Q. What is the value of 12 ÷ (2 + 4)? (2018)
Solution
12 ÷ (2 + 4) = 12 ÷ 6 = 2.
Correct Answer: B — 3
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Q. What is the value of 12 ÷ 4 × 3? (2023)
Solution
12 ÷ 4 = 3, then 3 × 3 = 9.
Correct Answer: B — 6
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Q. What is the value of 12% of 250? (2020)
Solution
12% of 250 = (12/100) * 250 = 30.
Correct Answer: A — 30
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Q. What is the value of 15% of 200? (2014)
Solution
15% of 200 = (15/100) * 200 = 30.
Correct Answer: A — 30
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Q. What is the value of 5 × (6 + 4)? (2016)
Solution
6 + 4 = 10, then 5 × 10 = 50.
Correct Answer: A — 50
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Q. What is the value of 5! (5 factorial)? (2016) 2016
-
A.
120
-
B.
60
-
C.
100
-
D.
150
Solution
5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer: A — 120
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Q. What is the value of 5! (5 factorial)? (2023) 2023
-
A.
120
-
B.
100
-
C.
150
-
D.
110
Solution
5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer: A — 120
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Q. What is the value of 7^2 + 3^2? (2023) 2023
Solution
7^2 = 49 and 3^2 = 9, so 49 + 9 = 58.
Correct Answer: A — 58
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Q. What is the value of 8 × (2 + 3)? (2023) 2023
Solution
2 + 3 = 5, so 8 × 5 = 40.
Correct Answer: A — 40
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Q. What is the value of 9 - 3 × 2? (2015)
Solution
Using BODMAS, 3 × 2 = 6, so 9 - 6 = 3.
Correct Answer: B — 6
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Q. What is the value of 9 × 9? (2014)
Q. What is the value of 9^2 - 4^2? (2016)
Solution
9^2 = 81 and 4^2 = 16, so 81 - 16 = 65.
Correct Answer: A — 65
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Q. What is the value of cot(45°)?
Solution
cot(45°) = 1/tan(45°) = 1/1 = 1
Correct Answer: B — 1
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Q. What is the value of cot(90°)? (2018)
-
A.
0
-
B.
1
-
C.
undefined
-
D.
∞
Solution
cot(90°) = 1/tan(90°) = 1/0 = undefined.
Correct Answer: C — undefined
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Q. What is the value of f''(x) for f(x) = 4x^3 - 6x^2 + 2 at x = 1? (2022)
Solution
f''(x) = 24x - 12. At x = 1, f''(1) = 24(1) - 12 = 12.
Correct Answer: B — 6
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Q. What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)
Solution
The product of the roots is k = 2 * 4 = 8.
Correct Answer: B — 12
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Q. What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022)
Solution
For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, thus k < -8 or k > 8.
Correct Answer: A — -8
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Q. What is the value of k if the equation x² - 4x + k = 0 has no real roots? (2021)
Solution
For no real roots, the discriminant must be less than zero: (-4)² - 4*1*k < 0, hence k > 4.
Correct Answer: B — 6
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Q. What is the value of k if the equation x² - kx + 16 = 0 has roots 4 and 4? (2021)
Solution
Since the roots are equal, k = 4 + 4 = 8.
Correct Answer: A — 8
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Q. What is the value of sec(0°)?
Solution
sec(0°) = 1/cos(0°) = 1/1 = 1
Correct Answer: B — 1
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Q. What is the value of sec(30°)? (2015)
-
A.
√3/2
-
B.
2/√3
-
C.
2
-
D.
√3
Solution
sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3 = √3
Correct Answer: D — √3
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Q. What is the value of sec(45°)? (2019)
Solution
sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.
Correct Answer: B — √2
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Q. What is the value of sin(45°)? (2016)
-
A.
1/√2
-
B.
1/2
-
C.
√3/2
-
D.
1
Solution
sin(45°) = 1/√2
Correct Answer: A — 1/√2
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Q. What is the value of tan(0°)? (2018)
-
A.
0
-
B.
1
-
C.
undefined
-
D.
∞
Q. What is the value of tan(90°)? (2022)
-
A.
0
-
B.
1
-
C.
undefined
-
D.
∞
Solution
tan(90°) is undefined.
Correct Answer: C — undefined
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Q. What is the value of the 3rd term in the expansion of (3x - 4)^5? (2020)
-
A.
-240
-
B.
240
-
C.
-180
-
D.
180
Solution
The 3rd term is C(5,2) * (3x)^3 * (-4)^2 = 10 * 27x^3 * 16 = -240.
Correct Answer: A — -240
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Q. What is the value of the 5th term in the expansion of (3x - 2)^6? (2023)
-
A.
-540
-
B.
540
-
C.
720
-
D.
360
Solution
The 5th term is given by C(6,4) * (3x)^4 * (-2)^2 = 15 * 81 * 4 = -4860.
Correct Answer: A — -540
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Q. What is the value of the azimuthal quantum number (l) for a d orbital? (2021) 2021
Solution
The azimuthal quantum number l for d orbitals is 2.
Correct Answer: C — 2
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Q. What is the value of the azimuthal quantum number (l) for a p-orbital? (2015)
Solution
The azimuthal quantum number (l) for a p-orbital is 1.
Correct Answer: B — 1
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Q. What is the value of the coefficient of x^4 in the expansion of (x - 2)^6? (2023)
-
A.
-15
-
B.
-60
-
C.
-90
-
D.
-120
Solution
The coefficient of x^4 is C(6,4) * (-2)^2 = 15 * 4 = -60.
Correct Answer: B — -60
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