.3\hat{j}E=6.3j^​ V / m.. The corresponding magnetic field B⃗\vec{B}B, at that point will be
  1. (A)18.9×10−8 k^18.9 \times 10^{-8}\ \hat{k}18.9×10−8 k^T
  2. (B)2.1×10−8 k^2.1 \times 10^{-8}\ \hat{k}2.1×10−8 k^T
  3. (C)6.3×10−8 k^6.3 \times 10^{-8}\ \hat{k}6.3×10−8 k^T
  4. (D)18.9×108 k^18.9 \times 10^{8}\ \hat{k}18.9×108 k^T

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by +Q, placed at x = 0, is zero, then value of q is
  1. (A)-Q/4
  2. (B)+Q/2
  3. (C)+Q/4
  4. (D)-Q/2

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
A copper wire is stretched to make it 0.5% longer. The percentage change in its electric resistance if its volume remains unchanged is
  1. (A)2.0%
  2. (B)2.5%
  3. (C)1.0%
  4. (D)0.5%

Correct answer: (C)

Step-by-step solution →
Q19·PhysicsSingle correct
A sample of radioactive material A, that has an activity of 10 mCi (1 Ci = 3.7×10103.7 \times 10^{10}3.7×1010 decays/s), has twice the number of nuclei as another sample of different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively:
  1. (A)5 days and 10 days
  2. (B)10 days and 40 days
  3. (C)20 days and 5 days
  4. (D)20 days and 10 days

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
A heavy ball of mass M is suspended from the ceiling of car by a light string of mass m (m << M). When the car is at rest, the speed of transverse waves in the string is 60 ms−1^{-1}−1. When the car has acceleration a, the wave-speed increases to 60.5 ms−1^{-1}−1. The value of a, in terms of gravitational acceleration g is closest to:
  1. (A)g30\frac{g}{30}30g​
  2. (B)g5\frac{g}{5}5g​
  3. (C)g10\frac{g}{10}10g​
  4. (D)g20\frac{g}{20}20g​

Correct answer: (B)

Step-by-step solution →
Q21·PhysicsSingle correct
An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. the radius of the loop is a and distance of its centre from the wire is d (d >> a). If the loop applies a force F on the wire then:
  1. (A)F = 0
  2. (B)F∝adF \propto \frac{a}{d}F∝da​
  3. (C)F∝a2d3F \propto \frac{a^2}{d^3}F∝d3a2​
  4. (D)F∝(ad)2F \propto \left(\frac{a}{d}\right)^2F∝(da​)2

Correct answer: (D)

Step-by-step solution →
Q22·PhysicsSingle correct
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g=10 ms−2g = 10\text{ ms}^{-2}g=10 ms−2)
  1. (A)32 N
  2. (B)18 N
  3. (C)23 N
  4. (D)25 N

Correct answer: (A)

Step-by-step solution →
Q23·PhysicsSingle correct
A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d(d <<a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is
  1. (A)Kε0a22d(K+1)\frac{K\varepsilon_0 a^2}{2d(K+1)}2d(K+1)Kε0​a2​
  2. (B)Kε0a2d(K−1)ln⁡K\frac{K\varepsilon_0 a^2}{d(K-1)}\ln Kd(K−1)Kε0​a2​lnK
  3. (C)Kε0a2dln⁡K\frac{K\varepsilon_0 a^2}{d}\ln KdKε0​a2​lnK
  4. (D)12Kε0a2d\frac{1}{2}\frac{K\varepsilon_0 a^2}{d}21​dKε0​a2​

Correct answer: (B)

Step-by-step solution →
Q24·PhysicsSingle correct
A rod of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α\alphaα/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by ΔT\Delta TΔTK. Young's modulus, Y, for this metal is
  1. (A)FAαΔT\frac{F}{A\alpha \Delta T}AαΔTF​
  2. (B)FAα(ΔT−273)\frac{F}{A\alpha(\Delta T-273)}Aα(ΔT−273)F​
  3. (C)F2AαΔT\frac{F}{2A \alpha \Delta T}2AαΔTF​
  4. (D)2FAαΔT\frac{2F}{A \alpha \Delta T}AαΔT2F​

Correct answer: (A)

Step-by-step solution →
Q25·PhysicsSingle correct
A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is
  1. (A)285 A/m
  2. (B)2600 A/m
  3. (C)520 A/m
  4. (D)1200 A/m

Correct answer: (B)

Step-by-step solution →
Q26·PhysicsSingle correct
When the switch S, in the circuit shown, is closed, then the value of current i will be
  1. (A)3 A
  2. (B)5 A
  3. (C)4 A
  4. (D)2 A

