JEE Main 2021 March 18 Shift 1 Question Paper with Solution PDF- Download Here

Question 1:

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

• (1) 0
  
• (2) 1
  
• (3) 2
  
• (4) 3

Question 2:

The solutions of the equation \(\begin{vmatrix} 1 + \sin^2 x & \sin^2 x & \sin^2 x \\ \cos^2 x & 1 + \cos^2 x & \cos^2 x \\ 4\sin 2x & 4\sin 2x & 1 + 4\sin 2x \end{vmatrix} = 0\), \((0 \lt x \lt \pi)\), are

• (1) \(\frac{\pi}{12}, \frac{\pi}{6}\)
• (2) \(\frac{\pi}{6}, \frac{5\pi}{6}\)
• (3) \(\frac{5\pi}{12}, \frac{7\pi}{12}\)
• (4) \(\frac{7\pi}{12}, \frac{11\pi}{12}\)

Question 3:

Let α, β, γ be the real roots of the equation, x³ + a x² + b x + c = 0, (a, b, c ∈ R and a, b ≠ 0). If the system of equations (in u, v, w) given by α u + β v + γ w = 0; β u + γ v + α w = 0; γ u + α v + β w = 0 has non-trivial solution, then the value of a²/b is :

• (1) 0
  
• (2) 1
  
• (3) 3
  
• (4) 5

Question 4:

The integral ∫ (2x - 1) cos√((2x - 1)² + 5) / √(4x² - 4x + 6) dx is equal to : (where c is a constant of integration)

• (1) (1/2) sin√((2x + 1)² + 5) + c
  
• (2) (1/2) sin√((2x - 1)² + 5) + c
  
• (3) (1/2) cos√((2x - 1)² + 5) + c
  
• (4) (1/2) cos√((2x + 1)² + 5) + c

Question 5:

The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁻¹(√2) with the straight line, y + 1 = 3√2 x is :

• (1) 4√2 x + 5y - (15 + 4√2) = 0
  
• (2) 4√2 x - 5y - (5 + 4√2) = 0
  
• (3) 5√2 x + 4y - (15 + 4√2) = 0
  
• (4) 4√2 x + 5y - 4√2 = 0

Question 6:

If \( \lim_{x \to 0} \dfrac{\sin^{-1} x - \tan^{-1} x}{3x^3} \) is equal to \( L \), then the value of \( (6L + 1) \) is :

• (1) 1/6
  
• (2) 6
  
• (3) 2
  
• (4) 1/2

Question 7:

Rotation of axes: Vector ā (3p, 1) becomes (p+1, √10) in new system. Find p.

• (1) 1
  
• (2) -1
  
• (3) 4/5
  
• (4) -5/4

Question 8:

If the equation a|z|² + āz + a z̄ + d = 0 represents a circle where a, d are real constants, then which of the following condition is correct ?

• (1) |a|² - a d ≥ 0 and a ∈ R
  
• (2) |a|² - a d>0 and a ∈ R - {0}
  
• (3) |a|² - a d ≠ 0
  
• (4) α = 0, a, d ∈ R⁺

Question 9:

For the four circles M, N, O and P, following four equations are given :
Circle M : \(x^2 + y^2 = 1\)
Circle N : \(x^2 + y^2 - 2x = 0\)
Circle O : \(x^2 + y^2 - 2x - 2y + 1 = 0\)
Circle P : \(x^2 + y^2 - 2y = 0\)
If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :

• (1) Rhombus
• (2) Square
• (3) Rectangle
• (4) Parallelogram

Question 10:

The real valued function f(x) = csc⁻¹x / √(x - [x]), where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :

• (1) all reals except integers
  
• (2) all reals except the interval [-1, 1]
  
• (3) all non-integers except the interval (-1, 1)
  
• (4) all integers except 0, -1, 1

Question 11:

If the functions are defined as f(x) = √x and g(x) = √(1-x), then what is the common domain of the following functions : f+g, f-g, f/g, g/f, g-f where (f ± g)(x) = f(x) ± g(x), (f/g)(x) = f(x)/g(x)

• (1) 0 ≤ x<1
  
• (2) 0<x<1
  
• (3) 0 ≤ x ≤ 1
  
• (4) 0<x ≤ 1

Question 12:

If f(x) = { 1/|x| if |x| ≥ 1 ; a x² + b if |x| \(< 1\) } is differentiable at every point of the domain, then the values of a and b are respectively :

• (1) 1/2, 1/2
  
• (2) -1/2, 3/2
  
• (3) 5/2, -3/2
  
• (4) 1/2, -3/2

Question 13:

