Engineering Entrance
Q. If the perimeter of a square is 40 cm, what is the length of one side? (2018)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer: A — 10 cm
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Q. If the pH of a solution is 3, what is the concentration of H+ ions? (2023)
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
0.0001 M
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Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer: B — 0.01 M
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Q. If the pKa of acetic acid is 4.76, what is the pH of a 0.1 M solution?
A.
4.76
B.
5.76
C.
6.76
D.
3.76
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Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer: A — 4.76
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Q. If the radius of a circle is 7 cm, what is its circumference? (Use π = 22/7) (2014)
A.
44 cm
B.
22 cm
C.
14 cm
D.
28 cm
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Solution
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Correct Answer: A — 44 cm
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Q. If the radius of a circle is doubled, how does the area change? (2021)
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
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Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer: C — It quadruples
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Q. If the radius of a circle is halved, how does the circumference change? (2021)
A.
Halved
B.
Remains the same
C.
Doubled
D.
Tripled
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Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
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Q. If the radius of a circle is halved, how does the circumference change? (2022) 2022
A.
Halved
B.
Remains the same
C.
Doubled
D.
Quadrupled
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Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
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Q. If the rate of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy? (2020)
A.
20 kJ/mol
B.
40 kJ/mol
C.
60 kJ/mol
D.
80 kJ/mol
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Solution
Using the Arrhenius equation, if the rate doubles for a 10°C increase, Ea is approximately 40 kJ/mol.
Correct Answer: B — 40 kJ/mol
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Q. If the rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 3, what is the order of the reaction? (2023)
A.
Zero
B.
First
C.
Second
D.
Third
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Solution
The order of the reaction is third because the rate is proportional to the concentration raised to the power of 3.
Correct Answer: D — Third
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Q. If the rate of a reaction is given by rate = k[A]², what is the order of the reaction? (2021)
A.
Zero
B.
First
C.
Second
D.
Third
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Solution
The reaction is second-order because the rate depends on the square of the concentration of A.
Correct Answer: C — Second
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Q. If the resistance of a conductor is doubled, what happens to the current flowing through it when the voltage remains constant? (2022)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by 1.5 times
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Solution
According to Ohm's law, I = V/R. If R is doubled, I will be halved.
Correct Answer: B — Halves
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Q. If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
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Solution
Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.
Correct Answer: B — 50
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Q. If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)
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Solution
Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.
Correct Answer: C — 3
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Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 1
B.
k < 1
C.
k > 4
D.
k < 4
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Solution
The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer: C — k > 4
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Q. If the roots of the equation x² + 5x + k = 0 are -2 and -3, find k. (2020)
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Solution
Using the product of roots: k = (-2)(-3) = 6.
Correct Answer: A — 6
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Q. If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)
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Solution
Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.
Correct Answer: D — 7
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Q. If the roots of the equation x² + 7x + p = 0 are -3 and -4, find p. (2019)
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Solution
Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.
Correct Answer: A — 12
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Q. If the roots of the equation x² + px + 12 = 0 are 3 and 4, find p. (2020)
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Solution
Using the sum of the roots: p = -(3 + 4) = -7.
Correct Answer: A — -7
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Q. If the speed of light in vacuum is 3 x 10^8 m/s, what is its speed in glass (n = 1.5)?
A.
2 x 10^8 m/s
B.
2.5 x 10^8 m/s
C.
3 x 10^8 m/s
D.
1.5 x 10^8 m/s
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Solution
The speed of light in a medium is given by v = c/n. Therefore, v = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.
Correct Answer: A — 2 x 10^8 m/s
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Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50 ohms, what is the current? (2023)
A.
2A
B.
0.5A
C.
5A
D.
10A
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Solution
Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.
Correct Answer: A — 2A
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Q. If the voltage across a capacitor in an AC circuit is 100V and the capacitive reactance is 50Ω, what is the current? (2021)
A.
2A
B.
0.5A
C.
5A
D.
100A
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Solution
Using Ohm's law, I = V/Xc = 100V/50Ω = 2A.
Correct Answer: B — 0.5A
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Q. If the voltage across a capacitor is 100V and the capacitive reactance is 50 ohms, what is the current through the capacitor? (2022)
A.
2 A
B.
1 A
C.
0.5 A
D.
0.25 A
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Solution
I = V/Xc = 100/50 = 2 A.
Correct Answer: B — 1 A
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Q. If the voltage across a resistor is 240V and the resistance is 60 ohms, what is the current flowing through it? (2020)
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Solution
I = V / R = 240V / 60Ω = 4A.
Correct Answer: C — 6A
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Q. If the voltage across a resistor is halved, what happens to the current through it? (2020)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
According to Ohm's law, if voltage is halved and resistance remains constant, the current also halves.
Correct Answer: B — It halves
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Q. If the volume of a gas is halved while keeping the temperature constant, what happens to the pressure of the gas?
A.
Halves
B.
Doubles
C.
Remains the same
D.
Increases by 50%
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Solution
According to Boyle's Law, if the volume is halved, the pressure doubles.
Correct Answer: B — Doubles
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Q. If the wavelength of light used in a single-slit diffraction experiment is increased, what will happen to the position of the first minimum? (2022)
A.
It moves closer to the center
B.
It moves away from the center
C.
It remains unchanged
D.
It disappears
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Solution
The position of the first minimum in single-slit diffraction is given by a sin(θ) = λ. Increasing λ will cause θ to increase, moving the minimum away from the center.
Correct Answer: B — It moves away from the center
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Q. If two dice are rolled, what is the probability that the sum is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
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Solution
Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer: D — 5/36
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Q. If two identical capacitors of 4 µF each are connected in series, what is the equivalent capacitance?
A.
2 µF
B.
4 µF
C.
6 µF
D.
8 µF
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Solution
C_eq = 1 / (1/C1 + 1/C2) = 1 / (1/4 + 1/4) = 2 µF.
Correct Answer: A — 2 µF
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Q. If x = 3, what is the value of 2x^2 - 5x + 1? (2022)
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Solution
2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.
Correct Answer: D — 6
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Q. If x = 5, what is the value of 2x + 3? (2022)
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Solution
Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.
Correct Answer: B — 13
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