Correct answer: (B)

Step-by-step solution →
Q27·PhysicsSingle correct
If the angular momentum of a planet of mass m, moving a round the Sun in a circular orbit its L, about the center of the Sun, its areal velocity is:
  1. (A)Lm\frac{L}{m}mL​
  2. (B)4Lm\frac{4L}{m}m4L​
  3. (C)L2m\frac{L}{2m}2mL​
  4. (D)2Lm\frac{2L}{m}m2L​

Correct answer: (C)

Step-by-step solution →
Q28·PhysicsSingle correct
Two masses mmm and m2\dfrac{m}{2}2m​ are connected at the two ends of a massless rigid rod of length ℓ\ellℓ. The rod is suspended by a thin wire of torsional constant kkk at the centre of mass of the rod-mass system (see figure). Because of torsional constant kkk, the restoring torque is τ=kθ\tau = k\thetaτ=kθ for angular displacement θ\thetaθ. If the rod is rotated by θ0\theta_0θ0​ and released, the tension in it when it passes through its mean position will be
  1. (A)3kθ02ℓ\dfrac{3k\theta_0^2}{\ell}ℓ3kθ02​​
  2. (B)2kθ02ℓ\dfrac{2k\theta_0^2}{\ell}ℓ2kθ02​​
  3. (C)kθ02ℓ\dfrac{k\theta_0^2}{\ell}ℓkθ02​​
  4. (D)kθ022ℓ\dfrac{k\theta_0^2}{2\ell}2ℓkθ02​​

Correct answer: (C)

Step-by-step solution →

Chemistry — JEE Main 9 January 2019 Shift 1

Q29·ChemistrySingle correct
Two complexes [Cr(H2_{2}2​O)6_{6}6​]Cl3_{3}3​ (A) and [Cr(NH3_{3}3​)6_{6}6​]Cl3_{3}3​ (B) are violet and yellow coloured respectively. The incorrect statement regarding them is
  1. (A)Δ0\Delta_{0}Δ0​ values of (A) and (B) are calculated from the energies of violet and yellow light, respectively.
  2. (B)both are paramagnetic with three unpaired electrons
  3. (C)both absorbs energies corresponding to their complementary colours
  4. (D)Δ0\Delta_{0}Δ0​ value for (A) is less than that of (B)

Correct answer: (A)

Step-by-step solution →
Q30·ChemistrySingle correct
The correct decreasing order for acidic strength is
  1. (A)NO2_{2}2​CH2_{2}2​COOH > FCH2_{2}2​COOH > CNCH2_{2}2​COOH > ClCH2_{2}2​COOH
  2. (B)FCH2_{2}2​COOH > NCCH2_{2}2​COOH > NO2_{2}2​CH2_{2}2​COOH > ClCH2_{2}2​COOH
  3. (C)CNCH2_{2}2​COOH > O2_{2}2​NCH2_{2}2​COOH > FCH2_{2}2​COOH > ClCH2_{2}2​COOH
  4. (D)NO2_{2}2​CH2_{2}2​COOH > NCCH2_{2}2​COOH > FCH2_{2}2​COOH > ClCH2_{2}2​COOH

Correct answer: (D)

Step-by-step solution →
Q31·ChemistrySingle correct
The major product of the following reaction is R −-− C ≡\equiv≡ N →(2) H2O(1) AlH(i−Bu)2\xrightarrow[(2)\ H_{2}O]{(1)\ AlH(i-Bu)_{2}}(1) AlH(i−Bu)2​(2) H2​O​ ?
  1. (A)RCOOH
  2. (B)RCONH2_{2}2​
  3. (C)RCHO
  4. (D)RCH2_{2}2​NH2_{2}2​

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
The highest value of the calculated spin-only magnetic moment (in BM) among all the transition metal complexes is
  1. (A)5.92
  2. (B)6.93
  3. (C)3.87
  4. (D)4.90

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m3^{3}3 at 1000 K. Given R is the gas constant in JK−1^{-1}−1mol−1^{-1}−1, x is
  1. (A)2R4+R\dfrac{2R}{4+R}4+R2R​
  2. (B)2R4−R\dfrac{2R}{4-R}4−R2R​
  3. (C)4+R2R\dfrac{4+R}{2R}2R4+R​
  4. (D)4−R2R\dfrac{4-R}{2R}2R4−R​

Correct answer: (D)

Step-by-step solution →
Q34·ChemistrySingle correct
The one that is extensively used as a piezoelectric material is
  1. (A)tridymite
  2. (B)amorphous silica
  3. (C)quartz
  4. (D)mica

