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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)
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A.
√3/2
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B.
2/√3
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C.
2
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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
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B.
1/2
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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
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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 5th term in the expansion of (3x - 2)^6? (2023)
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A.
-540
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B.
540
-
C.
720
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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^5 in the expansion of (x + 2)^7?
Solution
The coefficient of x^5 is given by 7C5 * (2)^2 = 21 * 4 = 84.
Correct Answer: C — 56
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Q. What is the value of the determinant of the matrix B = [[2, 3], [5, 7]]? (2020)
Solution
Determinant of B = (2*7) - (3*5) = 14 - 15 = -1.
Correct Answer: C — 11
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Q. What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)
Solution
Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.
Correct Answer: A — 10
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Q. What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.
Correct Answer: B — 56
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Q. What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)
-
A.
112
-
B.
128
-
C.
256
-
D.
64
Solution
The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.
Correct Answer: B — 128
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Q. What is the value of x where f(x) = x^3 - 3x has a local maximum? (2022)
Solution
f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.
Correct Answer: C — 1
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Q. What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \)? (2023)
Solution
The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).
Correct Answer: A — 1
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Q. What is the van 't Hoff factor (i) for a non-electrolyte solute? (2023)
Solution
The van 't Hoff factor (i) for a non-electrolyte solute is 1, as it does not dissociate into ions.
Correct Answer: A — 1
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