JEE Advanced Practice Set 1

A projectile is fired at an angle θ with the horizontal with speed u. At the highest point, its speed is u/2. The angle of projection θ is:

1. A.30°
2. B.45°
3. C.60°✓
4. D.75°

Correct answer: C

A particle undergoes uniform circular motion with angular velocity ω in a circle of radius R. If the centripetal acceleration is 4π²R and the time period is T, then T equals:

1. A.0.5 s
2. B.1 s✓
3. C.2 s
4. D.π s

Correct answer: B

A uniform rod of mass M and length L is pivoted at one end and released from a horizontal position. The angular velocity of the rod when it becomes vertical is:

1. A.√(g/L)
2. B.√(2g/L)
3. C.√(3g/L)✓
4. D.√(6g/L)

Correct answer: C

An ideal gas undergoes an isothermal expansion to twice its original volume. If the initial pressure is P, the work done by the gas is:

1. A.PV
2. B.PV ln 2✓
3. C.2PV
4. D.PV/ln 2

Correct answer: B

In a double-slit experiment, the fringe width is β when the wavelength used is 600 nm. If the wavelength is changed to 400 nm, the new fringe width is:

1. A.β/2
2. B.2β/3✓
3. C.3β/2
4. D.3β/4

Correct answer: B

A particle executes SHM with amplitude A. At what displacement from the mean position is its kinetic energy equal to its potential energy?

1. A.A/2
2. B.A/√2✓
3. C.A/4
4. D.A√3/2

Correct answer: B

An ideal gas at temperature T has rms speed v. If the temperature is increased to 4T, the new rms speed is:

1. A.v/2
2. B.v
3. C.2v✓
4. D.4v

Correct answer: C

Two charged conducting spheres of radii R and 2R are connected by a wire. If the total charge is Q, the charge on the smaller sphere after equilibrium is:

1. A.Q/2
2. B.Q/3✓
3. C.Q/4
4. D.2Q/3

Correct answer: B

In the Bohr model of hydrogen, the ratio of the kinetic energy to the total energy of an electron in the nth orbit is:

1. A.1
2. B.-1✓
3. C.2
4. D.-2

Correct answer: B

A copper wire of length L and area of cross-section A has resistance R. If the wire is stretched uniformly to length 3L, the new resistance is:

1. A.3R
2. B.6R
3. C.9R✓
4. D.27R

Correct answer: C

For a first-order reaction, the time required for 99% completion is approximately how many times the time required for 90% completion?

1. A.1.5
2. B.2✓
3. C.5
4. D.10

Correct answer: B

The boiling point of a solution containing 18 g of glucose (molar mass 180 g/mol) in 100 g of water is (Kᵇ for water = 0.52 K·kg/mol, boiling point of water = 100°C):

1. A.100.26°C
2. B.100.52°C✓
3. C.101.04°C
4. D.100.78°C

Correct answer: B

The common ion effect causes a decrease in the solubility of a sparingly soluble salt. If the Kₛₚ of AgCl is 1.6 × 10⁻¹⁰, the solubility of AgCl in 0.1 M NaCl solution is:

1. A.1.6 × 10⁻⁵ M
2. B.1.6 × 10⁻⁹ M✓
3. C.1.6 × 10⁻¹¹ M
4. D.1.26 × 10⁻⁵ M

Correct answer: B

According to molecular orbital theory, the bond order of O₂⁺ is:

1. A.1.5
2. B.2.0
3. C.2.5✓
4. D.3.0

Correct answer: C

The d-block element that shows the maximum number of oxidation states is:

1. A.Chromium
2. B.Manganese✓
3. C.Iron
4. D.Cobalt

Correct answer: B

The number of geometrical isomers possible for the complex [Ma₂b₂] in a square planar geometry is:

1. A.1
2. B.2✓
3. C.3
4. D.4

Correct answer: B

The major product formed when phenol reacts with bromine water is:

1. A.2-Bromophenol
2. B.4-Bromophenol
3. C.2,4-Dibromophenol
4. D.2,4,6-Tribromophenol✓

Correct answer: D

Aniline can be distinguished from N-methylaniline by which of the following tests?

1. A.Hinsberg test
2. B.Carbylamine test✓
3. C.Litmus test
4. D.Biuret test

Correct answer: B

The reaction of chlorobenzene with sodium in dry ether to form biphenyl is known as:

1. A.Friedel-Crafts reaction
2. B.Wurtz reaction
3. C.Fittig reaction✓
4. D.Sandmeyer reaction

Correct answer: C

For an exothermic reaction at equilibrium, if the temperature is increased, which of the following is true?

1. A.Equilibrium shifts forward, K increases
2. B.Equilibrium shifts backward, K decreases✓
3. C.Equilibrium shifts forward, K decreases
4. D.No change in equilibrium or K

Correct answer: B

The solution of the differential equation dy/dx = y/x, with y(1) = 2, is:

1. A.y = x + 1
2. B.y = 2x✓
3. C.y = x² + 1
4. D.y = 2x²

Correct answer: B

The value of ∫₀⁻ x² e⁻ˣ dx is (where the integral is from 0 to infinity, using the Gamma function):

1. A.1
2. B.2✓
3. C.π
4. D.√π

Correct answer: B

The eccentricity of the ellipse x²/25 + y²/16 = 1 is:

1. A.3/5✓
2. B.4/5
3. C.5/3
4. D.3/4

Correct answer: A

The angle between the planes 2x - y + z = 6 and x + y + 2z = 7 is:

1. A.π/6
2. B.π/4
3. C.π/3✓
4. D.π/2

Correct answer: C

If vectors a⃗ = 2î + 3ĵ + k̂ and b⃗ = î - ĵ + 2k̂, then a⃗ × b⃗ is:

1. A.7î - 3ĵ - 5k̂✓
2. B.7î + 3ĵ - 5k̂
3. C.-7î + 3ĵ + 5k̂
4. D.7î - 3ĵ + 5k̂

Correct answer: A

Five persons are to be seated in a row. The probability that two particular persons are always adjacent is:

1. A.1/5
2. B.2/5✓
3. C.3/5
4. D.1/10

Correct answer: B

If A is a 3×3 matrix with |A| = -2, then |adj(A)| is:

1. A.-4
2. B.4✓
3. C.-8
4. D.8

Correct answer: B

The value of lim(x→0) (eˣ - 1 - x)/x² is:

1. A.0
2. B.1/2✓
3. C.1
4. D.Does not exist

Correct answer: B

If z = (1 + i)/(1 - i), then z⁴ equals:

1. A.1✓
2. B.-1
3. C.i
4. D.-i

Correct answer: A

The number of ways in which 5 boys and 5 girls can be seated in a row so that no two girls sit together is:

1. A.86400✓
2. B.14400
3. C.7200
4. D.120 × 120

Correct answer: A