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
Correct statements among a to d regarding silicones are (i) they are polymers with hydrophobic character (ii) they are biocompatible (iii) in general, they have high thermal stability and low dielectric strength (iv) usually they are resistant to oxidation and used as greases.
  1. (A)(i), (ii), (iii) and (iv)
  2. (B)(i), (ii) and (iii)
  3. (C)(i) and (ii) only
  4. (D)(i), (ii) and (iv)

Correct answer: (D)

Step-by-step solution →
Q36·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 →
Q37·ChemistrySingle correct
In general, the properties that decrease and increase down a group in the periodic table respectively are
  1. (A)atomic radius and electronegativity
  2. (B)electron gain enthalpy and electronegativity
  3. (C)electronegativity and atomic radius
  4. (D)electronegativity and electron gain enthalpy

Correct answer: (C)

Step-by-step solution →
Q38·ChemistrySingle correct
A solution of sodium sulphate contains 92 g of Na+^{+}+ ions per kilogram of water. The Molality of Na+^{+}+ ions in that solution in mol kg−1^{-1}−1 is
  1. (A)12
  2. (B)4
  3. (C)8
  4. (D)16

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
The correct match between Item-I and Item-II is:
Item-I (drug)Item-II (test)
a.Chloroxylenolp.Carbylamine test
b.Norethindroneq.Sodium hydrogen carbonate test
c.Sulpha pyridiner.Ferric chloride test
d.Penicillins.Bayer's test
  1. (A)a →\rightarrow→ r, b →\rightarrow→ p, c →\rightarrow→ s, d →\rightarrow→ q
  2. (B)a →\rightarrow→ q, b →\rightarrow→ s, c →\rightarrow→ p, d →\rightarrow→ r
  3. (C)a →\rightarrow→ r, b →\rightarrow→ s, c →\rightarrow→ p, d →\rightarrow→ q
  4. (D)a →\rightarrow→ q, b →\rightarrow→ p, c →\rightarrow→ s, d →\rightarrow→ r

Correct answer: (C)

Step-by-step solution →
Q40·ChemistrySingle correct
A water sample has ppm level concentration of the following metals: Fe = 0.2, Mn = 5.0, Cu = 3.0, Zn = 5.0. The metal that makes the water sample unsuitable for drinking is
  1. (A)Cu
  2. (B)Mn
  3. (C)Fe
  4. (D)Zn

Correct answer: (B)

Step-by-step solution →
Q41·ChemistrySingle correct
The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO4_{4}4​ electrolyzed in g during the process is: (Molar mass of PbSO4_{4}4​ = 303 g mol−1^{-1}−1)
  1. (A)22.8
  2. (B)15.2
  3. (C)7.6
  4. (D)11.4

Correct answer: (C)

Step-by-step solution →
Q42·ChemistrySingle correct
Which one of the following statements regarding Henry's law is not correct?
  1. (A)Higher the value of KH_{H}H​ at a given pressure, higher is the solubility of the gas in the liquids
  2. (B)Different gases have different KH_{H}H​(Henry's law constant) values at the same temperature
  3. (C)The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution
  4. (D)The value of KH_{H}H​ increases with increase of temperature and KH_{H}H​ is function of the nature of the gas.

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
The following results were obtained during kinetic studies of the reaction 2A + B ⟶\longrightarrow⟶ products. The time (in minutes) required to consume half of A is
Experiment[A] (in mol L−1^{-1}−1)[B] (in mol L−1^{-1}−1)Initial rate of reaction (in mol L−1^{-1}−1 min−1^{-1}−1)
I0.100.206.93 ×\times× 10−3^{-3}−3
II0.100.256.93 ×\times× 10−3^{-3}−3
III0.200.301.386 ×\times× 10−2^{-2}−2
  1. (A)5
  2. (B)10
  3. (C)1
  4. (D)100

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
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 →
Q45·ChemistrySingle correct
The alkaline earth metal nitrate that does not crystallise with water molecules is
  1. (A)Mg(NO3_{3}3​)2_{2}2​
  2. (B)Sr(NO3_{3}3​)2_{2}2​
  3. (C)Ca(NO3_{3}3​)2_{2}2​
  4. (D)Ba(NO3_{3}3​)2_{2}2​

Correct answer: (D)

Step-by-step solution →
Q46·ChemistrySingle correct
20 mL of 0.1 M H2_{2}2​SO4_{4}4​ is added to 30 mL of 0.2 M NH4_{4}4​OH solution. The pH of the resultant mixture is [pkb_{b}b​ of NH4_{4}4​OH = 4.7]
  1. (A)5.2
  2. (B)9.0
  3. (C)5.0
  4. (D)9.4

Correct answer: (B)

