Mathematics for Competitive Exam Success

Mathematics

3D Geometry Applications of Derivatives Binomial Theorem Circles Complex Numbers Conic Sections Coordinate Geometry Differential Equations Differentiation Integration Limits & Continuity Matrices & Determinants Permutations & Combinations Probability Quadratic Equations Sequences & Series Sets & Relations Straight Lines Trigonometry Vector Algebra

Q. What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)

A. 2
B. 4
C. 6
D. 8

Solution

The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.

Correct Answer: A — 2

Learn More →

Q. What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

A. -2
B. 2
C. 1
D. 7

Solution

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

Correct Answer: A — -2

Learn More →

Q. What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)

A. -2
B. 2
C. 10
D. 12

Solution

The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.

Correct Answer: A — -2

Learn More →

Q. What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)

A. -2
B. 2
C. 0
D. 4

Solution

The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

Learn More →

Q. What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)? (2022)

A. -14
B. 14
C. 0
D. 6

Solution

Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).

Correct Answer: A — -14

Learn More →

Q. What is the determinant of the matrix \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \)? (2023)

A. 1
B. 4
C. 7
D. 11

Solution

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: A — 1

Learn More →

Q. What is the determinant of the matrix \( I = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} \)? (2021)

A. 10
B. 8
C. 6
D. 12

Solution

The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).

Correct Answer: A — 10

Learn More →

Q. What is the diameter of a circle if its area is 50π square units? (2017)

A. 10 units
B. 5 units
C. 20 units
D. 15 units

Solution

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

Correct Answer: A — 10 units

Learn More →

Q. What is the diameter of a circle if its area is 78.5 cm²? (2020)

A. 10 cm
B. 8 cm
C. 6 cm
D. 12 cm

Solution

Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.

Correct Answer: A — 10 cm

Learn More →

Q. What is the diameter of a circle with a radius of 9 cm? (2022)

A. 9 cm
B. 18 cm
C. 27 cm
D. 36 cm

Solution

Diameter = 2 * radius = 2 * 9 cm = 18 cm.

Correct Answer: B — 18 cm

Learn More →

Q. What is the diameter of a circle with an area of 50.24 cm²? (2019)

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.

Correct Answer: B — 10 cm

Learn More →

Q. What is the diameter of a circle with an area of 50π square units? (2017)

A. 10 units
B. 5 units
C. 20 units
D. 15 units

Solution

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

Correct Answer: A — 10 units

Learn More →

Q. What is the discriminant of the equation 3x² - 12x + 12 = 0? (2023)

A. 0
B. 12
C. 36
D. 24

Solution

The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

Correct Answer: A — 0

Learn More →

Q. What is the discriminant of the equation 3x² - 12x + 9 = 0? (2023)

A. 0
B. 9
C. 12
D. 36

Solution

The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.

Correct Answer: A — 0

Learn More →

Q. What is the distance between the center of a circle and a point on its circumference if the radius is 12 cm? (2022)

A. 6 cm
B. 12 cm
C. 18 cm
D. 24 cm

Solution

The distance from the center to a point on the circumference is the radius, which is 12 cm.

Correct Answer: B — 12 cm

Learn More →

Q. What is the distance between the center of a circle and a point on its circumference if the radius is 8 cm? (2023)

A. 8 cm
B. 16 cm
C. 4 cm
D. 0 cm

Solution

The distance from the center to a point on the circumference is the radius, which is 8 cm.

Correct Answer: A — 8 cm

Learn More →

Q. What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)

A. 5/√14
B. 10/√14
C. 15/√14
D. 20/√14

Solution

Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.

Correct Answer: B — 10/√14

Learn More →

Q. What is the distance between the points (-1, -1) and (2, 3)? (2022) 2022

A. 5
B. 4
C. 6
D. 7

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the distance between the points (-1, -1) and (2, 3)? (2023)

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the distance between the points (2, 3) and (5, 7)?

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the distance between the points (3, 4) and (7, 1)? (2021) 2021

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Correct Answer: A — 5

Learn More →

Q. What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

A. 3√2
B. 3√3
C. 3
D. √27

Solution

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

Correct Answer: A — 3√2

Learn More →

Q. What is the distance from the point (1, 1) to the line x + y = 2? (2023)

A. 1
B. 2
C. 0
D. 3

Solution

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

Correct Answer: A — 1

Learn More →

Q. What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.

Correct Answer: B — 2

Learn More →

Q. What is the distance from the point (1, 2) to the line x + y = 5? (2020)

A. 3
B. 2
C. 1
D. 4

Solution

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Correct Answer: A — 3

Learn More →

Q. What is the distance from the point (3, 4) to the line x + y = 5? (2022)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

Correct Answer: B — 2

Learn More →

Q. What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

A. 5
B. 10
C. 11
D. 14

Solution

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

Correct Answer: B — 10

Learn More →

Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (2, 5)? (2022)

A. y = 3x - 1
B. y = 3x + 1
C. y = 3x + 2
D. y = 3x + 3

Solution

Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.

Correct Answer: B — y = 3x + 1

Learn More →

Q. What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?

A. y = 3x - 8
B. y = 3x + 5
C. y = 3x - 1
D. y = 3x + 1

Solution

Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.

Correct Answer: A — y = 3x - 8

Learn More →

Q. What is the equation of the line passing through (0, 0) and (2, 4)? (2019)

A. y = 2x
B. y = x
C. y = 4x
D. y = 3x

Solution

Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.

Correct Answer: A — y = 2x

Learn More →

Showing 421 to 450 of 590 (20 Pages)

Mathematics

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