JEE Main 2021 Feb 24 Shift 2 Question Paper with Solution PDF- Download Here

Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A²B² - B²A²) X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has :

• (1) no solution
  
• (2) a unique solution
  
• (3) exactly two solutions
  
• (4) infinitely many solutions

The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where \( [x] \) denotes the greatest integer less than or equal to \( x \), is:

• (1) \(-\sqrt{2}-\sqrt{3}+1\)
• (2) \(-\sqrt{2}-\sqrt{3}-1\)
• (3) -5
• (4) -4

Let a, b ∈ R. If the mirror image of the point P(a, 6, 9) with respect to the line (x-3)/7 = (y-2)/5 = (z-1)/(-9) is (20, b, -a - 9), then |a + b| is equal to :

• (1) 84
  
• (2) 86
  
• (3) 88
  
• (4) 90

For the system of linear equations : x - 2y = 1, x - y + kz = -2, ky + 4z = 6, k ∈ ℝ, consider the following statements : (A) Unique solution if k ≠ 2, k ≠ -2. (B) Unique solution if k = -2. (C) Unique solution if k = 2. (D) No-solution if k = 2. (E) Infinite solutions if k ≠ -2. Which of the following statements are correct ?

• (1) (A) and (D) only
  
• (2) (A) and (E) only
  
• (3) (C) and (D) only
  
• (4) (B) and (E) only

Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2-x) for all x ∈ (0, 2), f(0) = 1 and f(2) = e². Then the value of ∫ from 0 to 2 f(x) dx is :

• (1) 1 - e²
  
• (2) 1 + e²
  
• (3) 2(1 + e²)
  
• (4) 2(1 - e²)

Let f be a twice differentiable function defined on ℝ such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x ∈ ℝ. If \(| f(x) \ f'(x) | \ | f'(x) \ f''(x) | = 0\), then the value of f(1) lies in the interval :

• (1) (0, 3)
  
• (2) (3, 6)
  
• (3) (6, 9)
  
• (4) (9, 12)

Let f(x) = -55x (x<-5), 2x³ - 3x² - 120x (-5 ≤ x ≤ 4), 2x³ - 3x² - 36x - 336 (x>4). Let A = {x ∈ ℝ : f is increasing}. Then A is equal to :

• (1) (-∞, -5) ∪ (4, ∞)
  
• (2) (-5, -4) ∪ (4, ∞)
  
• (3) (-∞, -5) ∪ (-4, ∞)
  
• (4) (-5, ∞)

If \(P\) is a point on the parabola \(y=x^{2}+4\) which is closest to the straight line \(y =4 x -1\), then the co-ordinates of \(P\) are

• (1) (3,13)
• (2) (1,5)
• (3) (-2,8)
• (4) (2,8)

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

• (1) 65 / 2\^7
  
• (2) 65 / 2\^8
  
• (3) 135 / 2\^9
  
• (4) 35 / 2\^7

A possible value of \( \tan\!\left(\frac{1}{4}\sin^{-1}\!\left(\frac{\sqrt{63}}{8}\right)\right) \) is :

• (1) 1/√7
  
• (2) 1/2√2
  
• (3) √7 - 1
  
• (4) 2√2 - 1

The area of the region : R = {(x, y) : 5x² ≤ y ≤ 2x² + 9} is :

• (1) 6√3
  
• (2) 9√3
  
• (3) 11√3
  
• (4) 12√3

If n ≥ 2 is a positive integer, then the sum of the series \(^{n+1}C_2 + 2( ^2C_2 + ^3C_2 + ^4C_2 + ....... + ^nC_2 )\) is :

• (1) n(n-1)(2n+1)/6
  
• (2) n(n+1)(2n+1)/6
  
• (3) n(2n+1)(3n+1)/6
  
• (4) n(n+1)\^2(n+2)/12

Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (10/3, 7/3). If α, β are the roots of the equation ax² + bx + 1 = 0, then the value of α² + β² - αβ is :

• (1) 69/256
  
• (2) 71/256
  
• (3) 69/256
  
• (4) 71/256

If the curve \(y=a x^{2}+b x+c, x \in R,\) passes through the point (1,2) and the tangent line to this curve at origin is \(y = x ,\) then the possible values of \(a , b , c\) are :

• (1) \(a =\frac{1}{2}, b =\frac{1}{2}, c =1\)
• (2) \(a =1, b =0, c =1\)
• (3) \(a =1, b =1, c =0\)
• (4) \(a=-1, b=1, c=1\)

If \( y = f(x) \) passes through \( (1, 2) \) and \( x \frac{dy}{dx} + y = b x^4 \), then for what value of \( b \), \( \displaystyle \int_{1}^{2} f(x)\,dx = \frac{62}{5} \) ?

