Q. What is the capital city of Australia? (2021)
-
A.
Sydney
-
B.
Canberra
-
C.
Melbourne
-
D.
Brisbane
Solution
The capital city of Australia is Canberra.
Correct Answer:
B
— Canberra
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Q. What is the capital city of the Indian state of Maharashtra?
-
A.
Mumbai
-
B.
Pune
-
C.
Nagpur
-
D.
Nashik
Solution
Mumbai is the capital city of the Indian state of Maharashtra.
Correct Answer:
A
— Mumbai
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Q. What is the capital of India?
-
A.
Mumbai
-
B.
New Delhi
-
C.
Kolkata
-
D.
Chennai
Solution
The capital of India is New Delhi.
Correct Answer:
B
— New Delhi
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Q. What is the capital of the Indian state of Kerala?
-
A.
Kochi
-
B.
Thiruvananthapuram
-
C.
Kozhikode
-
D.
Kottayam
Solution
The capital of Kerala is Thiruvananthapuram.
Correct Answer:
B
— Thiruvananthapuram
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Q. What is the capital of the Indian state of Maharashtra?
-
A.
Mumbai
-
B.
Pune
-
C.
Nagpur
-
D.
Nashik
Solution
Mumbai is the capital of the Indian state of Maharashtra.
Correct Answer:
A
— Mumbai
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Q. What is the capital of the Indian state of Tamil Nadu?
-
A.
Chennai
-
B.
Coimbatore
-
C.
Madurai
-
D.
Tiruchirappalli
Solution
Chennai is the capital of the Indian state of Tamil Nadu.
Correct Answer:
A
— Chennai
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Q. What is the change in internal energy of a gas that absorbs 500 J of heat and does 200 J of work? (2022)
-
A.
300 J
-
B.
500 J
-
C.
700 J
-
D.
1000 J
Solution
Using the first law of thermodynamics: ΔU = Q - W = 500 J - 200 J = 300 J.
Correct Answer:
A
— 300 J
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Q. What is the change in internal energy of a gas that absorbs 500 J of heat and does 200 J of work on the surroundings? (2023)
-
A.
300 J
-
B.
500 J
-
C.
700 J
-
D.
900 J
Solution
ΔU = Q - W = 500 J - 200 J = 300 J.
Correct Answer:
A
— 300 J
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Q. What is the change in internal energy of a system if 500 J of work is done on it and 200 J of heat is lost? (2023)
-
A.
300 J
-
B.
500 J
-
C.
700 J
-
D.
900 J
Solution
Change in internal energy (ΔU) = Q - W = -200 J - 500 J = -300 J.
Correct Answer:
A
— 300 J
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Q. What is the characteristic polynomial of the matrix E = [[2, 1], [1, 2]]? (2021)
-
A.
λ^2 - 3λ + 1
-
B.
λ^2 - 5λ + 4
-
C.
λ^2 - 4λ + 3
-
D.
λ^2 - 2λ + 1
Solution
The characteristic polynomial is det(E - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 1.
Correct Answer:
A
— λ^2 - 3λ + 1
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Q. What is the characteristic polynomial of the matrix G = [[2, 1], [1, 2]]? (2020)
-
A.
λ^2 - 3λ + 1
-
B.
λ^2 - 5λ + 4
-
C.
λ^2 - 2λ + 1
-
D.
λ^2 - 4λ + 4
Solution
The characteristic polynomial is given by det(G - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.
Correct Answer:
A
— λ^2 - 3λ + 1
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Q. What is the chemical formula for sulfuric acid? (2023)
-
A.
H2SO4
-
B.
H2SO3
-
C.
H2S
-
D.
SO2
Solution
The chemical formula for sulfuric acid is H2SO4, which consists of two hydrogen atoms, one sulfur atom, and four oxygen atoms.
Correct Answer:
A
— H2SO4
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Q. What is the circumference of a circle with a diameter of 14 cm? (2023)
-
A.
22 cm
-
B.
28 cm
-
C.
44 cm
-
D.
56 cm
Solution
The circumference C of a circle is given by C = π * diameter. Here, C = π * 14 cm ≈ 3.14 * 14 ≈ 44 cm.
Correct Answer:
B
— 28 cm
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Q. What is the circumference of a circle with a radius of 7 cm? (2019)
-
A.
14π cm
-
B.
21π cm
-
C.
7π cm
-
D.
28π cm
Solution
Circumference = 2 * π * radius = 2 * π * 7 = 14π cm
Correct Answer:
A
— 14π cm
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Q. What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)
-
A.
