Q. What is the total capacitance of two capacitors of 3 µF and 6 µF in parallel?
-
A.
9 µF
-
B.
2 µF
-
C.
18 µF
-
D.
1.5 µF
Solution
In parallel, the total capacitance is the sum: C_total = C1 + C2 = 3 µF + 6 µF = 9 µF.
Correct Answer:
A
— 9 µF
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Q. What is the total capacitance of two capacitors of 4 microfarads and 6 microfarads connected in series? (2019)
-
A.
2.4 microfarads
-
B.
10 microfarads
-
C.
24 microfarads
-
D.
1.5 microfarads
Solution
For capacitors in series, 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/4 + 1/6 = 5/12. Therefore, C_eq = 2.4 microfarads.
Correct Answer:
A
— 2.4 microfarads
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Q. What is the total capacitance of two capacitors, C1 = 3μF and C2 = 6μF, connected in series? (2022)
-
A.
2μF
-
B.
9μF
-
C.
1.5μF
-
D.
18μF
Solution
The formula for total capacitance in series is 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/3 + 1/6 = 1/2, so C_eq = 2μF.
Correct Answer:
A
— 2μF
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Q. What is the total current in a parallel circuit with three branches carrying 2 A, 3 A, and 5 A respectively?
-
A.
10 A
-
B.
5 A
-
C.
3 A
-
D.
2 A
Solution
In a parallel circuit, the total current is the sum of the currents in each branch: I_total = 2 A + 3 A + 5 A = 10 A.
Correct Answer:
A
— 10 A
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Q. What is the total current in a parallel circuit with two branches carrying 3 A and 5 A?
-
A.
8 A
-
B.
15 A
-
C.
5 A
-
D.
3 A
Solution
In a parallel circuit, the total current is the sum of the currents in each branch: I_total = I1 + I2 = 3 A + 5 A = 8 A.
Correct Answer:
A
— 8 A
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Q. What is the total energy stored in a capacitor of capacitance 20 microfarads charged to 10 volts?
-
A.
1 joule
-
B.
0.1 joule
-
C.
0.01 joule
-
D.
0.5 joule
Solution
Energy (E) stored in a capacitor is given by E = 0.5 * C * V^2. Thus, E = 0.5 * 20 x 10^-6 F * (10 V)^2 = 0.1 joules.
Correct Answer:
B
— 0.1 joule
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Q. What is the total mechanical energy of a system if the potential energy is 50 J and the kinetic energy is 30 J?
-
A.
80 J
-
B.
50 J
-
C.
30 J
-
D.
20 J
Solution
Total Mechanical Energy (TME) = Potential Energy + Kinetic Energy = 50 J + 30 J = 80 J.
Correct Answer:
A
— 80 J
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Q. What is the total number of degrees in a triangle formed by the intersection of the medians of a triangle? (2021)
-
A.
90 degrees
-
B.
180 degrees
-
C.
270 degrees
-
D.
360 degrees
Solution
The sum of the angles in any triangle is always 180 degrees.
Correct Answer:
B
— 180 degrees
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Q. What is the total number of electrons in a neutral atom of carbon? (2019)
Solution
A neutral carbon atom has an atomic number of 6, which means it has 6 electrons.
Correct Answer:
B
— 6
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Q. What is the total number of members in the Rajya Sabha?
-
A.
250
-
B.
245
-
C.
300
-
D.
200
Solution
The Rajya Sabha, the upper house of India's Parliament, has a total of 245 members.
Correct Answer:
B
— 245
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Q. What is the total number of neutrons in an atom of carbon-14? (2021)
Solution
Carbon-14 has an atomic number of 6 (6 protons). The mass number is 14, so the number of neutrons is 14 - 6 = 8.
Correct Answer:
B
— 7
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Q. What is the total number of states in India as of 2021? (2021)
Solution
As of 2021, India has 28 states.
Correct Answer:
A
— 28
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Q. What is the total resistance in a series circuit with resistors of 4 ohms, 6 ohms, and 10 ohms? (2023)
-
A.
20 ohms
-
B.
10 ohms
-
C.
6 ohms
-
D.
4 ohms
Solution
In a series circuit, total resistance (R_total) is the sum of individual resistances: R_total = 4 + 6 + 10 = 20 ohms.