• (1) 10
  
• (2) 31/5
  
• (3) 5
  
• (4) 62/5

For which of the following curves, the line x + √3 y = 2√3 is the tangent at the point (3√3 / 2, 1/2) ?

• (1) x² + y² = 7
  
• (2) y² = (1 / 6√3) x
  
• (3) 2x² - 18y² = 9
  
• (4) x² + 9y² = 9

For p and q, consider: (a) (~ q ∧ (p → q)) → ~ p, (b) ((p ∨ q) ∧ ~ p) → q. Which is correct ?

• (1) (a) is a tautology but not (b).
  
• (2) (b) is a tautology but not (a).
  
• (3) (a) and (b) both are tautologies.
  
• (4) (a) and (b) both are not tautologies.

The angle of elevation of a jet plane from a point A on the ground is \(60^{\circ}\). After a flight of 20 seconds at the speed of \(432 km /\) hour, the angle of elevation changes to \(30^{\circ} .\) If the jet plane is flying at a constant height, then its height is :

• (1) \(1800 \sqrt{3} m\)
• (2) \(3600 \sqrt{3} m\)
• (3) \(2400 \sqrt{3} m\)
• (4) \(1200 \sqrt{3} m\)

The negation of the statement ~p ∧ (p ∨ q) is :

• (1) ~ P ∨ q
  
• (2) ~ P ∧ q
  
• (3) P ∧ ~ q
  
• (4) P ∨ ~ q

The vector equation of the plane passing through the intersection of the planes \(\vec{ r } .(\hat{ i }+\hat{ j }+\hat{ k })=1\) and \(\vec{ r } .(\hat{ i }-2 \hat{ j })=-2,\) and the point (1,0,2) is :

• (1) \(\vec{ r } .(\hat{ i }+7 \hat{ j }+3 \hat{ k })=\frac{7}{3}\)
• (2) \(\vec{ r } \cdot(3 \hat{ i }+7 \hat{ j }+3 \hat{ k })=7\)
• (3) \(\vec{ r } \cdot(\hat{ i }+7 \hat{ j }+3 \hat{ k })=7\)
• (4) \(\vec{ r } .(\hat{ i }-7 \hat{ j }+3 \hat{ k })=\frac{7}{3}\)

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________

If the variance of 10 natural numbers 1, 1, 1, ......., 1, k is less than 10, then the maximum possible value of k is ______

If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______

If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________

Let i = √-1. If \(\frac{(-1 + i\sqrt{3})^{21}}{(1 - i)^{24}} + \frac{(1 + i\sqrt{3})^{21}}{(1 + i)^{24}} = k\), and \(n = \lfloor |k| \rfloor\). Then \(\sum_{j=0}^{n+5} (j + 5)^2 - \sum_{j=0}^{n+5} (j + 5)\) is equal to __________.

The number of the real roots of the equation \( (x+1)^2 + |x-5| = \dfrac{27}{4} \) is _______

The students S1, S2, ......., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _________

The sum of first 4 terms of a G.P. is 65/12 and sum of their reciprocals is 65/18. If product of first 3 terms is 1 and the 3rd term is α, then 2α is _________

If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle \( (x-2)^2 + (y-3)^2 = 25 \) at the point \( (5, 7) \) is \( A \), then \( 24A \) is equal to _______

The maximum value of k for which the sum \(\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}\) exists, is equal to __________.

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. If each spring has spring constant k, the frequency of oscillation of given body is : 

• (1) \(\frac{1}{2\pi} \sqrt{\frac{k}{Mg \sin \alpha}}\)
  
• (2) \(\frac{1}{2\pi} \sqrt{\frac{2k}{Mg \sin \alpha}}\)
  
• (3) \(\frac{1}{2\pi} \sqrt{\frac{2k}{M}}\)
  
• (4) \(\frac{1}{2\pi} \sqrt{\frac{k}{2M}}\)

If the source of light used in a Young's double slit experiment is changed from red to violet :

• (1) the fringes will become brighter.
  
• (2) consecutive fringe lines will come closer.
  
• (3) the intensity of minima will increase.
  
• (4) the central bright fringe will become a dark fringe.

