Major Competitive Exams
Q. What is the total resistance of two resistors of 8Ω and 12Ω connected in series?
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A.
20Ω
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B.
24Ω
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C.
16Ω
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D.
18Ω
Solution
In series, R_eq = R1 + R2 = 8 + 12 = 20Ω.
Correct Answer: A — 20Ω
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Q. What is the total resistance of two resistors, 4 ohms and 6 ohms, connected in series? (2021)
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A.
10 ohms
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B.
24 ohms
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C.
2.4 ohms
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D.
0.67 ohms
Solution
In series, total resistance R = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.
Correct Answer: A — 10 ohms
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Q. What is the total sales of all products combined in Q1?
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A.
1200 units
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B.
1500 units
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C.
1000 units
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D.
1300 units
Solution
The total sales in Q1 is 1200 units when all products are summed up.
Correct Answer: A — 1200 units
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Q. What is the total sales of Product A over the four quarters as per the table?
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A.
1200
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B.
1300
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C.
1400
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D.
1500
Solution
The total sales of Product A over the four quarters is 1300 units.
Correct Answer: B — 1300
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Q. What is the total voltage across a parallel circuit with two branches, one with 10Ω and 20Ω resistors, if the total current is 3A?
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A.
6V
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B.
9V
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C.
12V
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D.
15V
Solution
Using the formula V = I * R_eq. First, find R_eq = 1 / (1/10 + 1/20) = 6.67Ω. Then, V = 3A * 6.67Ω = 20V.
Correct Answer: C — 12V
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Q. What is the total voltage in a series circuit with a 9V battery and two resistors of 2Ω and 3Ω?
Solution
In a series circuit, the total voltage is equal to the voltage of the battery, which is 9V.
Correct Answer: A — 9V
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Q. What is the trace of a square matrix? (2022)
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A.
Sum of all elements
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B.
Product of diagonal elements
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C.
Sum of diagonal elements
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D.
Difference of diagonal elements
Solution
The trace of a square matrix is defined as the sum of the elements on its main diagonal.
Correct Answer: C — Sum of diagonal elements
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Q. What is the trace of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Solution
The trace of A is the sum of the diagonal elements: 1 + 5 + 9 = 15.
Correct Answer: A — 15
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Q. What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 + 4 = 9.
Correct Answer: C — 7
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Q. What is the trend in atomic radius as you move down a group in the periodic table?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Increases then decreases
Solution
Atomic radius increases down a group due to the addition of electron shells.
Correct Answer: A — Increases
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Q. What is the trend in atomic radius as you move down the alkali metal group? (2022)
-
A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Increases then decreases
Solution
The atomic radius increases as you move down the alkali metal group due to the addition of electron shells.
Correct Answer: A — Increases
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Q. What is the trend in atomic radius as you move down the group of alkali metals?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Varies irregularly
Solution
The atomic radius increases as you move down the group of alkali metals.
Correct Answer: A — Increases
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Q. What is the trend in electronegativity as you move from left to right across a period?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Varies irregularly
Solution
Electronegativity increases from left to right across a period.
Correct Answer: A — Increases
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Q. What is the trend in ionization energy as you move down the group in s-block elements?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Varies irregularly
Solution
Ionization energy decreases as you move down the group in s-block elements due to increased atomic size.
Correct Answer: B — Decreases
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Q. What is the trend in ionization energy for alkali metals down the group?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Fluctuates
Solution
Ionization energy decreases down the group for alkali metals.
Correct Answer: B — Decreases
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Q. What is the trend in metallic character as you move from left to right across a period?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Increases then decreases
Solution
Metallic character decreases from left to right across a period.
Correct Answer: B — Decreases
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Q. What is the truth value of the expression A AND (B OR C) when A = 1, B = 0, and C = 1?
Solution
First, evaluate B OR C, which is 0 OR 1 = 1. Then, A AND 1 = 1 AND 1 = 1.
Correct Answer: B — 1
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Q. What is the truth value of the expression A AND (B OR C) when A = 1, B = 0, C = 1?
-
A.
0
-
B.
1
-
C.
2
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D.
Undefined
Solution
B OR C = 0 OR 1 = 1. Then, A AND 1 = 1 AND 1 = 1.
Correct Answer: B — 1
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Q. What is the Tyndall effect? (2023)
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A.
Scattering of light by particles
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B.
Absorption of light by particles
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C.