Step-by-step solution →
Q47·ChemistrySingle correct
Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of gas adsorbed on mass m of the adsorbent at pressure p. xm\frac{x}{m}mx​ is proportional to
  1. (A)p2^{2}2
  2. (B)p1/4^{1/4}1/4
  3. (C)p1/2^{1/2}1/2
  4. (D)p

Correct answer: (C)

Step-by-step solution →
Q48·ChemistrySingle correct
Which amongst the following is the strongest acid?
  1. (A)CHBr3_{3}3​
  2. (B)CHI3_{3}3​
  3. (C)CH(CN)3_{3}3​
  4. (D)CHCl3_{3}3​

Correct answer: (C)

Step-by-step solution →
Q49·ChemistrySingle correct
The ore that contains both iron and copper is
  1. (A)copper pyrites
  2. (B)malachite
  3. (C)dolomite
  4. (D)azurite

Correct answer: (A)

Step-by-step solution →
Q50·ChemistrySingle correct
For emission line of atomic hydrogen from n1_{1}1​= 8 to nf_{f}f​ = n, the plot of wave number (vˉ\bar{v}vˉ) against (1n2)\left(\frac{1}{n^{2}}\right)(n21​) will be(The Rydberg constant, RH_{H}H​ is in wave number unit)
  1. (A)Linear with intercept - RH_{H}H​
  2. (B)Non linear
  3. (C)Linear with slope RH_{H}H​
  4. (D)Linear with slope – RH_{H}H​

Correct answer: (C)

Step-by-step solution →
Q51·ChemistrySingle correct
The isotopes of hydrogen are
  1. (A)tritium and protium only
  2. (B)protium and deuterium only
  3. (C)protium, deuterium and tritium
  4. (D)deuterium and tritium only

Correct answer: (C)

Step-by-step solution →
Q52·ChemistrySingle correct
According to molecular orbital theory, which of the following is true with respect to Li2+_{2}^{+}2+​ and Li2−_{2}^{-}2−​?
  1. (A)Li2+_{2}^{+}2+​ is unstable and Li2−_{2}^{-}2−​ is stable
  2. (B)Li2+_{2}^{+}2+​ is stable and Li2−_{2}^{-}2−​ is unstable
  3. (C)Both are stable
  4. (D)Both are unstable

Correct answer: (C)

Step-by-step solution →
Q53·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 →
Q54·ChemistrySingle correct
Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3 oxidation states. This is due to
  1. (A)inert pair effect
  2. (B)diagonal relationship
  3. (C)lattice effect
  4. (D)lanthanoid contraction

Correct answer: (A)

Step-by-step solution →
Q55·ChemistrySingle correct
The increasing order of pKa of following amino acids in aqueous solution is Gly, Asp, Lys, Arg
  1. (A)Asp < Gly < Arg < Lys
  2. (B)Gly < Asp < Arg < Lys
  3. (C)Asp < Gly < Lys < Arg
  4. (D)Arg < Lys < Gly < Asp

Correct answer: (C)

Step-by-step solution →
Q56·ChemistrySingle correct
The compounds A and B in the following reaction are, respectively
  1. (A)A = Benzyl alcohol, B = Benzyl cyanide
  2. (B)A = Benzyl chloride, B = Benzyl cyanide
  3. (C)A = Benzyl alcohol, B = Benzyl isocyanide
  4. (D)A = Benzyl chloride, B = Benzyl isocyanide

Correct answer: (D)

Step-by-step solution →

Mathematics — JEE Main 9 January 2019 Shift 1

Q57·MathematicsSingle correct
The value of ∫0π∣cos⁡x∣3 dx\displaystyle\int_{0}^{\pi} |\cos x|^3\, dx∫0π​∣cosx∣3dx is:
  1. (A)0
  2. (B)43\dfrac{4}{3}34​
  3. (C)23\dfrac{2}{3}32​
  4. (D)−43-\dfrac{4}{3}−34​

Correct answer: (B)

Step-by-step solution →
Q58·MathematicsSingle correct
The maximum volume (in cu.m) of the right circular cone having slant height 3 m is
  1. (A)6π6\pi6π
  2. (B)33 π3\sqrt{3}\,\pi33​π
  3. (C)43π\dfrac{4}{3}\pi34​π
  4. (D)23π2\sqrt{3}\pi23​π

Correct answer: (D)