The logic circuit shown above is equivalent to : 

• (1) A
• (2) B
• (3) C
• (4) D

Figure shows a circuit that contains four identical resistors with resistance R=2.0 Ω, two identical inductors with inductance L=2.0 mH and an ideal battery with emf E=9 V. The current 'i' just after the switch 'S' is closed will be : 

• (1) 2.25 A
  
• (2) 3.0 A
  
• (3) 3.37 A
  
• (4) 9 A

A particle is projected with velocity \(v_0\) along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. \(ma = -ax^2\). The distance at which the particle stops :

• (1) \(\left(\frac{2v_0^2}{3a}\right)^{1/2}\)
  
• (2) \(\left(\frac{3v_0^2}{2a}\right)^{1/2}\)
  
• (3) \(\left(\frac{3v_0^2}{2a}\right)^{1/3}\)
  
• (4) \(\left(\frac{2v_0^2}{3a}\right)^{1/3}\)

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

• (1) \(10^{-1}\) nm
  
• (2) \(10^{-2}\) nm
  
• (3) \(10^{-3}\) nm
  
• (4) \(10^{-4}\) nm

If one mole of an ideal gas at \((P_1, V_1)\) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure. This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B → C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to :

• (1) RT ln 2 - \(\frac{1}{2(\gamma - 1)}\)
  
• (2) \(-\frac{RT}{2(\gamma - 1)}\)
  
• (3) RT ln 2
  
• (4) 0

A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use \(g = \frac{GM}{R^2} = 9.8 \text{ ms}^{-2}\) and radius of earth, \(R = 6400 \text{ km}\).]

• (1) 49.17 N
  
• (2) 49 N
  
• (3) 48.83 N
  
• (4) 49.83 N

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

• (1) circular
  
• (2) elliptical
  
• (3) parabolic
  
• (4) straight line

The period of oscillation of a simple pendulum is \(T = 2\pi \sqrt{\frac{L}{g}}\). Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :

• (1) 1.33 %
  
• (2) 1.03 %
  
• (3) 1.13 %
  
• (4) 1.30 %

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

• (1) increase in size but no change in orientation.
  
• (2) decrease in size and changes orientation.
  
• (3) may increase or decrease in size and change its orientation.
  
• (4) have no relation with external magnetic field.

Which of the following equations represents a travelling wave ?

• (1) \(y = Ae^{k\cos(\omega t - \theta)}\)
  
• (2) \(y = Ae^{-x^2} (vt + \theta)\)
  
• (3) \(y = A\sin(15x - 2t)\)
  
• (4) \(y = A\sin x \cos \omega t\)

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)

• (1) \(\left( \frac{q^2}{2\pi \varepsilon_0 md^3} \right)^{\frac{1}{2}}\)
  
• (2) \(\left( \frac{2q^2}{\pi \varepsilon_0 md^3} \right)^{\frac{1}{2}}\)
  
• (3) \(\left( \frac{\pi \varepsilon_0 md^3}{2q^2} \right)^{\frac{1}{2}}\)
  
• (4) \(\left( \frac{2\pi \varepsilon_0 md^3}{q^2} \right)^{\frac{1}{2}}\)

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

• (1) continuously lose their energy till it reaches wall.
  
• (2) continuously stick to the walls of container.
  
• (3) are attracted by the walls of container.
  
• (4) suffer change in momentum when impinge on the walls of container.

• (1) (a)-(vi), (b)-(v), (c)-(i), (d)-(iv)
• (2) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
• (3) (a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)
• (4) (a)-(vi), (b)-(iv), (c)-(i), (d)-(v)

A circular hole of radius \(\left(\frac{a}{2}\right)\) is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be : 

• (1) \(\frac{1}{6}a\)
  
• (2) \(\frac{5}{6}a\)
  
• (3) \(\frac{2}{3}a\)
  
• (4) \(\frac{10}{11}a\)

Zener breakdown occurs in a p-n junction having p and n both :

• (1) lightly doped and have narrow depletion layer.
  
• (2) lightly doped and have wide depletion layer.
  
• (3) heavily doped and have narrow depletion layer.
  
• (4) heavily doped and have wide depletion layer.

The de Broglie wavelength of a proton and α-particle are equal. The ratio of their velocities is :

• (1) 4 : 1
  
• (2) 4 : 2
  
• (3) 4 : 3
  
• (4) 1 : 4

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

• (1) n = 2 to n = 1
  
• (2) n = 3 to n = 2
  
• (3) n = 4 to n = 3
  
• (4) n = 5 to n = 4

Given below are two statements : Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement II : In the study of transistor, the amplification factor β indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer.