Correct Answer:
A
— 20 ohms
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Q. What is the trace of a 2x2 matrix A = [[3, 2], [1, 4]]? (2022)
Solution
The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is 3 + 4 = 7.
Correct Answer:
B
— 6
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Q. What is the trace of a 2x2 matrix A = [[a, b], [c, d]]? (2022)
-
A.
a + b + c + d
-
B.
a + d
-
C.
b + c
-
D.
a * d
Solution
The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is a + d.
Correct Answer:
B
— a + d
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Q. What is the trace of a 2x2 matrix [[a, b], [c, d]]? (2019)
-
A.
a + b
-
B.
b + c
-
C.
a + d
-
D.
c + d
Solution
The trace of a matrix is the sum of its diagonal elements. For the matrix [[a, b], [c, d]], the trace is a + d.
Correct Answer:
C
— a + d
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Q. What is the trace of a matrix?
-
A.
Sum of all elements
-
B.
Sum of diagonal elements
-
C.
Product of diagonal elements
-
D.
None of the above
Solution
The trace of a matrix is defined as the sum of the elements on the main diagonal.
Correct Answer:
B
— Sum of diagonal elements
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Q. What is the trace of a square matrix? (2022)
-
A.
Sum of all elements
-
B.
Product of diagonal elements
-
C.
Sum of diagonal elements
-
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 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 trace of the matrix H = [[2, 1], [1, 3]]?
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 = 5.
Correct Answer:
B
— 4
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Q. What is the trace of the matrix I = [[3, 2], [1, 4]]? (2023)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(I) = 3 + 4 = 7.
Correct Answer:
B
— 6
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Q. What is the trace of the matrix I = [[5, 2], [3, 4]]? (2022)
Solution
The trace of a matrix is the sum of its diagonal elements. Thus, trace(I) = 5 + 4 = 9.
Correct Answer:
C
— 9
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Q. What is the unit vector in the direction of vector A = 4i + 3j?
-
A.
(4/5)i + (3/5)j
-
B.
(3/4)i + (4/3)j
-
C.
(4/3)i + (3/4)j
-
D.
(3/5)i + (4/5)j
Solution
Unit vector = A / |A| = (4i + 3j) / √(4^2 + 3^2) = (4i + 3j) / 5 = (4/5)i + (3/5)j.
Correct Answer:
A
— (4/5)i + (3/5)j
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Q. What is the value of (1 + 2)^5 using the binomial theorem?
-
A.
32
-
B.
64
-
C.
128
-
D.
256
Solution
Using the binomial theorem, (1 + 2)^5 = 3^5 = 243.
Correct Answer:
B
— 64
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Q. What is the value of (1 + i)²?
-
A.
2i
-
B.
2
-
C.
0
-
D.
1 + 2i
Solution
(1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.
Correct Answer:
B
— 2
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Q. What is the value of (2 + 3i) + (4 - 2i)?
-
A.
6 + i
-
B.
6 + i
-
C.
2 + 5i
-
D.
8 + i
Solution
To add the complex numbers, we combine the real parts and the imaginary parts: (2 + 4) + (3 - 2)i = 6 + 1i = 6 + i.
Correct Answer:
A
— 6 + i
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Q. What is the value of (2x + 3)(2x - 3)?
-
A.
4x² - 9
-
B.
4x² + 9
-
C.
4x² - 6x + 9
-
D.
4x² + 6x - 9
Solution
(2x + 3)(2x - 3) = 4x² - 9.
Correct Answer:
A
— 4x² - 9
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Q. What is the value of (2x + 3)²?
-
A.
4x² + 9
-
B.
4x² + 12x + 9
-
C.
4x² + 6x + 9
-
D.
2x² + 6x + 9
Solution
(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.
Correct Answer:
B
— 4x² + 12x + 9
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Q. What is the value of (3/4) + (1/2)?
-
A.
1
-
B.
5/4
-
C.
3/2
-
D.
7/4
Solution
Convert 1/2 to 2/4, then (3/4) + (2/4) = 5/4.
Correct Answer:
B
— 5/4
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Q. What is the value of (3x + 4)(3x - 4)?
-
A.
9x² - 16
-
B.
9x² + 16
-
C.
12x² - 16
-
D.
12x² + 16
Solution
(3x + 4)(3x - 4) = (3x)² - 4² = 9x² - 16.
Correct Answer:
A
— 9x² - 16
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