Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?
-
A.
108
-
B.
72
-
C.
36
-
D.
144
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: B — 72
Learn More →
Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (3)^2 = 15 * 16 * 9 = 2160.
Correct Answer: B — 720
Learn More →
Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?
-
A.
108
-
B.
72
-
C.
36
-
D.
144
Solution
The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: A — 108
Learn More →
Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?
-
A.
300
-
B.
600
-
C.
450
-
D.
500
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer: A — 300
Learn More →
Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
-
A.
-9
-
B.
-18
-
C.
-27
-
D.
-6
Solution
The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.
Correct Answer: B — -18
Learn More →
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
-
A.
-15
-
B.
-30
-
C.
30
-
D.
15
Solution
The coefficient of x^1 is C(5,1) * (2)^1 * (-3)^4 = 5 * 2 * 81 = 810.
Correct Answer: B — -30
Learn More →
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^2?
-
A.
-90
-
B.
-120
-
C.
-150
-
D.
-180
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-3)^3 = 10 * 4 * (-27) = -1080.
Correct Answer: B — -120
Learn More →
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^3?
-
A.
-540
-
B.
-720
-
C.
-960
-
D.
-1080
Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = -720.
Correct Answer: C — -960
Learn More →
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^4?
-
A.
-90
-
B.
-120
-
C.
-150
-
D.
-180
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer: B — -120
Learn More →
Q. In the expansion of (x + 1/x)^6, what is the coefficient of x^0?
Solution
The coefficient of x^0 in (x + 1/x)^6 is given by 6C3 = 20.
Correct Answer: C — 20
Learn More →
Q. In the expansion of (x + 1/x)^8, what is the coefficient of x^4?
Solution
The coefficient of x^4 is C(8,4) = 70.
Correct Answer: B — 56
Learn More →
Q. In the expansion of (x + 2)^5, what is the coefficient of x^3?
Solution
The coefficient of x^3 is C(5,3) * (2)^2 = 10 * 4 = 40.
Correct Answer: B — 60
Learn More →
Q. In the expansion of (x + 2)^6, what is the term containing x^4?
-
A.
240
-
B.
360
-
C.
720
-
D.
480
Solution
The term containing x^4 is C(6,4) * (2)^2 * (x)^4 = 15 * 4 * x^4 = 60x^4.
Correct Answer: C — 720
Learn More →
Q. In the expansion of (x + 2)^7, what is the term containing x^5?
-
A.
672
-
B.
6720
-
C.
67200
-
D.
672000
Solution
The term containing x^5 is given by 7C5 * (2)^2 * (x)^5 = 21 * 4 * x^5 = 84x^5. Thus, the term is 84x^5.
Correct Answer: B — 6720
Learn More →
Q. In the expansion of (x + 5)^6, what is the coefficient of x^3?
-
A.
150
-
B.
200
-
C.
250
-
D.
300
Solution
The coefficient of x^3 is C(6, 3) * 5^3 = 20 * 125 = 250.
Correct Answer: B — 200
Learn More →
Q. In the expansion of (x - 2)^6, what is the coefficient of x^4?
Solution
The coefficient of x^4 is given by C(6,4) * (-2)^2 = 15 * 4 = 60.
Correct Answer: C — 90
Learn More →
Q. In the expansion of (x - 2)^8, what is the coefficient of x^5?
-
A.
-2240
-
B.
-1280
-
C.
-1120
-
D.
-960
Solution
The coefficient of x^5 is C(8,5) * (-2)^3 = 56 * (-8) = -448.
Correct Answer: A — -2240
Learn More →
Q. Solve for x: 3(x - 2) = 2(x + 1).
Solution
Expanding both sides gives 3x - 6 = 2x + 2. Rearranging gives x = 8.
Correct Answer: B — 0
Learn More →
Q. Solve for x: log_3(x + 1) - log_3(x - 1) = 1.
Solution
Using properties of logarithms, log_3((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 3 => x + 1 = 3(x - 1) => x = 2.
Correct Answer: A — 2
Learn More →
Q. Solve for x: log_3(x) = 2.
Solution
log_3(x) = 2 implies x = 3^2 = 9.
Correct Answer: B — 9
Learn More →
Q. Solve for x: log_5(x + 1) - log_5(x - 1) = 1.
Solution
Using properties of logarithms: log_5((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 5 => x + 1 = 5(x - 1) => 4x = 6 => x = 2.
Correct Answer: A — 2
Learn More →
Q. Solve for x: log_5(x) = 2.
Solution
log_5(x) = 2 implies x = 5^2 = 25.
Correct Answer: C — 25
Learn More →
Q. Solve the inequality -2x + 4 > 0. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x < -2
-
D.
x > -2
Solution
-2x + 4 > 0 => -2x > -4 => x < 2
Correct Answer: B — x > 2
Learn More →
Q. Solve the inequality -2x + 4 < 0.
-
A.
x > 2
-
B.
x < 2
-
C.
x > 4
-
D.
x < 4
Solution
-2x + 4 < 0 => -2x < -4 => x > 2.
Correct Answer: A — x > 2
Learn More →
Q. Solve the inequality -2x + 5 > 1.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
-2x + 5 > 1 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
Learn More →
Q. Solve the inequality -3x + 2 ≤ 5. What is the solution?
-
A.
x ≤ -1
-
B.
x ≥ -1
-
C.
x < -1
-
D.
x > -1
Solution
-3x + 2 ≤ 5 => -3x ≤ 3 => x ≥ -1.
Correct Answer: B — x ≥ -1
Learn More →
Q. Solve the inequality -4x + 1 > 9.
-
A.
x < -2
-
B.
x > -2
-
C.
x < 2
-
D.
x > 2
Solution
Subtract 1 from both sides: -4x > 8. Then divide by -4 (reverse the inequality): x < -2.
Correct Answer: B — x > -2
Learn More →
Q. Solve the inequality -4x + 8 > 0.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 4
-
D.
x > 4
Solution
-4x + 8 > 0 => -4x > -8 => x < 2.
Correct Answer: B — x > 2
Learn More →
Q. Solve the inequality -4x + 8 ≤ 0. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
-4x + 8 ≤ 0 => -4x ≤ -8 => x ≥ 2.
Correct Answer: C — x ≤ 2
Learn More →
Q. Solve the inequality -5x + 3 < 2. What is the solution?
-
A.
x > 1
-
B.
x < 1
-
C.
x ≤ 1
-
D.
x ≥ 1
Solution
-5x + 3 < 2 => -5x < -1 => x > 1.
Correct Answer: B — x < 1
Learn More →
Showing 541 to 570 of 862 (29 Pages)