• (1) Both Statement I and Statement II are true
  
• (2) Both Statement I and Statement II are false
  
• (3) Statement I is true but Statement II is false
  
• (4) Statement I is false but Statement II is true

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ________ × 10⁻² cm.

A cylindrical wire of radius 0.5 mm and conductivity \(5 \times 10^7\) S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be \(x^3 \pi\) mA. The value of \(x\) is ______.

Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be A/1, so the value of A will be ______

The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 m s⁻¹. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is \( \dfrac{x}{\sqrt{3}} \) m s⁻¹. The value of \( x \) will be __________.

A series LCR circuit is designed to resonate at an angular frequency \( \omega_0 = 10^5 \) rad/s. The circuit draws 16 W power from a 120 V source at resonance. The value of resistance \( R \) in the circuit is _____ Ω.

A point charge of +12 µC is at a distance 6 cm vertically above the centre of a square of side 12 cm. The magnitude of the electric flux through the square will be ________ × 10³ Nm²/C. 

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is __________ x 10\^{-1} kg m².

A signal of 0.1 kW is transmitted in a cable. The attenuation of the cable is −5 dB per km and the cable length is 20 km. The power received at the receiver is \(10^{-x}\) W. The value of \(x\) is __________.

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m/s.]

The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is : (Note: The compounds are chloro benzene with different nitro positions: (i) Chlorobenzene, (ii) 4-nitrochlorobenzene, (iii) 2,4-dinitrochlorobenzene, (iv) 2,4,6-trinitrochlorobenzene)

• (1) \((iv)<(iii)<(ii)<(i)\)
  
• (2) \((iv)<(i)<(iii)<(ii)\)
  
• (3) \((i)<(ii)<(iii)<(iv)\)
  
• (4) \((iv)<(i)<(ii)<(iii)\)

The incorrect statement among the following is :

• (1) VOSO₄ is a reducing agent
  
• (2) RuO₄ is an oxidizing agent
  
• (3) Cr₂O₃ is an amphoteric oxide
  
• (4) Red colour of ruby is due to the presence of Co³⁺

Which one of the following compounds is non-aromatic ? 

• (1) A
• (2) B
• (3) C
• (4) D

According to Bohr's atomic theory :- (A) Kinetic energy of electron is \(\propto \frac{ Z ^{2}}{ n ^{2}}\). (B) The product of velocity (v) of electron and principal quantum number (n), 'vn' \(\propto Z ^{2}\). (C) Frequency of revolution of electron in an orbit is \(\propto \frac{ Z ^{3}}{ n ^{3}}\). (D) Coulombic force of attraction on the electron is \(\propto \frac{ Z ^{3}}{ n ^{4}}\). Choose the most appropriate answer from the options given below:

• (1) (C) Only
• (2) (A) Only
• (3) (A), (C) and (D) only
• (4) (A) and (D) only

Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of HgSO₄ and H₂SO₄ ?

• (1) Formaldehyde
  
• (2) Acetaldehyde
  
• (3) Propanal
  
• (4) 2-Butanone

The correct set from the following in which both pairs are in correct order of melting point is :

• (1) LiCl>LiF ; MgO>NaCl
  
• (2) LiF>LiCl ; MgO>NaCl
  
• (3) LiCl>LiF ; NaCl>MgO
  
• (4) LiF>LiCl ; NaCl>MgO

What is the correct sequence of reagents used for converting nitrobenzene into m-dibromobenzene ? 

• (1) Sn/HCl / KBr / Br2 / H+
  
• (2) NaNO2 / HCl / KBr / H+
  
• (3) Sn/HCl / NaNO2/HCl / CuBr/HBr
  
• (4) Br2/Fe / Sn/HCl / NaNO2/HCl / CuBr/HBr

The calculated magnetic moments (spin only value) for species \([FeCl_4]^{2-}\), \([Co(C_2O_4)_3]^{3-}\) and \(MnO_4^{2-}\) respectively are :

• (1) 4.90, 0 and 1.73 BM
  
• (2) 5.92, 4.90 and 0 BM
  
• (3) 5.82, 0 and 0 BM
  
• (4) 4.90, 0 and 2.83 BM

Which of the following reagent is suitable for the preparation of the product in the above reaction ? (reaction of ketone to alkane)

• (1) NaBH4
  
• (2) NH2-NH2/C2H5ONa
  
• (3) Ni/H2
  
• (4) Red P + Cl2

What is the correct order of the following elements with respect to their density ?