2 cm
-
B.
3 cm
-
C.
4 cm
-
D.
5 cm
Solution
For a right triangle, the circumradius R = hypotenuse/2 = 5/2 = 2.5 cm.
Correct Answer:
D
— 5 cm
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Q. What is the coefficient of O2 when balancing the equation: C4H10 + O2 → CO2 + H2O? (2023)
Solution
The balanced equation is C4H10 + 6O2 → 4CO2 + 5H2O, so the coefficient of O2 is 6.
Correct Answer:
B
— 6
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Q. What is the coefficient of x^0 in the expansion of (x - 1)^5?
Solution
The coefficient of x^0 in (x - 1)^5 is given by 5C5 * (-1)^5 = -1.
Correct Answer:
C
— -5
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Q. What is the coefficient of x^2 in the expansion of (2x + 5)^4?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
Using the binomial theorem, the coefficient of x^2 in (2x + 5)^4 is given by 4C2 * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 60
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Q. What is the coefficient of x^2 in the expansion of (2x - 5)^5? (2019)
-
A.
-300
-
B.
-600
-
C.
600
-
D.
300
Solution
The coefficient of x^2 in (2x - 5)^5 is given by 5C2 * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer:
B
— -600
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Q. What is the coefficient of x^2 in the expansion of (3x + 4)^5?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
The coefficient of x^2 in (3x + 4)^5 is C(5, 2) * (3)^2 * (4)^3 = 10 * 9 * 64 = 5760.
Correct Answer:
B
— 80
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Q. What is the coefficient of x^3 in the expansion of (3x + 2)^5? (2023)
-
A.
90
-
B.
180
-
C.
270
-
D.
360
Solution
The coefficient of x^3 in (3x + 2)^5 is given by 5C3 * (3)^3 * (2)^2 = 10 * 27 * 4 = 1080.
Correct Answer:
B
— 180
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^6?
-
A.
150
-
B.
300
-
C.
450
-
D.
600
Solution
The coefficient of x^3 in (x + 5)^6 is C(6, 3) * (5)^3 = 20 * 125 = 2500.
Correct Answer:
B
— 300
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Q. What is the coefficient of x^4 in the expansion of (x + 3)^6?
-
A.
81
-
B.
162
-
C.
243
-
D.
324
Solution
The coefficient of x^4 in (x + 3)^6 is C(6, 4) * 3^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
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Q. What is the conjugate base of sulfuric acid (H2SO4)?
-
A.
HSO4-
-
B.
SO4^2-
-
C.
H3O+
-
D.
None of the above
Solution
The conjugate base of sulfuric acid (H2SO4) is HSO4-.
Correct Answer:
B
— SO4^2-
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Q. What is the conjugate of the complex number z = 7 - 4i? (2021)
-
A.
7 + 4i
-
B.
7 - 4i
-
C.
-7 + 4i
-
D.
-7 - 4i
Solution
The conjugate of z is given by z* = 7 + 4i.
Correct Answer:
A
— 7 + 4i
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Q. What is the continuity of the function f(x) = sqrt(x) at x = 0? (2022)
-
A.
Continuous
-
B.
Not continuous
-
C.
Only left continuous
-
D.
Only right continuous
Solution
The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.
Correct Answer:
A
— Continuous
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Q. What is the critical angle for a glass medium (n = 1.5) when light travels from glass to air? (2020)
-
A.
30 degrees
-
B.
41.8 degrees
-
C.
48.6 degrees
-
D.
60 degrees
Solution
Using the formula for critical angle: sin(c) = n2/n1, we find c = sin^(-1)(1/1.5) ≈ 41.8 degrees.
Correct Answer:
B
— 41.8 degrees
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Q. What is the critical angle for light traveling from glass (n = 1.5) to air (n = 1)? (2019)
-
A.
30 degrees
-
B.
41.8 degrees
-
C.
48.6 degrees
-
D.
60 degrees
Solution
Using the formula sin(c) = n2/n1, we find sin(c) = 1/1.5, thus c = sin^(-1)(2/3) ≈ 41.8 degrees.
Correct Answer:
B
— 41.8 degrees
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Q. What is the critical point of f(x) = x^2 - 4x + 4? (2022)
Solution
Set f'(x) = 2x - 4 = 0; solving gives x = 2.
Correct Answer:
B
— 2
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Q. What is the critical point of the function f(x) = x^2 - 4x + 4? (2022)
Solution
Find f'(x) = 2x - 4. Set f'(x) = 0, giving 2x - 4 = 0, hence x = 2.
Correct Answer:
B
— 2
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