Step-by-step solution →
Q59·MathematicsSingle correct
For x2≠nπ+1x^2 \neq n\pi + 1x2=nπ+1, n∈Nn \in Nn∈N (the set of natural numbers), the integral ∫x.2sin⁡(x2−1)−sin⁡2(x2−1)2sin⁡(x2−1)+sin⁡2(x2−1) dx\int x.\sqrt{\dfrac{2\sin(x^2-1) - \sin 2(x^2-1)}{2\sin(x^2-1) + \sin 2(x^2-1)}} \, dx∫x.2sin(x2−1)+sin2(x2−1)2sin(x2−1)−sin2(x2−1)​​dx is
  1. (A)log⁡e∣12sec⁡2(x2−1)∣+c\log_e \left| \dfrac{1}{2}\sec^2(x^2-1) \right| + cloge​​21​sec2(x2−1)​+c
  2. (B)12log⁡e∣sec⁡(x2−1)∣+c\dfrac{1}{2}\log_e \left| \sec(x^2-1) \right| + c21​loge​​sec(x2−1)​+c
  3. (C)12log⁡e∣sec⁡2(x2−12)∣+c\dfrac{1}{2}\log_e \left| \sec^2\left(\dfrac{x^2-1}{2}\right) \right| + c21​loge​​sec2(2x2−1​)​+c
  4. (D)log⁡e∣sec⁡(x2−12)∣+c\log_e \left| \sec\left(\dfrac{x^2-1}{2}\right) \right| + cloge​​sec(2x2−1​)​+c

Correct answer: (D)

Step-by-step solution →
Q60·MathematicsSingle correct
If y=y(x)y = y(x)y=y(x) is solution of the differential equation xdydx+2y=x2x\dfrac{dy}{dx} + 2y = x^2xdxdy​+2y=x2 satisfying y(1)=1y(1) = 1y(1)=1, then y(12)y\left(\dfrac{1}{2}\right)y(21​) is equal to
  1. (A)764\dfrac{7}{64}647​
  2. (B)14\dfrac{1}{4}41​
  3. (C)4916\dfrac{49}{16}1649​
  4. (D)1316\dfrac{13}{16}1613​

Correct answer: (C)

Step-by-step solution →
Q61·MathematicsSingle correct
Axis of a parabola lies along x - axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive x - axis then which of the following points does not lie on it?
  1. (A)(5,26)(5, 2\sqrt{6})(5,26​)
  2. (B)(8,6)(8, 6)(8,6)
  3. (C)(6,42)(6, 4\sqrt{2})(6,42​)
  4. (D)(4,−4)(4, -4)(4,−4)

Correct answer: (B)

Step-by-step solution →
Q62·MathematicsSingle correct
Let 0<θ<π20 < \theta < \dfrac{\pi}{2}0<θ<2π​. If the eccentricity of the hyperbola x2cos⁡2θ−y2sin⁡2θ=1\dfrac{x^2}{\cos^2\theta} - \dfrac{y^2}{\sin^2\theta} = 1cos2θx2​−sin2θy2​=1 is greater than 2, then the length of its latus rectum lies in the interval:
  1. (A)(3,∞)(3, \infty)(3,∞)
  2. (B)(32,2]\left(\dfrac{3}{2}, 2\right](23​,2]
  3. (C)(2,3](2, 3](2,3]
  4. (D)(1,32]\left(1, \dfrac{3}{2}\right](1,23​]

Correct answer: (A)

Step-by-step solution →
Q63·MathematicsSingle correct
For x∈R−[0,1]x \in R - [0,1]x∈R−[0,1], let f1(x)=1xf_1(x) = \dfrac{1}{x}f1​(x)=x1​, f2(x)=1−xf_2(x) = 1-xf2​(x)=1−x and f3(x)=11−xf_3(x) = \dfrac{1}{1-x}f3​(x)=1−x1​ be three given functions. If a function, J(x)J(x)J(x) satisfies (f2∘J∘f1)(x)=f3(x)(f_2 \circ J \circ f_1)(x) = f_3(x)(f2​∘J∘f1​)(x)=f3​(x) then J(x)J(x)J(x) is equal to:
  1. (A)f3(x)f_3(x)f3​(x)
  2. (B)1xf3(x)\dfrac{1}{x}f_3(x)x1​f3​(x)
  3. (C)f2(x)f_2(x)f2​(x)
  4. (D)f1(x)f_1(x)f1​(x)

Correct answer: (A)

Step-by-step solution →
Q64·MathematicsSingle correct
Let a⃗=i^−j^\vec a = \hat i - \hat ja=i^−j^​, b⃗=i^+j^+k^\vec b = \hat i + \hat j + \hat kb=i^+j^​+k^ and c⃗\vec cc be a vector such that a⃗×c⃗+b⃗=0\vec a \times \vec c + \vec b = 0a×c+b=0 and a⃗.c⃗=4\vec a . \vec c = 4a.c=4, then ∣c⃗∣2|\vec c|^2∣c∣2 is equal to:
  1. (A)192\dfrac{19}{2}219​
  2. (B)9
  3. (C)8
  4. (D)172\dfrac{17}{2}217​

