Algebra Study Resources for Competitive Exam Success

Algebra

Binomial theorem Complex numbers Determinants Inverse Trigonometric Functions Linear Inequalities Logarithms Matrices Permutations & combinations Quadratic equations Sequence & series Sets & Relations

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?

A. 6
B. 15
C. 20
D. 30

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?

A. 70
B. 56
C. 28
D. 84

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?

A. 40
B. 60
C. 80
D. 100

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?

A. 15
B. 60
C. 90
D. 120

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).

A. -1
B. 0
C. 1
D. 2

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.

A. 2
B. 3
C. 4
D. 5

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.

A. 6
B. 9
C. 3
D. 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.

A. 2
B. 3
C. 4
D. 5

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.

A. 5
B. 10
C. 25
D. 50

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)

Algebra

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?