Engineering Entrance
Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)
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Solution
For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.
Correct Answer: B — -4
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Q. How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
A.
5040
B.
10000
C.
9000
D.
7200
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Solution
The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.
Correct Answer: A — 5040
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Q. How many different 4-digit PINs can be formed using the digits 0-9 without repetition?
A.
5040
B.
9000
C.
10000
D.
1000
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Solution
The number of 4-digit PINs is P(10, 4) = 5040.
Correct Answer: A — 5040
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Q. How many different ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
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Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
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Q. How many different ways can the letters of the word 'MATH' be arranged?
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Solution
The number of arrangements of the letters in 'MATH' is 4! = 24.
Correct Answer: B — 24
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Q. How many grams are in 0.5 moles of glucose (C6H12O6)? (2023)
A.
90 g
B.
180 g
C.
45 g
D.
60 g
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Solution
Molar mass of C6H12O6 = 6*12 + 12*1 + 6*16 = 180 g/mol. Mass = 0.5 moles x 180 g/mol = 90 g.
Correct Answer: A — 90 g
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Q. How many grams are in 4 moles of potassium chloride (KCl)? (2022)
A.
74 g
B.
148 g
C.
296 g
D.
37 g
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Solution
Molar mass of KCl = 39 + 35.5 = 74.5 g/mol. Mass = 4 moles x 74.5 g/mol = 298 g.
Correct Answer: C — 296 g
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Q. How many grams are in 4 moles of sulfuric acid (H2SO4)? (2023)
A.
196 g
B.
98 g
C.
392 g
D.
294 g
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Solution
Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 4 moles x 98 g/mol = 392 g.
Correct Answer: C — 392 g
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Q. How many grams of KCl are needed to prepare 0.5 M solution in 500 mL of water? (2023)
A.
14.9 g
B.
7.45 g
C.
29.8 g
D.
3.73 g
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Solution
Molarity = moles/volume(L). Moles = 0.5 mol/L * 0.5 L = 0.25 mol. Mass = moles * molar mass = 0.25 mol * 74.5 g/mol = 18.625 g.
Correct Answer: B — 7.45 g
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Q. How many grams of KCl are needed to prepare 250 mL of a 0.5 M solution? (2023) 2023
A.
7.45 g
B.
12.5 g
C.
9.25 g
D.
5.25 g
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Solution
Molar mass of KCl = 74.55 g/mol. Grams = Molarity * Volume (L) * Molar mass = 0.5 M * 0.25 L * 74.55 g/mol = 9.31 g.
Correct Answer: A — 7.45 g
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Q. How many grams of KCl are needed to prepare 250 mL of a 2 M solution? (2023)
A.
37.25 g
B.
50 g
C.
75 g
D.
25 g
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Solution
Molar mass of KCl = 74.55 g/mol. Grams = moles × molar mass = 0.5 moles × 74.55 g/mol = 37.25 g.
Correct Answer: A — 37.25 g
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Q. How many grams of KCl are needed to prepare 250 mL of a 2 M solution? (Molar mass of KCl = 74.5 g/mol) (2023)
A.
37.25 g
B.
74.5 g
C.
18.625 g
D.
9.25 g
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Solution
Grams = moles × molar mass = (2 moles/L × 0.25 L) × 74.5 g/mol = 37.25 g.
Correct Answer: A — 37.25 g
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Q. How many liters of a 0.5 M NaOH solution are needed to obtain 1 mole of NaOH? (2023)
A.
1 L
B.
2 L
C.
0.5 L
D.
0.25 L
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Solution
Volume = moles / molarity = 1 mole / 0.5 M = 2 L.
Correct Answer: A — 1 L
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Q. How many liters of a 0.5 M solution contain 2 moles of solute? (2023)
A.
2 L
B.
4 L
C.
1 L
D.
0.5 L
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Solution
Volume = moles / molarity = 2 moles / 0.5 M = 4 L
Correct Answer: B — 4 L
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Q. How many liters of a 3 M solution can be made from 6 moles of solute? (2023)
A.