Correct answer: (A)

Step-by-step solution →
Q65·MathematicsSingle correct
If a, b and c be three distinct numbers in G.P. and a+b+c=xba + b + c = xba+b+c=xb then x can not be
  1. (A)−2-2−2
  2. (B)−3-3−3
  3. (C)444
  4. (D)222

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
If cos⁡−1(23x)+cos⁡−1(34x)=π2\cos^{-1}\left(\dfrac{2}{3x}\right) + \cos^{-1}\left(\dfrac{3}{4x}\right) = \dfrac{\pi}{2}cos−1(3x2​)+cos−1(4x3​)=2π​, x>34x > \dfrac{3}{4}x>43​ then x is equal to:
  1. (A)14512\dfrac{\sqrt{145}}{12}12145​​
  2. (B)14510\dfrac{\sqrt{145}}{10}10145​​
  3. (C)14612\dfrac{\sqrt{146}}{12}12146​​
  4. (D)14511\dfrac{\sqrt{145}}{11}11145​​

Correct answer: (A)

Step-by-step solution →
Q67·MathematicsSingle correct
Equation of a common tangent to the circle, x2+y2−6x=0x^2 + y^2 - 6x = 0x2+y2−6x=0 and the parabola, y2=4xy^2 = 4xy2=4x, is:
  1. (A)23y=12x+12\sqrt{3}y = 12x + 123​y=12x+1
  2. (B)3y=x+3\sqrt{3}y = x + 33​y=x+3
  3. (C)23y=−x−122\sqrt{3}y = -x - 1223​y=−x−12
  4. (D)3y=3x+1\sqrt{3}y = 3x + 13​y=3x+1

Correct answer: (B)

Step-by-step solution →
Q68·MathematicsSingle correct
The system of linear equation x+y+z=2x + y + z = 2x+y+z=2, 2x+3y+2z=52x + 3y + 2z = 52x+3y+2z=5, 2x+3y+(a2−1)z=a+12x + 3y + (a^2 - 1)z = a + 12x+3y+(a2−1)z=a+1 then
  1. (A)is inconsistent when a=4a = 4a=4
  2. (B)has a unique solution for ∣a∣=3|a| = \sqrt{3}∣a∣=3​
  3. (C)has infinitely many solutions for a=4a = 4a=4
  4. (D)inconsistent when ∣a∣=3|a| = \sqrt{3}∣a∣=3​

Correct answer: (D)

Step-by-step solution →
Q69·MathematicsSingle correct
If the fractional part of the number 240315\dfrac{2^{403}}{15}152403​ is k15\dfrac{k}{15}15k​, then k is equal to:
  1. (A)6
  2. (B)8
  3. (C)4
  4. (D)14

Correct answer: (B)

Step-by-step solution →
Q70·MathematicsSingle correct
Consider the set of all lines px+qy+r=0px + qy + r = 0px+qy+r=0 such that 3p+2q+4r=03p + 2q + 4r = 03p+2q+4r=0. Which one of the following statements is true?
  1. (A)The lines are concurrent at the point (34,12)\left(\dfrac{3}{4}, \dfrac{1}{2}\right)(43​,21​).
  2. (B)Each line passes through the origin.
  3. (C)The lines are all parallel
  4. (D)The lines are not concurrent

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
lim⁡y→01+1+y4−2y4=\displaystyle\lim_{y \to 0} \dfrac{\sqrt{1+\sqrt{1+y^4}}-\sqrt2}{y^4} =y→0lim​y41+1+y4​​−2​​=
  1. (A)exists and equals 142\dfrac{1}{4\sqrt2}42​1​
  2. (B)exists and equals 122(2+1)\dfrac{1}{2\sqrt2(\sqrt2+1)}22​(2​+1)1​
  3. (C)exists and equals 122\dfrac{1}{2\sqrt2}22​1​
  4. (D)does not exist

Correct answer: (A)

Step-by-step solution →
Q72·MathematicsSingle correct
The plane through the intersection of the plane x+y+z=1x+y+z=1x+y+z=1 and 2x+3y−z+4=02x+3y-z+4=02x+3y−z+4=0 and parallel to y – axis also pass through the point:
  1. (A)(−3, 0, −1)(-3,\ 0,\ -1)(−3, 0, −1)
  2. (B)(−3, 1, 1)(-3,\ 1,\ 1)(−3, 1, 1)
  3. (C)(3, 3, −1)(3,\ 3,\ -1)(3, 3, −1)
  4. (D)(3, 2, 1)(3,\ 2,\ 1)(3, 2, 1)