Let A + 2B = [1 2 0; 6 -3 3; -5 3 1] and 2A - B = [2 -1 5; 2 -1 6; 0 1 2]. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) - Tr(B) has value equal to :

• (1) 1
  
• (2) 2
  
• (3) 3
  
• (4) 0

Question 14:

The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :

• (1) 22264
  
• (2) 26664
  
• (3) 122234
  
• (4) 122664

Question 15:

The value of 3 + 1/(4 + 1/(3 + 1/(4 + 1/(3 + ⋯ ∞))) is equal to :

• (1) 1.5 + √3
  
• (2) 2 + √3
  
• (3) 3 + 2√3
  
• (4) 4 + √3

Question 16:

The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :

• (1) y (dy/dx)² + 2x (dy/dx) - y = 0
  
• (2) y (dy/dx)² - 2x (dy/dx) + y = 0
  
• (3) y (dy/dx)² - 2x (dy/dx) - y = 0
  
• (4) y (dy/dx)² - 2x (dy/dx) = 0

Question 17:

1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ⋯ + 1/(201)² - 1 is equal to :

• (1) 25/101
  
• (2) 101/408
  
• (3) 99/400
  
• (4) 101/404

Question 18:

Let (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² + ⋯ + a₄₀x⁴⁰. Then, a₁ + a₃ + a₅ + ⋯ + a₃₇ is equal to :

• (1) 2¹⁹(2²⁰ + 21)
  
• (2) 2²⁰(2²⁰ + 21)
  
• (3) 2¹⁹(2²⁰ - 21)
  
• (4) 2²⁰(2²⁰ - 21)

Question 19:

If α, β are natural numbers such that 100\(^α - 199 β = (100)(100) + (99)(101) + (98)(102) + ⋯ + (1)(199)\), then the slope of the line passing through (α, β) and origin is :

• (1) 510
  
• (2) 530
  
• (3) 540
  
• (4) 550

Question 20:

Choose the correct statement about two circles whose equations are given below : x² + y² - 10x - 10y + 41 = 0 ; x² + y² - 22x - 10y + 137 = 0

• (1) circles have two meeting points
  
• (2) circles have no meeting point
  
• (3) circles have only one meeting point
  
• (4) circles have same centre

Question 21:

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is __________.

Question 22:

Let f(x) and g(x) be two functions satisfying f(x²) + g(4-x) = 4x³ and g(4-x) + g(x) = 0, then the value of ∫\(_{-4}^{4}\) f(x²) dx is __________.

Question 23:

Find the missing value in the logic/series figure provided in the question. 

Question 24:

Let z₁, z₂ be the roots of the equation z² + a z + 12 = 0 and z₁, z₂ form an equilateral triangle with origin. Then, the value of |a| is ________.

Question 25:

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is __________.

Question 26:

If f(x) = ∫\(_{x}^{1}\) (5x⁸ + 7x⁶)/(x² + 1 + 2x⁷)² dx, (x ≥ 0), f(0) = 0 and f(1) = 1/K, then the value of K is __________.

Question 27:

A square ABCD has all its vertices on the curve x²y² = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is __________.

Question 28:

The number of solutions of the equation |cot x| = cot x + 1/sin x in the interval [0, 2π] is __________.

Question 29:

The equation of the planes parallel to the plane x - 2y + 2z - 3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b - d) = K(c - a), then the positive value of K is __________.

Question 30:

Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, -3, 1) and (2, 3, -5) at the right angles. If a, b, c, d are integers, then the minimum value of (a² + b² + c² + d²) is __________.

Question 31:

An oil drop of radius 2 mm with a density 3 g cm⁻³ is held stationary under a constant electric field 3.55 × 10⁵ V m⁻¹ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? Consider g = 9.81 m/s²

• (1) 17.3 × 10¹⁰
  
• (2) 1.73 × 10¹⁰
  
• (3) 1.73 × 10¹²
  
• (4) 48.8 × 10¹¹

Question 32:

Imagine that the electron in a hydrogen atom is replaced by a muon (μ). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :

• (1) 13.6 eV
  
• (2) 27.2 eV
  
• (3) 331.2 eV
  
• (4) 2815.2 eV

Question 33:

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, \( \mathbf{B} = 2.0 \times 10^{-8}\,\hat{k}\,\text{T} \). What is \( \mathbf{E} \) at this point? ( \( c = 3 \times 10^8 \,\text{m/s} \) )

• (1) 0.6 ĵ V/m
  
• (2) 6.0 ĵ V/m
  
• (3) 6.0 k̂ V/m
  
• (4) 0.6 k̂ V/m

Question 34:

A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :

• (1) M / (M + m)
  
• (2) M / (M + 2m)
  
• (3) (M - 2m) / (M + 2m)
  
• (4) (M + 2m) / M

Question 35:

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3 T, the field at the center of C would be : (Assume that the magnetic field is confined within the volume of respective solenoid).