• (1) Cr<Fe<Co<Cu<Zn
  
• (2) Zn<Cr<Fe<Co<Cu
  
• (3) Zn<Cu<Co<Fe<Cr
  
• (4) Cr<Zn<Co<Cu<Fe

Match List - I and List - II. List - I: (a) Valium, (b) Morphine, (c) Norethindrone, (d) Vitamin B12 List - II: (i) Antifertility drug, (ii) Pernicious anaemia, (iii) Analgesic, (iv) Tranquilizer

• (1) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
  
• (2) (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
  
• (3) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
  
• (4) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

The correct shape and I-I-I bond angles respectively in \(I_3^-\) ion are :

• (1) Linear; 180°
  
• (2) Distorted trigonal planar; 135° and 90°
  
• (3) T-shaped; 180° and 90°
  
• (4) Trigonal planar; 120°

The diazonium salt of which of the following compounds will form a coloured dye on reaction with β-Naphthol in NaOH ? 

• (1) A
• (2) B
• (3) C
• (4) D

• (1) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
• (2) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
• (3) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
• (4) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

• (1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
• (2) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
• (3) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
• (4) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

Given below are two statements : Statement I : The value of the parameter “Biochemical Oxygen Demand (BOD)” is important for survival of aquatic life. Statement II : The optimum value of BOD is 6.5 ppm. In the light of the above statements, choose the most appropriate answer from the options given below :

• (1) Both Statement I and Statement II are true
  
• (2) Both Statement I and Statement II are false
  
• (3) Statement I is true but Statement II is false
  
• (4) Statement I is false but Statement II is true

In polymer Buna-S : 'S' stands for :

• (1) Sulphur
  
• (2) Strength
  
• (3) Styrene
  
• (4) Sulphonation

Most suitable salt which can be used for efficient clotting of blood will be :

• (1) NaHCO₃
  
• (2) Mg(HCO₃)₂
  
• (3) FeCl₃
  
• (4) FeSO₄

Assertion A : Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the troposphere. Reason R : Hydrogen is the lightest element.

• (1) Both A and R are true and R is the correct explanation of A
  
• (2) Both A and R are true but R is NOT the correct explanation of A
  
• (3) A is true but R is false
  
• (4) A is false but R is true

• (1) (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
• (2) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
• (3) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
• (4) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

The formula of a gaseous hydrocarbon which requires 6 times of its own volume of O2 for complete oxidation and produces 4 times its own volume of CO2 is CxHy. The value of y is _________

The solubility product of PbI₂ is \( 8.0 \times 10^{-9} \). The solubility of lead iodide in 0.1 molar solution of lead nitrate is \( x \times 10^{-6} \) mol/L. The value of \( x \) is __________. (Rounded off to the nearest integer) [Given \( \sqrt{2} = 1.41 \)]

1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is _________ × 10⁻².

Assuming ideal behaviour, the magnitude of log K for the following reaction at 25 °C is \( x \times 10^{-1} \). The value of \( x \) is __________ . (Integer answer) \( 3\,\text{HC}\equiv\text{CH (g)} \rightleftharpoons \text{C}_6\text{H}_6 \text{ (l)} \) [Given : \( \Delta_f G^\circ (\text{HC}\equiv\text{CH}) = -2.04 \times 10^5 \,\text{J mol}^{-1} \); \( \Delta_f G^\circ (\text{C}_6\text{H}_6) = -1.24 \times 10^5 \,\text{J mol}^{-1} \); \( R = 8.314 \,\text{J K}^{-1} \text{ mol}^{-1} \)]

C6H6 freezes at 5.5°C. The temperature at which a solution of 10 g of C4H10 in 200 g of C6H6 freeze is ________ °C. (The molal freezing point depression constant of C6H6 is 5.12°C/m.)

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25 °C. After 9 h, the fraction of sucrose remaining is \( f \). The value of \( \log_{10}(1/f) \) is _______ × 10⁻². (Rounded off to the nearest integer)

The magnitude of the change in oxidising power of the MnO₄⁻ / Mn²⁺ couple is \( x \times 10^{-4} \) V, if the H⁺ concentration is decreased from 1 M to \( 10^{-4} \) M at 25 °C. (Assume concentration of MnO₄⁻ and Mn²⁺ to be same on change in H⁺ concentration). The value of \( x \) is __________ .

The total number of amines among the following which can be synthesized by Gabriel synthesis is _________. (A) ethylamine, (B) n-propylamine, (C) benzylamine, (D) aniline

The volume occupied by 4.75 g of acetylene gas at 50 °C and 740 mmHg pressure is _______ L. (Rounded off to the nearest integer) [Given \( R = 0.0826 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)]

Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is __________