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
If θ\thetaθ denotes the acute angle between the curves, y=10−x2y=10-x^{2}y=10−x2 and y=2+x2y=2+x^{2}y=2+x2 at a point of their intersection, then ∣tan⁡θ∣|\tan\theta|∣tanθ∣ is equal to
  1. (A)49\dfrac{4}{9}94​
  2. (B)815\dfrac{8}{15}158​
  3. (C)717\dfrac{7}{17}177​
  4. (D)817\dfrac{8}{17}178​

Correct answer: (B)

Step-by-step solution →
Q74·MathematicsSingle correct
If A=[cos⁡θ−sin⁡θsin⁡θcos⁡θ]A=\begin{bmatrix}\cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\end{bmatrix}A=[cosθsinθ​−sinθcosθ​], then the matrix A−50A^{-50}A−50 when θ=π12\theta=\dfrac{\pi}{12}θ=12π​, is equal to
  1. (A)[12−323212]\begin{bmatrix}\dfrac{1}{2} & -\dfrac{\sqrt{3}}{2}\\[4pt] \dfrac{\sqrt{3}}{2} & \dfrac{1}{2}\end{bmatrix}​21​23​​​−23​​21​​​
  2. (B)[32−121232]\begin{bmatrix}\dfrac{\sqrt{3}}{2} & -\dfrac{1}{2}\\[4pt] \dfrac{1}{2} & \dfrac{\sqrt{3}}{2}\end{bmatrix}​23​​21​​−21​23​​​​
  3. (C)[3212−1232]\begin{bmatrix}\dfrac{\sqrt{3}}{2} & \dfrac{1}{2}\\[4pt] -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2}\end{bmatrix}​23​​−21​​21​23​​​​
  4. (D)[1232−3212]\begin{bmatrix}\dfrac{1}{2} & \dfrac{\sqrt{3}}{2}\\[4pt] -\dfrac{\sqrt{3}}{2} & \dfrac{1}{2}\end{bmatrix}​21​−23​​​23​​21​​​

Correct answer: (C)

Step-by-step solution →
Q75·MathematicsSingle correct
If the Boolean expression (p⊕q)∧(∼p⊖q)(p\oplus q)\wedge(\sim p\ominus q)(p⊕q)∧(∼p⊖q) is equivalent to p∧qp\wedge qp∧q, where ⊕,⊖∈{∧,∨}\oplus,\ominus\in\{\wedge,\vee\}⊕,⊖∈{∧,∨}, then the ordered pair (⊕,⊖)(\oplus,\ominus)(⊕,⊖) is :
  1. (A)(∨,∧)(\vee,\wedge)(∨,∧)
  2. (B)(∨,∨)(\vee,\vee)(∨,∨)
  3. (C)(∧,∨)(\wedge,\vee)(∧,∨)
  4. (D)(∧,∧)(\wedge,\wedge)(∧,∧)

Correct answer: (C)

Step-by-step solution →
Q76·MathematicsSingle correct
5 students of a class have an average height 150 cm and variance 18 cm2cm^{2}cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2cm^{2}cm2) of the height of these six students is:
  1. (A)16
  2. (B)22
  3. (C)20
  4. (D)18

Correct answer: (C)

Step-by-step solution →
Q77·MathematicsSingle correct
For any θ∈(π4,π2)\theta\in\left(\dfrac{\pi}{4},\dfrac{\pi}{2}\right)θ∈(4π​,2π​), the expression 3(sin⁡θ−cos⁡θ)4+6(sin⁡θ+cos⁡θ)2+4sin⁡6θ3(\sin\theta-\cos\theta)^{4}+6(\sin\theta+\cos\theta)^{2}+4\sin^{6}\theta3(sinθ−cosθ)4+6(sinθ+cosθ)2+4sin6θ equals:
  1. (A)13−4cos⁡2θ+6sin⁡2θcos⁡2θ13-4\cos^{2}\theta+6\sin^{2}\theta\cos^{2}\theta13−4cos2θ+6sin2θcos2θ
  2. (B)13−4cos⁡6θ13-4\cos^{6}\theta13−4cos6θ
  3. (C)13−4cos⁡2θ+6cos⁡4θ13-4\cos^{2}\theta+6\cos^{4}\theta13−4cos2θ+6cos4θ
  4. (D)13−4cos⁡4θ+2sin⁡2θcos⁡2θ13-4\cos^{4}\theta+2\sin^{2}\theta\cos^{2}\theta13−4cos4θ+2sin2θcos2θ

Correct answer: (B)