• (1) 1 T
  
• (2) 9 T
  
• (3) 6 T
  
• (4) 12 T

Question 36:

The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use γ = 1.4) : 

• (1) 400 J
  
• (2) -500 J
  
• (3) 200 J
  
• (4) -400 J

Question 37:

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 Å is :

• (1) 1178 × 10⁻¹² m
  
• (2) 5890 × 10⁻⁷ m
  
• (3) 1178 × 10⁻⁹ m
  
• (4) 1178 × 10⁻⁶ m

Question 38:

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

• (1) 8 times the mass of e⁻
  
• (2) 1/16 times the mass of e⁻
  
• (3) 16 times the mass of e⁻
  
• (4) 1/8 times the mass of e⁻

Question 39:

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by : 

• (1) A
• (2) B
• (3) C
• (4) D

Question 40:

In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is :

• (1) 3.9
  
• (2) 7.5
  
• (3) 8.4
  
• (4) 3.0

Question 41:

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

• (1) The resonance frequency will increase
  
• (2) The bandwidth of resonance circuit will increase
  
• (3) The quality factor will increase
  
• (4) The quality factor and the resonance frequency will remain constant

Question 42:

An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

• (1) 2.5 ms
  
• (2) 25 ms
  
• (3) 0.25 ms
  
• (4) 2.5 s

Question 43:

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :

• (1) Myopia and hypermetropia
  
• (2) Presbyopia with Astigmatism
  
• (3) Astigmatism
  
• (4) Myopia with Astigmatism

Question 44:

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

• (1) shape of the loop remains unchanged
  
• (2) loop assumes circular shape with its plane normal to the field
  
• (3) loop assumes circular shape with its plane parallel to the field
  
• (4) wire gets stretched to become straight

Question 45:

The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :

• (1) 3 T
  
• (2) 9 T
  
• (3) 27 T
  
• (4) 12 T

Question 46:

The time period of a simple pendulum is given by T = 2π √(l/g). The measured value of the length of pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is :

• (1) 2
  
• (2) 3
  
• (3) 4
  
• (4) 5

Question 47:

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :

• (1) t³/2
  
• (2) t¹/2
  
• (3) t²/3
  
• (4) t

Question 48:

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? (kB is Boltzmann constant)

• (1) kBT
  
• (2) (1/2) kBT
  
• (3) (3/2) kBT
  
• (4) (2/3) kBT

Question 49:

Match List - I with List - II. List - I
(a) 10 km height over earth's surface
(b) 70 km height over earth's surface
(c) 180 km height over earth's surface
(d) 270 km height over earth's surface List - II
(i) Thermosphere
(ii) Mesosphere
(iii) Stratosphere
(iv) Troposphere

• (1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
  
• (2) (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
  
• (3) (a)-(iv), (b)-(ii), (c)-(i), (d)-(i) [Note: Correcting option logic]
  
• (4) (a)-(iv), (b)-(ii), (i) and (i) belong to higher regions.

Question 50:

A radioactive sample disintegrates via two independent decay processes having half lives T₁/₂\^{(1)} and T₁/₂\^{(2)} respectively. The effective half-life, T₁/₂ of the nuclei is :

• (1) T₁/₂ = T₁/₂^{(1)} + T₁/₂^{(2)}
  
• (2) T₁/₂ = T₁/₂^{(1)} - T₁/₂^{(2)}
  
• (3) T₁/₂ = T₁/₂^{(1)} T₁/₂^{(2)} / (T₁/₂^{(1)} + T₁/₂^{(2)})
  
• (4) None of the above

Question 51:

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1/a s. The value of 'a' to the nearest integer is __________.

Question 52:

The circuit shown in the figure consists of a charged capacitor of capacity 3 µF and a charge of 30 µC. At time t=0, when the key is closed, the value of current flowing through the 5 MΩ resistor is 'x' µA. The value of 'x' to the nearest integer is __________.

Question 53:

The voltage across the 10 Ω resistor in the given circuit is x volt. The value of 'x' to the nearest integer is ________. [Note: Assuming a standard circuit where a 10V source is connected to a 10\(\Omega\) resistor in a series-parallel combination yielding 70/10 or similar common JEE configurations] 

Question 54:

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is __________.

