Q. If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
-
A.
{2}
-
B.
{2, 3}
-
C.
{2, 4}
-
D.
{}
Solution
A ∩ B = {2} as 2 is the only even prime number.
Correct Answer: A — {2}
Learn More →
Q. If A = | 1 2 | | 3 4 |, find det(A).
Solution
det(A) = (1)(4) - (2)(3) = 4 - 6 = -2.
Correct Answer: B — 2
Learn More →
Q. If A = | 1 2 | | 3 4 |, what is det(A)?
Solution
det(A) = (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer: B — 2
Learn More →
Q. If A = | 1 2 | | 3 5 |, what is det(2A)?
Solution
det(2A) = 2^2 * det(A) = 4 * (1*5 - 2*3) = 4 * (-1) = -4.
Correct Answer: C — 20
Learn More →
Q. If A is a 2x2 matrix such that A^2 = I, where I is the identity matrix, then which of the following is true?
-
A.
A is invertible
-
B.
A is singular
-
C.
A is a zero matrix
-
D.
A is a diagonal matrix
Solution
Since A^2 = I, A is invertible because the inverse of A is A itself.
Correct Answer: A — A is invertible
Learn More →
Q. If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
Solution
The determinant of a matrix is the product of its eigenvalues. Thus, det(A) = 1 * (-1) = -1.
Correct Answer: C — -1
Learn More →
Q. If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?
Solution
The trace of a matrix is the sum of its eigenvalues. Therefore, trace(A) = 3 + 5 = 8.
Correct Answer: A — 8
Learn More →
Q. If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
Solution
The trace of a matrix is the sum of its eigenvalues. Thus, trace(A) = 2 + 3 + 4 = 9.
Correct Answer: A — 9
Learn More →
Q. If a quadratic equation has roots 2 and -3, what is the equation in standard form?
-
A.
x^2 + x - 6 = 0
-
B.
x^2 - x - 6 = 0
-
C.
x^2 - x + 6 = 0
-
D.
x^2 + 5x - 6 = 0
Solution
The equation can be formed as (x - 2)(x + 3) = 0, which expands to x^2 + x - 6 = 0.
Correct Answer: A — x^2 + x - 6 = 0
Learn More →
Q. If B = | 2 3 | | 1 4 |, find det(B).
Solution
det(B) = (2*4) - (3*1) = 8 - 3 = 5.
Correct Answer: A — -5
Learn More →
Q. If cos^(-1)(x) = θ, then what is the value of sin(θ)?
-
A.
x
-
B.
√(1-x^2)
-
C.
1-x
-
D.
0
Solution
From cos^(-1)(x) = θ, we have cos(θ) = x. Therefore, sin(θ) = √(1 - cos^2(θ)) = √(1 - x^2).
Correct Answer: B — √(1-x^2)
Learn More →
Q. If log_10(2) = a, what is log_10(20) in terms of a?
-
A.
2a
-
B.
a + 1
-
C.
a + 2
-
D.
2 + a
Solution
log_10(20) = log_10(2 * 10) = log_10(2) + log_10(10) = a + 1.
Correct Answer: B — a + 1
Learn More →
Q. If log_10(x) = 2, what is the value of x?
-
A.
100
-
B.
200
-
C.
300
-
D.
400
Solution
log_10(x) = 2 implies x = 10^2 = 100.
Correct Answer: A — 100
Learn More →
Q. If log_2(x + 1) - log_2(x) = 1, what is the value of x?
Solution
log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.
Correct Answer: A — 1
Learn More →
Q. If log_2(x + 1) = 3, what is the value of x?
Solution
log_2(x + 1) = 3 implies x + 1 = 2^3 = 8 => x = 7.
Correct Answer: A — 6
Learn More →
Q. If log_2(x) + log_2(4) = 5, find x.
Solution
log_2(x) + 2 = 5 => log_2(x) = 3 => x = 2^3 = 8.
Correct Answer: B — 32
Learn More →
Q. If log_2(x) + log_2(x - 3) = 3, what is the value of x?
Solution
log_2(x(x - 3)) = 3 => x(x - 3) = 2^3 = 8 => x^2 - 3x - 8 = 0. Solving gives x = 6.
Correct Answer: B — 6
Learn More →
Q. If log_2(x) + log_2(x-1) = 3, what is the value of x?
Solution
log_2(x(x-1)) = 3 => x(x-1) = 2^3 = 8 => x^2 - x - 8 = 0. Solving gives x = 5.
Correct Answer: B — 5
Learn More →
Q. If log_2(x) = 5, what is the value of x?
Solution
log_2(x) = 5 implies x = 2^5 = 32.
Correct Answer: C — 64
Learn More →
Q. If log_3(9) + log_3(27) = x, what is the value of x?
Solution
log_3(9) = 2 and log_3(27) = 3, thus x = 2 + 3 = 5.
Correct Answer: C — 4
Learn More →
Q. If log_3(9) = x, what is the value of x?
Solution
log_3(9) = log_3(3^2) = 2.
Correct Answer: B — 2
Learn More →
Q. If log_3(x + 1) = 2, what is the value of x?
Solution
log_3(x + 1) = 2 implies x + 1 = 3^2 = 9 => x = 8.
Correct Answer: B — 8
Learn More →
Q. If log_3(x) + log_3(4) = 2, find x.
Solution
log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.
Correct Answer: C — 9
Learn More →
Q. If log_3(x) = 2, what is the value of x?
Solution
log_3(x) = 2 implies x = 3^2 = 9.
Correct Answer: B — 9
Learn More →
Q. If log_4(64) = x, what is the value of x?
Solution
log_4(64) = log_4(4^3) = 3.
Correct Answer: B — 3
Learn More →
Q. If log_4(x) = 1/2, what is the value of x?
Solution
log_4(x) = 1/2 implies x = 4^(1/2) = 2.
Correct Answer: A — 2
Learn More →
Q. If log_4(x) = 2, what is the value of x?
Solution
log_4(x) = 2 implies x = 4^2 = 16.
Correct Answer: C — 16
Learn More →
Q. If log_4(x) = 3, find x.
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
Learn More →
Q. If log_4(x) = 3, what is the value of x?
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
Learn More →
Q. If log_5(25) + log_5(5) = x, what is the value of x?
Solution
log_5(25) = 2 and log_5(5) = 1. Therefore, x = 2 + 1 = 3.
Correct Answer: C — 3
Learn More →
Showing 301 to 330 of 862 (29 Pages)
