Mathematics
Q. Which of the following is equal to log_10(0.01)? (2019)
Solution
log_10(0.01) = log_10(10^-2) = -2.
Correct Answer: B — -2
Learn More →
Q. Which of the following is equivalent to log_2(32)?
Solution
log_2(32) = log_2(2^5) = 5.
Correct Answer: B — 5
Learn More →
Q. Which of the following is the correct expansion of (x - y)³?
-
A.
x³ - 3x²y + 3xy² - y³
-
B.
x³ - y³
-
C.
x³ - 3xy² + 3x²y - y³
-
D.
3x²y - 3xy²
Solution
(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.
Correct Answer: A — x³ - 3x²y + 3xy² - y³
Learn More →
Q. Which of the following is the correct identity for (x + y)³?
-
A.
x³ + y³ + 3xy(x + y)
-
B.
x³ + y³ - 3xy(x + y)
-
C.
x³ + y³ + 3xy²
-
D.
x³ - y³
Solution
(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.
Correct Answer: A — x³ + y³ + 3xy(x + y)
Learn More →
Q. Which of the following is true for log_a(bc)?
-
A.
log_a(b) + log_a(c)
-
B.
log_a(b) - log_a(c)
-
C.
log_a(bc) = log_a(b) * log_a(c)
-
D.
None of the above
Solution
log_a(bc) = log_a(b) + log_a(c) by the product rule of logarithms.
Correct Answer: A — log_a(b) + log_a(c)
Learn More →
Q. Which of the following matrices is symmetric? (2023)
-
A.
A = [[1, 2], [3, 4]]
-
B.
B = [[1, 2], [2, 1]]
-
C.
C = [[1, 0], [0, 1]]
-
D.
D = [[1, 2, 3], [4, 5, 6]]
Solution
A symmetric matrix is one that is equal to its transpose. Matrix B is symmetric because B = B^T.
Correct Answer: B — B = [[1, 2], [2, 1]]
Learn More →
Q. Which of the following numbers is a perfect square?
Solution
25 is a perfect square (5^2).
Correct Answer: C — 25
Learn More →
Q. Which of the following points lies on the parabola y = x^2 - 4?
-
A.
(2, 0)
-
B.
(0, -4)
-
C.
(1, -3)
-
D.
(3, 5)
Solution
Substituting x = 1 into the equation gives y = 1^2 - 4 = -3, so the point (1, -3) lies on the parabola.
Correct Answer: C — (1, -3)
Learn More →
Q. Which of the following statements is true about the function f(x) = 1/(x-3)?
-
A.
Continuous at x = 3
-
B.
Continuous everywhere
-
C.
Not continuous at x = 3
-
D.
Continuous at x = 0
Solution
The function f(x) = 1/(x-3) is not defined at x = 3, hence it is not continuous at that point.
Correct Answer: C — Not continuous at x = 3
Learn More →
Q. Which of the following statements is true regarding the function f(x) = |x|?
-
A.
Continuous everywhere
-
B.
Discontinuous at x = 0
-
C.
Continuous only for x > 0
-
D.
Discontinuous for x < 0
Solution
The function f(x) = |x| is continuous everywhere, including at x = 0.
Correct Answer: A — Continuous everywhere
Learn More →
Showing 301 to 310 of 310 (11 Pages)
