Engineering Entrance
Q. What is the chemical formula for table salt? (2019)
A.
NaCl
B.
KCl
C.
CaCl2
D.
MgCl2
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Solution
Table salt is chemically known as sodium chloride, which has the formula NaCl.
Correct Answer: A — NaCl
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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)
A.
-243
B.
243
C.
-81
D.
81
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Solution
The constant term is C(5,5)(-3)^5 = -243.
Correct Answer: A — -243
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Q. What is the coefficient of x^0 in the expansion of (3x + 2)^5? (2022)
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Solution
The coefficient of x^0 is C(5,5) * (3x)^0 * (2)^5 = 1 * 32 = 32.
Correct Answer: C — 64
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Q. What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)
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Solution
The coefficient of x^1 is C(10,1)(1)^9 = 10.
Correct Answer: A — 10
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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?
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Solution
The coefficient of x^1 is given by 5C1 * (-1)^4 = 5 * 1 = 5.
Correct Answer: A — -5
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Q. What is the coefficient of x^2 in the expansion of (x + 5)^4?
A.
50
B.
100
C.
150
D.
200
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Solution
The coefficient of x^2 is C(4,2) * (5)^2 = 6 * 25 = 150.
Correct Answer: B — 100
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Q. What is the coefficient of x^2 in the expansion of (x - 2)^5?
A.
-40
B.
-20
C.
20
D.
40
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Solution
The coefficient of x^2 is given by 5C2 * (-2)^3 = 10 * (-8) = -80.
Correct Answer: A — -40
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Q. What is the coefficient of x^3 in the expansion of (5x + 2)^6? (2000) 2000
A.
600
B.
720
C.
800
D.
900
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Solution
The coefficient of x^3 is C(6,3) * (5)^3 * (2)^3 = 20 * 125 * 8 = 20000.
Correct Answer: B — 720
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^8?
A.
2800
B.
3360
C.
4000
D.
4200
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Solution
The coefficient of x^3 is given by 8C3 * (5)^5 = 56 * 3125 = 175000.
Correct Answer: B — 3360
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Q. What is the coefficient of x^3 in the expansion of (x - 1)^5? (2022)
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Solution
The coefficient of x^3 is C(5,3)(-1)^2 = 10.
Correct Answer: A — -10
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Q. What is the coefficient of x^4 in the expansion of (3x + 2)^6?
A.
540
B.
720
C.
810
D.
900
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Solution
The coefficient of x^4 is C(6,4) * (3)^4 * (2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: B — 720
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Q. What is the coefficient of x^5 in the expansion of (x + 4)^7? (2020)
A.
672
B.
6720
C.
1680
D.
840
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Solution
The coefficient of x^5 is C(7,5) * (4)^2 = 21 * 16 = 336.
Correct Answer: C — 1680
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Q. What is the coefficient of x^6 in the expansion of (x + 3)^8? (2020)
A.
56
B.
84
C.
112
D.
128
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Solution
The coefficient of x^6 is C(8,6) * (3)^2 = 28 * 9 = 252.
Correct Answer: B — 84
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Q. What is the coefficient of x^6 in the expansion of (x + 3)^9? (2020)
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Solution
The coefficient of x^6 is C(9,6)(3)^3 = 84 * 27 = 2268.
Correct Answer: B — 126
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Q. What is the coefficient of x^7 in the expansion of (2x - 3)^8? (2022)
A.
-6720
B.
6720
C.
-3360
D.
3360
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Solution
The coefficient of x^7 is C(8,7)(2)^7(-3)^1 = 8 * 128 * -3 = -3072.
Correct Answer: A — -6720
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Q. What is the color of the complex [Cu(H2O)6]2+? (2023) 2023
A.
Green
B.
Blue
C.
Red
D.
Yellow
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Solution
[Cu(H2O)6]2+ is typically blue due to the d-d transitions of the copper ion in an octahedral field.
Correct Answer: B — Blue
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Q. What is the common oxidation state of Alkaline earth metals? (2014) 2014
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Solution
Alkaline earth metals commonly exhibit a +2 oxidation state.
Correct Answer: B — +2
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Q. What is the common oxidation state of Group 1 elements? (2021)
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Solution
Group 1 elements commonly exhibit an oxidation state of +1.
Correct Answer: C — +1
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Q. What is the common oxidation state of Group 13 elements? (2021)
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Solution
Group 13 elements commonly exhibit a +3 oxidation state due to the loss of three valence electrons.
Correct Answer: C — +3
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Q. What is the common oxidation state of nitrogen in ammonia (NH3)? (2023) 2023
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Solution
In ammonia (NH3), nitrogen has an oxidation state of -3.
Correct Answer: A — -3
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Q. What is the concentration in mol/L of a solution made by dissolving 58.5 grams of NaCl in 1 liter of water? (Molar mass of NaCl = 58.5 g/mol) (2023) 2023
A.
1 M
B.
0.5 M
C.
2 M
D.
0.25 M
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Solution
Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mole. Molarity = 1 mole / 1 L = 1 M.
Correct Answer: A — 1 M
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Q. What is the concentration of a solution if 5 g of NaOH is dissolved in 250 mL of water? (2020)
A.
0.5 M
B.
1 M
C.
0.2 M
D.
0.1 M
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Solution
Moles of NaOH = 5 g / 40 g/mol = 0.125 mol. Molarity = 0.125 mol / 0.25 L = 0.5 M.
Correct Answer: B — 1 M
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Q. What is the concentration of H+ ions in a solution with pH 3? (2019) 2019
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
1 M
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Solution
Concentration of H+ = 10^(-pH) = 10^(-3) = 0.001 M.
Correct Answer: B — 0.01 M
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Q. What is the concentration of H+ ions in a solution with pH 4?
A.
0.0001 M
B.
0.01 M
C.
0.1 M
D.
1 M
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Solution
[H+] = 10^(-pH) = 10^(-4) = 0.0001 M.
Correct Answer: A — 0.0001 M
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Q. What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)
A.
(3, 2)
B.
(2, 3)
C.
(3, 3)
D.
(4, 2)
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Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer: A — (3, 2)
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Q. What is the coordination number of the central metal ion in the complex ion [Co(NH3)6]Cl3? (2021)
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Solution
In the complex ion [Co(NH3)6]Cl3, the central metal ion Co is surrounded by 6 ammonia (NH3) ligands, which gives it a coordination number of 6.
Correct Answer: C — 6
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Q. What is the coordination number of the complex ion [Co(NH3)5Cl]Cl2? (2023)
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Solution
In the complex [Co(NH3)5Cl]Cl2, cobalt is surrounded by five ammonia ligands and one chloride ligand, giving it a coordination number of 6.
Correct Answer: C — 6
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Q. What is the coordination number of the complex ion [Co(NH3)6]Cl3? (2022) 2022
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Solution
The coordination number is determined by the number of ligands attached to the central metal ion. Here, Co is surrounded by 6 NH3 ligands.
Correct Answer: B — 6
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Q. What is the coordination number of the metal ion in the complex [Co(NH3)5Cl]Cl2? (2023)
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Solution
In the complex [Co(NH3)5Cl]Cl2, cobalt is surrounded by five ammonia ligands and one chloride ligand, giving it a coordination number of 6.
Correct Answer: C — 6
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Q. What is the cross product of vectors A = i + j and B = j + k? (2022)
A.
i + k
B.
i - k
C.
j - i
D.
k - j
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Solution
A × B = |i j k| |1 1 0| |0 1 1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.
Correct Answer: A — i + k
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