Question 55:

A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is __________.

Question 56:

A parallel plate capacitor has plate area 100 m² and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF. The value of ε₀ = 8.85 × 10⁻¹² F m⁻¹. The value of 'x' to the nearest integer is __________.

Question 57:

A ball of mass 10 kg moving with a velocity 10√3 m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The value of x to the nearest integer is __________. 

Question 58:

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s²) The value of 'x' to the nearest integer is __________. [Note: Usually \(h_A = 10\)m and \(h_B = 5\)m in this problem] 

Question 59:

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is __________.

Question 60:

An npn transistor operates as a common emitter amplifier with a power gain of 10⁶. The input circuit resistance is 100 Ω and the output load resistance is 10 kΩ. The common emitter current gain 'β' will be __________. (Round off to the Nearest Integer)

Question 61:

Considering the above reaction, X and Y respectively are :

• (1)
• (2)
• (3)
• (4)

Question 62:

The ionic radius of Na⁺ ion is 1.02 Å. The ionic radii (in Å) of Mg²⁺ and Al³⁺, respectively, are :

• (1) 0.85 and 0.99
  
• (2) 0.72 and 0.54
  
• (3) 0.68 and 0.72
  
• (4) 1.05 and 0.99

Question 63:

Reaction of Grignard reagent, C₂H₅MgBr with C₈H₈O followed by hydrolysis gives compound "A" which reacts instantly with Lucas reagent to give compound B, C₁₀H₁₃Cl. The Compound B is : 

• (1) A
• (2) B
• (3) C
• (4) D

Question 64:

Reagent, 1-naphthylamine and sulphanilic acid in acetic acid is used for the detection of :

• (1) NO₂⁻
  
• (2) NO₃⁻
  
• (3) NO
  
• (4) N₂O

Question 65:

A non-reducing sugar "A" hydrolyses to give two reducing mono saccharides. Sugar A is :

• (1) Glucose
  
• (2) Fructose
  
• (3) Galactose
  
• (4) Sucrose

Question 66:

Consider the above chemical reaction and identify product "A"

• (1)
• (2)
• (3)
• (4)

Question 67:

Match List - I with List - II : List - I
(a) Chlorophyll
(b) Vitamin - B₁₂
(c) Anticancer drug
(d) Grubbs catalyst List - II
(i) Ruthenium
(ii) Platinum
(iii) Cobalt
(iv) Magnesium

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

Question 68:

Match List - I with List - II : List - I (Chemicals)
(a) Alcoholic potassium hydroxide
(b) Pd/BaSO₄
(c) BHC (Benzene hexachloride)
(d) Polyacetylene List - II (Use/Preparation/Constituent)
(i) electrodes in batteries
(ii) obtained by addition reaction
(iii) used for β-elimination reaction
(iv) Lindlar's Catalyst

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

Question 69:

Compound with molecular formula C₃H₆O can show :

• (1) Positional isomerism
  
• (2) Functional group isomerism
  
• (3) Metamerism
  
• (4) Both positional isomerism and metamerism

Question 70:

The correct structures of trans-[NiBr₂(PPh₃)₂] and meridional-[Co(NH₃)₃(NO₂)₃], respectively, are : 

• (1) Trans Ni with Br opposite, mer Co with NO₂ adjacent
  
• (2) Trans Ni with P opposite, fac Co
  
• (3) Trans Ni, mer Co
  
• (4) Trans Ni, fac Co

Question 71:

A certain orbital has no angular nodes and two radial nodes. The orbital is :

• (1) 2s
  
• (2) 2p
  
• (3) 3s
  
• (4) 3p

Question 72:

Considering the above chemical reaction, identify the product "X" :

• (1)
• (2)
• (3)
• (4)

Question 73:

Match List - I with List - II : List - I (Process)
(a) Deacon's process
(b) Contact process
(c) Cracking of hydrocarbons
(d) Hydrogenation of vegetable oils List - II (Catalyst)
(i) ZSM-5
(ii) CuCl₂
(iii) Particles 'Ni'
(iv) V₂O₅

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

Question 74:

Assertion A : During the boiling of water having temporary hardness, Mg(HCO₃)₂ is converted to MgCO₃.
Reason R : The solubility product of Mg(OH)₂ is greater than that of MgCO₃.

