Engineering Entrance
Q. For the function f(x) = 3x^2 - 12x + 7, find the minimum value. (2022)
Show solution
Solution
The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 7 = -5.
Correct Answer: B — -4
Learn More →
Q. For the function f(x) = 3x^2 - 12x + 9, find the vertex. (2021)
A.
(2, 3)
B.
(3, 0)
C.
(0, 9)
D.
(1, 6)
Show solution
Solution
The vertex occurs at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 9 = 3.
Correct Answer: A — (2, 3)
Learn More →
Q. For the function f(x) = x^2 + 2x, find the local maximum. (2022)
Show solution
Solution
f'(x) = 2x + 2. Setting f'(x) = 0 gives x = -1. f(-1) = 1.
Correct Answer: A — -1
Learn More →
Q. For the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find det(E). (2021)
Show solution
Solution
Using the determinant formula, det(E) = 1*(1*0 - 4*6) - 2*(0*0 - 4*5) + 3*(0*6 - 1*5) = 1*(-24) - 2*(-20) - 15 = -24 + 40 - 15 = 1.
Correct Answer: A — -24
Learn More →
Q. For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)
Show solution
Solution
Determinant of E = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer: A — 0
Learn More →
Q. For which value of m does the equation x² - mx + 9 = 0 have roots 3 and 3? (2023)
Show solution
Solution
The sum of the roots is 3 + 3 = 6, hence m = 6.
Correct Answer: A — 6
Learn More →
Q. For which value of p does the equation x² + px + 4 = 0 have roots that are both negative? (2022)
Show solution
Solution
For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.
Correct Answer: C — -4
Learn More →
Q. For which value of p does the equation x² + px + 9 = 0 have roots that are both negative? (2021)
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
The number of 4-digit PINs is P(10, 4) = 5040.
Correct Answer: A — 5040
Learn More →
Q. How many different ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
Show solution
Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
Learn More →
Q. How many different ways can the letters of the word 'MATH' be arranged?
Show solution
Solution
The number of arrangements of the letters in 'MATH' is 4! = 24.
Correct Answer: B — 24
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Grams = moles × molar mass = (2 moles/L × 0.25 L) × 74.5 g/mol = 37.25 g.
Correct Answer: A — 37.25 g
Learn More →
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
Show solution
Solution
Volume = moles / molarity = 1 mole / 0.5 M = 2 L.
Correct Answer: A — 1 L
Learn More →
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
Show solution
Solution
Volume = moles / molarity = 2 moles / 0.5 M = 4 L
Correct Answer: B — 4 L
Learn More →
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
Show solution
Solution
Volume = moles / molarity = 6 moles / 3 M = 2 L.
Correct Answer: B — 2 L
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
Q. How many moles are in 100 grams of NaOH? (2022)
A.
2.5
B.
1.25
C.
0.5
D.
3
Show solution
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
Learn More →
Q. How many moles are in 32 grams of O2? (2021)
Show solution
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
Learn More →
Q. How many orbitals are present in the d-subshell? (2023)
Show solution
Solution
The d-subshell has 5 orbitals.
Correct Answer: C — 5
Learn More →
Q. How many orbitals are present in the p subshell? (2023)
Show solution
Solution
The p subshell has 3 orbitals (px, py, pz).
Correct Answer: C — 3
Learn More →
Q. How many ways can 2 students be selected from a group of 5? (2019)
Show solution
Solution
The number of ways to select 2 students from 5 is given by 5C2 = 10.
Correct Answer: A — 10
Learn More →
Q. How many ways can 3 books be selected from a shelf of 10 books? (2022)
A.
120
B.
210
C.
100
D.
30
Show solution
Solution
The number of ways to select 3 books from 10 is given by 10C3 = 120.
Correct Answer: B — 210
Learn More →
Q. How many ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
Show solution
Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
Learn More →
Showing 151 to 180 of 783 (27 Pages)
