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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Q. What is the value of the coefficient of x^5 in the expansion of (x + 1/2)^8?
-
A.
56
-
B.
112
-
C.
128
-
D.
64
Solution
The coefficient of x^5 is given by 8C5 * (1/2)^3 = 56 * 1/8 = 7.
Correct Answer: A — 56
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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 discriminant for the equation 3x² + 6x + 2 = 0? (2020)
Solution
The discriminant D = b² - 4ac = 6² - 4*3*2 = 36 - 24 = 12.
Correct Answer: B — 4
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Q. What is the value of the discriminant for the equation 3x² - 12x + 12 = 0? (2020)
Solution
The discriminant D = b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.
Correct Answer: A — 0
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Q. What is the value of the discriminant for the equation x² - 2x + 1 = 0? (2022)
Solution
The discriminant is b² - 4ac = (-2)² - 4*1*1 = 0.
Correct Answer: A — 0
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Q. What is the value of the discriminant for the equation x² - 4x + 4 = 0? (2022)
Solution
The discriminant is b² - 4ac = (-4)² - 4*1*4 = 0.
Correct Answer: A — 0
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Q. What is the value of the gravitational constant (G) in SI units? (2023)
-
A.
6.67 x 10^-11 N m²/kg²
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B.
9.81 m/s²
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C.
3.00 x 10^8 m/s
-
D.
1.60 x 10^-19 C
Solution
The gravitational constant (G) is 6.67 x 10^-11 N m²/kg².
Correct Answer: A — 6.67 x 10^-11 N m²/kg²
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Q. What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^4 is C(8,4) * (1/2)^4 = 70 * 1/16 = 4.375.
Correct Answer: A — 70
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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 \( \begin{vmatrix} 2 & 1 \\ 3 & 4 \end{vmatrix} \)? (2022)
Solution
The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).
Correct Answer: A — 5
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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 value of \( |H| \) for \( H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \)? (2021)
Solution
The determinant of the identity matrix is always 1.
Correct Answer: B — 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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Q. What is the van 't Hoff factor (i) for a solution of glucose (C6H12O6)? (2023)
Solution
Glucose does not dissociate in solution, so the van 't Hoff factor (i) = 1.
Correct Answer: A — 1
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Q. What is the van 't Hoff factor (i) for a strong electrolyte like Na2SO4 in solution? (2023)
Solution
Na2SO4 dissociates into 3 ions (2 Na⁺ and 1 SO4²⁻), so i = 3.
Correct Answer: C — 3
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Q. What is the vapor pressure of a solution containing 1 mole of solute in 10 moles of solvent, assuming ideal behavior? (2019)
-
A.
0.1 P0
-
B.
0.9 P0
-
C.
0.5 P0
-
D.
0.2 P0
Solution
Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (10 / 11) * P0 ≈ 0.909 P0.
Correct Answer: B — 0.9 P0
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Q. What is the vapor pressure of a solution containing 1 mole of solute in 9 moles of solvent, assuming ideal behavior? (2019)
-
A.
0.1 P0
-
B.
0.9 P0
-
C.
0.5 P0
-
D.
0.2 P0
Solution
Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (9 / 10) * P0 = 0.9 P0.
Correct Answer: B — 0.9 P0
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Q. What is the vapor pressure of a solution containing 2 moles of solute and 3 moles of solvent, assuming ideal behavior? (2022)
-
A.
0.4 P0
-
B.
0.6 P0
-
C.
0.2 P0
-
D.
0.8 P0
Solution
Vapor pressure of solution = (moles of solvent / total moles) * P0 = (3 / (2 + 3)) * P0 = 0.6 P0.
Correct Answer: B — 0.6 P0
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Q. What is the vapor pressure of a solution containing 2 moles of solute and 4 moles of solvent compared to pure solvent? (2022)
-
A.
1/3
-
B.
1/2
-
C.
2/3
-
D.
1/4
Solution
Vapor pressure lowering = (moles of solute / total moles) = 2 / (2 + 4) = 2/6 = 1/3. Thus, vapor pressure is 1/2 of pure solvent.
Correct Answer: B — 1/2
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Q. What is the vapor pressure of a solution containing 2 moles of solute and 4 moles of solvent, assuming ideal behavior? (2022)
-
A.
0.33 P0
-
B.
0.50 P0
-
C.
0.67 P0
-
D.
0.75 P0
Solution
Vapor pressure = (moles of solvent / total moles) * P0 = (4 / (2 + 4)) * P0 = (4/6) * P0 = 0.67 P0.
Correct Answer: C — 0.67 P0
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Q. What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)
-
A.
(2, -1)
-
B.
(2, 1)
-
C.
(1, 2)
-
D.
(3, 0)
Solution
The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.
Correct Answer: A — (2, -1)
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