Reflection of light by particles
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D.
Refraction of light by particles
Solution
The Tyndall effect is the scattering of light by colloidal particles, making the path of the light visible.
Correct Answer: A — Scattering of light by particles
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Q. What is the typical band gap of germanium?
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A.
0.66 eV
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B.
1.1 eV
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C.
1.5 eV
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D.
2.0 eV
Solution
The typical band gap of germanium is approximately 0.66 eV.
Correct Answer: A — 0.66 eV
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Q. What is the typical charge of s-block metal ions?
Solution
S-block metals typically form ions with a charge of +2.
Correct Answer: B — +2
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Q. What is the typical range of energy band gaps for semiconductors?
-
A.
0.1 - 0.5 eV
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B.
0.5 - 1.5 eV
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C.
1.5 - 3.0 eV
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D.
3.0 - 5.0 eV
Solution
The typical range of energy band gaps for semiconductors is between 0.5 eV and 1.5 eV.
Correct Answer: B — 0.5 - 1.5 eV
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Q. What is the typical range of the energy band gap for semiconductors?
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A.
0.1 - 0.5 eV
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B.
0.5 - 2.5 eV
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C.
2.5 - 5 eV
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D.
5 - 10 eV
Solution
The typical range of the energy band gap for semiconductors is between 0.5 eV and 2.5 eV.
Correct Answer: B — 0.5 - 2.5 eV
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Q. What is the uncertainty in a measurement of 50.0 ± 0.5 g when converted to kilograms?
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A.
0.0005 kg
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B.
0.005 kg
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C.
0.05 kg
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D.
0.5 kg
Solution
To convert grams to kilograms, divide by 1000. The uncertainty in kilograms is 0.5 g / 1000 = 0.0005 kg.
Correct Answer: B — 0.005 kg
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Q. What is the uncertainty in position if the uncertainty in momentum of a particle is 1.0 x 10^-24 kg m/s?
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A.
1.0 x 10^-10 m
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B.
6.63 x 10^-10 m
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C.
1.0 x 10^-34 m
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D.
6.63 x 10^-34 m
Solution
Using Heisenberg's uncertainty principle, ΔxΔp ≥ ħ/2, we find Δx ≥ ħ/(2Δp) = (1.055 x 10^-34)/(2 x 1.0 x 10^-24) = 5.27 x 10^-11 m.
Correct Answer: D — 6.63 x 10^-34 m
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Q. What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when calculating the area?
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A.
0.04 cm²
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B.
0.10 cm²
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C.
0.20 cm²
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D.
0.50 cm²
Solution
Area = length² = (5.00 cm)² = 25.00 cm². The uncertainty in area is calculated using the formula: ΔA = 2LΔL = 2(5.00 cm)(0.02 cm) = 0.20 cm².
Correct Answer: B — 0.10 cm²
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Q. What is the uncertainty in the result of adding 5.0 cm and 3.0 cm, each with an uncertainty of 0.1 cm?
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A.
0.1 cm
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B.
0.2 cm
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C.
0.3 cm
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D.
0.4 cm
Solution
When adding, the uncertainties are added: 0.1 cm + 0.1 cm = 0.2 cm.
Correct Answer: B — 0.2 cm
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Q. What is the uncertainty principle formulated by Heisenberg?
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A.
ΔxΔp ≥ ħ/2
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B.
ΔEΔt ≥ ħ
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C.
ΔxΔE ≥ ħ
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D.
ΔpΔt ≥ ħ
Solution
The uncertainty principle states that the product of the uncertainties in position (Δx) and momentum (Δp) is greater than or equal to ħ/2.
Correct Answer: A — ΔxΔp ≥ ħ/2
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Q. What is the uncertainty principle in quantum mechanics?
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A.
ΔxΔp ≥ ħ/2
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B.
ΔEΔt ≥ ħ/2
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C.
Both A and B
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D.
None of the above
Solution
The uncertainty principle states that ΔxΔp ≥ ħ/2 and ΔEΔt ≥ ħ/2, where ħ is the reduced Planck's constant.
Correct Answer: C — Both A and B
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Q. What is the underlying message of the passage regarding consumerism?
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A.
It is beneficial for society
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B.
It leads to environmental degradation
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C.
It fosters innovation
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D.
It is a personal choice
Solution
The passage conveys that consumerism has detrimental effects on the environment.
Correct Answer: B — It leads to environmental degradation
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