Q. What is the value of gravitational acceleration at the height equal to the radius of the Earth?
-
A.
g/2
-
B.
g/4
-
C.
g/3
-
D.
g/8
Solution
At height R, g' = g / (2^2) = g / 4.
Correct Answer: B — g/4
Learn More →
Q. What is the value of gravitational acceleration at the surface of the Earth?
-
A.
9.8 m/s^2
-
B.
10 m/s^2
-
C.
9.81 m/s^2
-
D.
8.9 m/s^2
Solution
The standard value of gravitational acceleration at the surface of the Earth is approximately 9.81 m/s^2.
Correct Answer: C — 9.81 m/s^2
Learn More →
Q. What is the value of gravitational acceleration on the surface of the Earth?
-
A.
9.8 m/s²
-
B.
10 m/s²
-
C.
9.81 m/s²
-
D.
9.6 m/s²
Solution
The standard value of gravitational acceleration on the surface of the Earth is approximately 9.8 m/s².
Correct Answer: A — 9.8 m/s²
Learn More →
Q. What is the value of i^4?
Solution
i^4 = (i^2)^2 = (-1)^2 = 1.
Correct Answer: A — 1
Learn More →
Q. What is the value of k for which the equation x^2 + kx + 16 = 0 has equal roots?
Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or 8. The answer is -4.
Correct Answer: B — -4
Learn More →
Q. What is the value of k for which the equation x^2 + kx + 9 = 0 has no real roots?
-
A.
k < 6
-
B.
k > 6
-
C.
k = 6
-
D.
k <= 6
Solution
The discriminant must be negative: k^2 - 4*1*9 < 0 => k^2 < 36 => |k| < 6, hence k > 6.
Correct Answer: B — k > 6
Learn More →
Q. What is the value of k for which the equation x^2 - 2kx + 3 = 0 has roots that are reciprocals of each other?
Solution
If the roots are reciprocals, then k = sum of roots = 0 and product = 1. Thus, k = 2.
Correct Answer: B — 2
Learn More →
Q. What is the value of k for which the equation x^2 - 4x + k = 0 has roots that are equal?
Solution
For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 => 16 - 4k = 0 => k = 4.
Correct Answer: A — 4
Learn More →
Q. What is the value of k for which the function f(x) = { kx + 2, x < 2; x^2 - 4, x >= 2 is continuous at x = 2?
Solution
Setting 2k + 2 = 0 gives k = 2.
Correct Answer: C — 2
Learn More →
Q. What is the value of k for which the function f(x) = { kx, x < 0; x^2 + 1, x >= 0 is continuous at x = 0?
Solution
Setting k(0) = 0^2 + 1 gives k = 1.
Correct Answer: B — 0
Learn More →
Q. What is the value of k for which the function f(x) = { kx, x < 2; x^2, x >= 2 } is continuous at x = 2?
Solution
Setting k(2) = 2^2 gives 2k = 4, thus k = 2.
Correct Answer: C — 4
Learn More →
Q. What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
Solution
The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.
Correct Answer: B — -2
Learn More →
Q. What is the value of k if the equation x^2 + kx + 16 = 0 has no real roots?
Solution
For no real roots, the discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => |k| < 8.
Correct Answer: B — -4
Learn More →
Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has equal roots?
Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or k = 8. The answer is -8.
Correct Answer: B — -4
Learn More →
Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has no real roots?
Solution
The discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => k < 8 and k > -8.
Correct Answer: B — -4
Learn More →
Q. What is the value of k if the quadratic equation x^2 + kx + 25 = 0 has one real root?
Solution
For one real root, the discriminant must be zero: k^2 - 4*1*25 = 0, thus k^2 = 100, giving k = -10 or k = 10.
Correct Answer: A — -10
Learn More →
Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has no real roots?
-
A.
k < 6
-
B.
k > 6
-
C.
k = 6
-
D.
k < 0
Solution
For no real roots, the discriminant must be less than zero: k^2 - 4*1*9 < 0, thus k > 6.
Correct Answer: B — k > 6
Learn More →
Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has one real root?
Solution
For one real root, the discriminant must be zero: k^2 - 4*1*9 = 0 => k^2 = 36 => k = ±6.
Correct Answer: B — -3
Learn More →
Q. What is the value of k if the roots of the equation x^2 + kx + 16 = 0 are equal?
Solution
For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0 => k^2 = 64 => k = 8 or k = -8.
Correct Answer: B — 8
Learn More →
Q. What is the value of k if the roots of the equation x^2 - kx + 12 = 0 are 3 and 4?
Solution
Using Vieta's formulas, k = 3 + 4 = 7.
Correct Answer: A — 7
Learn More →
Q. What is the value of l for a d orbital?
Solution
For d orbitals, the azimuthal quantum number l is equal to 2.
Correct Answer: C — 2
Learn More →
Q. What is the value of log2(8)?
Solution
log2(8) = 3 because 2^3 = 8.
Correct Answer: B — 3
Learn More →
Q. What is the value of log_10(1000) + log_10(0.01)?
Solution
log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.
Correct Answer: C — -1
Learn More →
Q. What is the value of log_10(1000)?
Solution
log_10(1000) = log_10(10^3) = 3.
Correct Answer: C — 3
Learn More →
Q. What is the value of log_2(32) - log_2(4)?
Solution
log_2(32) = 5 and log_2(4) = 2. Therefore, 5 - 2 = 3.
Correct Answer: C — 3
Learn More →
Q. What is the value of log_2(32) - log_2(8)?
Solution
log_2(32) = 5 and log_2(8) = 3. Therefore, 5 - 3 = 2.
Correct Answer: C — 3
Learn More →
Q. What is the value of log_2(32)?
Solution
Since 32 = 2^5, log_2(32) = 5.
Correct Answer: B — 5
Learn More →
Q. What is the value of log_3(27) - log_3(9)?
Solution
log_3(27) = 3 and log_3(9) = 2. Therefore, 3 - 2 = 1.
Correct Answer: B — 1
Learn More →
Q. What is the value of log_3(27)?
Solution
Since 27 = 3^3, log_3(27) = 3.
Correct Answer: B — 3
Learn More →
Q. What is the value of log_3(81)?
Solution
log_3(81) = log_3(3^4) = 4.
Correct Answer: C — 4
Learn More →
Showing 8641 to 8670 of 10700 (357 Pages)