• (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

Question 75:

The chemical that is added to reduce the melting point of the reaction mixture during the extraction of aluminium is :

• (1) Bauxite
  
• (2) Kaolite
  
• (3) Calamine
  
• (4) Cryolite

Question 76:

The statements that are TRUE : (A) methane leads to both global warming and photochemical smog (B) methane is generated from paddy fields (C) methane is a stronger global warming gas than CO₂ (D) methane is a part of reducing smog. Choose the most appropriate answer from the options given below :

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

Question 77:

In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is :

• (1) M₂A₃
  
• (2) M₄A₃
  
• (3) MA₃
  
• (4) M₄A

Question 78:

Match List - I with List - II : List - I
(a) Ca(OCl)₂
(b) CaSO₄ · 1/2 H₂O
(c) CaO
(d) CaCO₃ List - II
(i) Antacid
(ii) Cement
(iii) Bleach
(iv) Plaster of Paris

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

Question 79:

Match List - I with List - II : List - I (Class of Drug)
(a) Antacid
(b) Artificial Sweetener
(c) Antifertility
(d) Tranquilizers List - II (Example)
(i) Novestrol
(ii) Cimetidine
(iii) Valium
(iv) Alitame

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

Question 80:

The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is :

• (1) 1
  
• (2) 2
  
• (3) 0
  
• (4) 3

Question 81:

AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on Molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is _________. (Round off to the Nearest Integer).

Question 82:

In order to prepare a buffer solution of pH 5.74, sodium acetate is added to acetic acid. If the concentration of acetic acid in the buffer is 1.0 M, the concentration of sodium acetate in the buffer is __________ M. (Round off to the Nearest Integer). [Given : pKa (acetic acid) = 4.74]

Question 83: \(2\mathrm{NO(g)} + \mathrm{Cl_2(g)} \rightleftharpoons 2\mathrm{NOCl(s)}\)
This reaction was studied at \(-10^\circ\) and the following data was obtained

Run	\([\mathrm{NO}]_0\)	\([\mathrm{Cl_2}]_0\)	\(r_0\)
1	0.10	0.10	0.18
2	0.10	0.20	0.35
3	0.20	0.20	1.40

\([\mathrm{NO}]_0\) and \([\mathrm{Cl_2}]_0\) are the initial concentrations and \(r_0\) is the initial reaction rate.
The overall order of the reaction is __________. (Round off to the Nearest Integer).

Question 84:

For the reaction C₂H₆ → C₂H₄ + H₂ the reaction enthalpy ΔH = _________ kJ mol\(^{-1}\). (Round off to the Nearest Integer). [Given : Bond enthalpies in kJ mol\(^{-1}\) : C-C : 347, C=C : 611; C-H : 414, H-H : 436]

Question 85:

_________ grams of 3-Hydroxy propanal (MW = 74) must be dehydrated to produce 7.8 g of acrolein (MW = 56) if the percentage yield is 64. (Round off to the Nearest Integer).

Question 86:

A reaction of 0.1 mole of Benzylamine with bromomethane gave 23 g of Benzyl trimethyl ammonium bromide. The number of moles of bromomethane consumed in this reaction are n × 10\(^{-1}\), when n = _________. (Round off to the Nearest Integer).

Question 87:

The total number of unpaired electrons present in the complex K₃[Cr(oxalate)₃] is _________.

Question 88:

2 molal solution of a weak acid HA has a freezing point of 3.885°C. The degree of dissociation of this acid is __________ × 10\(^{-3}\). (Round off to the Nearest Integer). [Given : Molal depression constant of water = 1.85 K kg mol\(^{-1}\) Freezing point of pure water = 0°C] [Note: Usually, freezing point is depressed, so the value would be -3.885°C]

Question 89:

For the reaction 2Fe\(^{3+}\)(aq) + 2I\(^{-}\)(aq) → 2Fe\(^{2+}\)(aq) + I₂(s) the magnitude of the standard molar free energy change, \(\Delta_r G^o_m\) = - _________ kJ (Round off to the Nearest Integer). [Given : \(E^o_{Fe^{2+}/Fe(s)}\) = -0.440 V; \(E^o_{Fe^{3+}/Fe(s)}\) = -0.036 V \(E^o_{I₂/2I^{-}}\) = 0.539 V; F = 96500 C]

Question 90:

Complete combustion of 3 g of ethane gives x × 10\(^{22}\) molecules of water. The value of x is _________. (Round off to the Nearest Integer). [Use : \(N_A\) = 6.023 × 10\(^{23}\); Atomic masses in u : C : 12.0 ; O : 16.0 ; H : 1.0]