1 L
B.
2 L
C.
3 L
D.
4 L
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Solution
Volume = moles / molarity = 6 moles / 3 M = 2 L.
Correct Answer: B — 2 L
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Q. How many molecules are in 0.1 moles of oxygen gas (O2)? (2021)
A.
6.022 x 10^22
B.
6.022 x 10^23
C.
1.2044 x 10^23
D.
3.011 x 10^23
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Solution
Number of molecules = moles x Avogadro's number = 0.1 moles x 6.022 x 10^23 molecules/mole = 6.022 x 10^22 molecules.
Correct Answer: A — 6.022 x 10^22
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Q. How many molecules are in 0.25 moles of oxygen gas (O2)? (2022)
A.
3.011 x 10^23
B.
6.022 x 10^22
C.
1.2044 x 10^23
D.
1.5055 x 10^23
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Solution
Number of molecules = moles x Avogadro's number = 0.25 moles x 6.022 x 10^23 molecules/mole = 1.5055 x 10^23 molecules.
Correct Answer: B — 6.022 x 10^22
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Q. How many molecules are present in 2 moles of water (H2O)? (2022) 2022
A.
6.022 x 10^23
B.
1.2044 x 10^24
C.
3.011 x 10^23
D.
1.2044 x 10^23
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Solution
Number of molecules = moles x Avogadro's number = 2 moles x 6.022 x 10^23 molecules/mole = 1.2044 x 10^24 molecules.
Correct Answer: B — 1.2044 x 10^24
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Q. How many moles are in 100 grams of NaOH? (2022)
A.
2.5
B.
1.25
C.
0.5
D.
3
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Solution
Molar mass of NaOH = 23 + 16 + 1 = 40 g/mol. Number of moles = mass/molar mass = 100 g / 40 g/mol = 2.5 moles.
Correct Answer: B — 1.25
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Q. How many moles are in 32 grams of O2? (2021)
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Solution
Molar mass of O2 = 16*2 = 32 g/mol. Number of moles = mass/molar mass = 32g/32g/mol = 1 mole.
Correct Answer: A — 1
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Q. How many moles of solute are present in 500 mL of a 0.2 M solution? (2021) 2021
A.
0.1 moles
B.
0.5 moles
C.
0.2 moles
D.
0.25 moles
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Solution
Moles = Molarity * Volume (L) = 0.2 M * 0.5 L = 0.1 moles.
Correct Answer: A — 0.1 moles
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Q. How many orbitals are present in the d-subshell? (2023)
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Solution
The d-subshell has 5 orbitals.
Correct Answer: C — 5
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Q. How many orbitals are present in the p subshell? (2023)
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Solution
The p subshell has 3 orbitals (px, py, pz).
Correct Answer: C — 3
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Q. How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?
A.
100
B.
150
C.
200
D.
250
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Solution
The number of ways is 5C2 * 6C3 = 10 * 20 = 200.
Correct Answer: B — 150
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Q. How many ways can 2 students be selected from a group of 5? (2019)
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Solution
The number of ways to select 2 students from 5 is given by 5C2 = 10.
Correct Answer: A — 10
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Q. How many ways can 3 books be selected from a shelf of 10 books? (2022)
A.
120
B.
210
C.
100
D.
30
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Solution
The number of ways to select 3 books from 10 is given by 10C3 = 120.
Correct Answer: B — 210
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Q. How many ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
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Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
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Q. How many ways can 3 different trophies be awarded to 5 students? (2022)
A.
60
B.
100
C.
120
D.
30
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Solution
The number of ways to award 3 trophies to 5 students is given by P(5,3) = 5! / (5-3)! = 60.
Correct Answer: C — 120
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Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)
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Solution
The number of ways to choose 3 balls from 8 is given by 8C3 = 56.
Correct Answer: A — 56
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Q. How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?
A.
720
B.
1000
C.
1200
D.
100
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Solution
The number of ways to award 3 prizes is P(10, 3) = 720.
Correct Answer: A — 720
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