Step-by-step solution →
Q78·MathematicsSingle correct
The area (in sq. units) bounded by the parabola y=x2−1y=x^{2}-1y=x2−1, the tangent at the point (2, 3) to it and the y – axis is:
  1. (A)83\dfrac{8}{3}38​
  2. (B)323\dfrac{32}{3}332​
  3. (C)533\dfrac{53}{3}353​
  4. (D)143\dfrac{14}{3}314​

Correct answer: (A)

Step-by-step solution →
Q79·MathematicsSingle correct
Let f:R→Rf:R \rightarrow Rf:R→R be a function defined as f(x)={5,if x≤1a+bx,if 1<x<3b+5x,if 3≤x<530,if x≥5f(x)=\begin{cases} 5, & \text{if } x \le 1 \\ a+bx, & \text{if } 1 < x < 3 \\ b+5x, & \text{if } 3 \le x < 5 \\ 30, & \text{if } x \ge 5 \end{cases}f(x)=⎩⎨⎧​5,a+bx,b+5x,30,​if x≤1if 1<x<3if 3≤x<5if x≥5​. Then fff is:
  1. (A)continuous if a=5a = 5a=5 and b=5b = 5b=5
  2. (B)continuous if a=5a = 5a=5 and b=10b = 10b=10
  3. (C)continuous if a=0a = 0a=0 and b=5b = 5b=5
  4. (D)not continuous for any values of aaa and bbb

Correct answer: (D)

Step-by-step solution →
Q80·MathematicsSingle correct
Let A={θ∈(−π2,π):3+2isin⁡θ1−2isin⁡θ purely imaginary}A=\left\{\theta\in\left(-\dfrac{\pi}{2},\pi\right):\dfrac{3+2i\sin\theta}{1-2i\sin\theta}\ \text{purely imaginary}\right\}A={θ∈(−2π​,π):1−2isinθ3+2isinθ​ purely imaginary}. Then the sum of the elements in A is:
  1. (A)5π6\dfrac{5\pi}{6}65π​
  2. (B)π\piπ
  3. (C)3π4\dfrac{3\pi}{4}43π​
  4. (D)2π3\dfrac{2\pi}{3}32π​

Correct answer: (D)

Step-by-step solution →
Q81·MathematicsSingle correct
Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:
  1. (A)500
  2. (B)200
  3. (C)300
  4. (D)350

Correct answer: (C)

Step-by-step solution →
Q82·MathematicsSingle correct
Let α\alphaα and β\betaβ be two roots of the equation x2+2x+2=0x^{2}+2x+2=0x2+2x+2=0, then α15+β15\alpha^{15}+\beta^{15}α15+β15 is equal to:
  1. (A)−256-256−256
  2. (B)512512512
  3. (C)−512-512−512
  4. (D)256256256

Correct answer: (A)

Step-by-step solution →
Q83·MathematicsSingle correct
Three circles of radii a, b, c ( a < b < c ) touch each other externally. If they have x – axis as a common tangent, then:
  1. (A)1a=1b+1c\dfrac{1}{\sqrt{a}}=\dfrac{1}{\sqrt{b}}+\dfrac{1}{\sqrt{c}}a​1​=b​1​+c​1​
  2. (B)1b=1a+1c\dfrac{1}{\sqrt{b}}=\dfrac{1}{\sqrt{a}}+\dfrac{1}{\sqrt{c}}b​1​=a​1​+c​1​
  3. (C)a, b, c are in A.P.
  4. (D)a,b,c\sqrt{a},\sqrt{b},\sqrt{c}a​,b​,c​ are in A.P.

Correct answer: (A)

Step-by-step solution →
Q84·MathematicsSingle correct
Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X=1)+P(X=2)P(X=1)+P(X=2)P(X=1)+P(X=2) equals:
  1. (A)49169\dfrac{49}{169}16949​
  2. (B)52169\dfrac{52}{169}16952​
  3. (C)24169\dfrac{24}{169}16924​
  4. (D)25169\dfrac{25}{169}16925​

Correct answer: (D)

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • p-Block Elements 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • 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
  • Limits and Continuity 149/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Laws of Motion 130/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Oscillations 117/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Parabola 101/186
  • Statistics 118/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Electronic Effects and Stability 74/186
  • Hyperbola 77/186
  • Experimental Skills 68/186
  • Indefinite Integration 66/186
  • Polymers 64/186
  • Carboxylic Acids and Derivatives 54/186
  • Solid State 63/186
  • Chemistry in Everyday Life 60/186
  • States of Matter: Gases and Liquids 52/186
  • Magnetism and Matter 50/186
  • Reaction Mechanism 29/186
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