Major Competitive Exams
Q. If the mole fraction of a solvent in a solution is 0.8, what is the mole fraction of the solute?
-
A.
0.2
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B.
0.8
-
C.
0.5
-
D.
0.1
Solution
The mole fraction of the solute is 1 - X_solvent = 1 - 0.8 = 0.2.
Correct Answer: A — 0.2
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Q. If the mole fraction of solute in a solution is 0.2, what is the mole fraction of the solvent?
-
A.
0.8
-
B.
0.2
-
C.
0.5
-
D.
0.6
Solution
The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.
Correct Answer: A — 0.8
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Q. If the moment of inertia of a body is 10 kg m², what is the angular momentum when it rotates with an angular velocity of 5 rad/s?
-
A.
50 kg m²/s
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B.
10 kg m²/s
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C.
5 kg m²/s
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D.
2 kg m²/s
Solution
Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.
Correct Answer: A — 50 kg m²/s
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Q. If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
-
A.
125 J
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B.
50 J
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C.
100 J
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D.
75 J
Solution
Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.
Correct Answer: A — 125 J
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Q. If the moment of inertia of a body is 10 kg·m² and it is subjected to a torque of 20 N·m, what is the angular acceleration?
-
A.
2 rad/s²
-
B.
0.5 rad/s²
-
C.
5 rad/s²
-
D.
10 rad/s²
Solution
Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².
Correct Answer: A — 2 rad/s²
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Q. If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?
-
A.
Doubles
-
B.
Halves
-
C.
Remains the same
-
D.
Quadruples
Solution
Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.
Correct Answer: A — Doubles
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Q. If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
-
A.
Doubles
-
B.
Halves
-
C.
Remains the same
-
D.
Increases by a factor of four
Solution
Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.
Correct Answer: B — Halves
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Q. If the moment of inertia of a body is doubled, what will happen to its angular momentum if the angular velocity remains constant?
-
A.
Doubles
-
B.
Halves
-
C.
Remains the same
-
D.
Quadruples
Solution
Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.
Correct Answer: A — Doubles
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Q. If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?
-
A.
Increases
-
B.
Decreases
-
C.
Remains the same
-
D.
Becomes zero
Solution
According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.
Correct Answer: B — Decreases
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Q. If the mortality rate of a disease is 5% and 2000 people are diagnosed, how many deaths are expected? (2023)
-
A.
50
-
B.
75
-
C.
100
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D.
125
Solution
Expected deaths = 5% of 2000 = 0.05 * 2000 = 100 deaths.
Correct Answer: C — 100
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Q. If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?
-
A.
4.8 rad/s
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B.
5 rad/s
-
C.
5.2 rad/s
-
D.
5.5 rad/s
Solution
Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.
Correct Answer: A — 4.8 rad/s
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Q. If the nth term of a harmonic progression is given by 1/(1/n + 1/a), what does 'a' represent?
-
A.
The first term
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B.
The last term
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C.
The common difference
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D.
The sum of the terms
Solution
'a' represents the first term of the harmonic progression in the formula for the nth term.
Correct Answer: A — The first term
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Q. If the nth term of a sequence is given by a_n = 5n - 3, what is the value of a_7? (2023)
Solution
Substituting n = 7 into the formula gives a_7 = 5*7 - 3 = 35 - 3 = 32.
Correct Answer: B — 34
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Q. If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?
Solution
a_4 = 4^2 + 4 = 16 + 4 = 20.
Correct Answer: A — 20
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Q. If the object distance is equal to the focal length of a convex lens, what is the nature of the image formed?
-
A.
Real and inverted
-
B.
Virtual and upright
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C.
At infinity
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D.
No image formed
Solution
When the object distance equals the focal length, the image is formed at infinity.
Correct Answer: C — At infinity
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Q. If the object distance is equal to the focal length of a convex lens, what type of image is formed?
-
A.
Real and inverted
-
B.
Virtual and upright
-
C.
At infinity
-
D.
No image formed
Solution
When the object is at the focal length, the image is formed at infinity.
Correct Answer: C — At infinity
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Q. If the odds in favor of an event are 3:2, what is the probability of the event occurring?
-
A.
0.6
-
B.
0.4
-
C.
0.5
-
D.
0.3
Solution
Probability = Odds in favor / (Total odds) = 3 / (3 + 2) = 3/5 = 0.6.
Correct Answer: A — 0.6
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Q. If the osmotic pressure of a solution is 3.0 atm at 25 °C, what is the molarity of the solution? (R = 0.0821 L atm/(K mol))
-
A.
0.12 M
-
B.
0.15 M
-
C.
0.18 M
-
D.
0.20 M
Solution
Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M
Correct Answer: C — 0.18 M
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Q. If the osmotic pressure of a solution is 3.0 atm, what is the molarity of the solution? (R = 0.0821 L atm/(K mol), T = 298 K)
-
A.
0.12 M
-
B.
0.15 M
-
C.
0.10 M
-
D.
0.20 M
Solution
Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M
Correct Answer: B — 0.15 M
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Q. If the pair of lines represented by ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
-
A.
a + b = 0
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B.
a - b = 0
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C.
h = 0
-
D.
a = b
Solution
For the lines to be perpendicular, the condition a + b = 0 must hold.
Correct Answer: A — a + b = 0
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Q. If the pair of lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
-
A.
a + b = 0
-
B.
a - b = 0
-
C.
h = 0
-
D.
a = b
Solution
For the lines to be perpendicular, the condition a*b + h^2 = 0 must hold.
Correct Answer: A — a + b = 0
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Q. If the paper is folded in half, which shape will appear?
-
A.
Shape A
-
B.
Shape B
-
C.
Shape C
-
D.
Shape D
Solution
Shape A will appear when the paper is folded in half along the specified line.
Correct Answer: A — Shape A
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Q. If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?
Solution
Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.
Correct Answer: B — 2
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Q. If the parabola y^2 = 16x opens to the right, what is the value of p?
Solution
In the equation y^2 = 4px, we have 4p = 16, thus p = 4.
Correct Answer: B — 4
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Q. If the parabola y^2 = 20x opens to the right, what is the value of p?
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.
Correct Answer: A — 5
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Q. If the Parliament has 790 members and 20% are women, how many women are there in the Parliament?
-
A.
158
-
B.
160
-
C.
150
-
D.
170
Solution
Number of women = 20% of 790 = 0.2 * 790 = 158.
Correct Answer: A — 158
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Q. If the Parliament has 790 members and 40% are from the opposition, how many members are from the opposition?
-
A.
316
-
B.
320
-
C.
300
-
D.
310
Solution
Opposition members = 40% of 790 = 0.4 * 790 = 316.
Correct Answer: A — 316
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Q. If the Parliament is in session for 120 days in a year and the Lok Sabha meets for 75% of those days, how many days does the Lok Sabha meet?
Solution
Days Lok Sabha meets = 75% of 120 = 0.75 * 120 = 90.
Correct Answer: A — 90
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Q. If the peak current in an AC circuit is 5 A, what is the average current over one complete cycle?
-
A.
5 A
-
B.
2.5 A
-
C.
0 A
-
D.
7.07 A
Solution
The average current over one complete cycle is I_avg = I_peak/√2 = 5/√2 = 2.5 A.
Correct Answer: B — 2.5 A
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Q. If the peak voltage of an AC source is 200 V, what is the RMS voltage?
-
A.
100 V
-
B.
141.42 V
-
C.
200 V
-
D.
282.84 V
Solution
The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 200 V / √2 = 141.42 V.
Correct Answer: B — 141.42 V
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