Q. If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q?
-
A.
q = 2p
-
B.
q = p/2
-
C.
q = p^2
-
D.
q = p + 1
Solution
log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.
Correct Answer: A — q = 2p
Learn More →
Q. If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?
-
A.
q = 2p
-
B.
q = p/2
-
C.
q = p^2
-
D.
q = p + 1
Solution
log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.
Correct Answer: A — q = 2p
Learn More →
Q. If log_a(b) = c, what is b in terms of a and c?
-
A.
a^c
-
B.
c^a
-
C.
a/c
-
D.
c/a
Solution
From the definition of logarithms, b = a^c.
Correct Answer: A — a^c
Learn More →
Q. If log_a(b) = c, which of the following is equivalent?
-
A.
a^c = b
-
B.
b^c = a
-
C.
c^a = b
-
D.
b^a = c
Solution
The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.
Correct Answer: A — a^c = b
Learn More →
Q. If log_a(b) = p and log_a(c) = q, then log_a(bc) is equal to?
-
A.
p + q
-
B.
pq
-
C.
p - q
-
D.
p/q
Solution
log_a(bc) = log_a(b) + log_a(c) = p + q.
Correct Answer: A — p + q
Learn More →
Q. If log_a(b) = p and log_a(c) = q, what is log_a(bc)?
-
A.
p + q
-
B.
pq
-
C.
p - q
-
D.
p/q
Solution
log_a(bc) = log_a(b) + log_a(c) = p + q.
Correct Answer: A — p + q
Learn More →
Q. If log_b(25) = 2, what is the value of b?
Solution
log_b(25) = 2 implies b^2 = 25. Therefore, b = 5.
Correct Answer: A — 5
Learn More →
Q. If log_b(27) = 3, what is the value of b?
Solution
log_b(27) = 3 implies b^3 = 27 => b = 3.
Correct Answer: A — 3
Learn More →
Q. If log_x(16) = 4, what is the value of x?
Solution
log_x(16) = 4 implies x^4 = 16 => x^4 = 2^4 => x = 2.
Correct Answer: B — 4
Learn More →
Q. If log_x(27) = 3, find x.
Solution
log_x(27) = 3 implies x^3 = 27 => x = 3.
Correct Answer: B — 9
Learn More →
Q. If log_x(4) = 2, what is the value of x?
Solution
log_x(4) = 2 implies x^2 = 4 => x = 2.
Correct Answer: C — 8
Learn More →
Q. If log_x(64) = 6, what is the value of x? (2023)
Solution
log_x(64) = 6 implies x^6 = 64. Since 64 = 2^6, we have x = 2.
Correct Answer: C — 8
Learn More →
Q. If log_x(81) = 4, find x.
Solution
log_x(81) = 4 implies x^4 = 81 => x^4 = 3^4 => x = 3.
Correct Answer: A — 3
Learn More →
Q. If log_x(81) = 4, what is the value of x?
Solution
log_x(81) = 4 implies x^4 = 81 => x = 3.
Correct Answer: A — 3
Learn More →
Q. If M = (1, 2, 3) and N = (4, 5, 6), what is the scalar product M · N?
Solution
M · N = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.
Correct Answer: A — 32
Learn More →
Q. If M = (2, 2, 2) and N = (3, 3, 3), what is M · N?
Solution
M · N = 2*3 + 2*3 + 2*3 = 6 + 6 + 6 = 18.
Correct Answer: A — 12
Learn More →
Q. If M is the grandfather of N and O is the father of N, how is M related to O? (2023)
-
A.
Son
-
B.
Father
-
C.
Grandfather
-
D.
Uncle
Solution
M is the father of O, making M the father of N's father.
Correct Answer: B — Father
Learn More →
Q. If M is the sister of N and N is the father of O, how is M related to O?
-
A.
Aunt
-
B.
Mother
-
C.
Sister
-
D.
Cousin
Solution
M is the aunt of O because she is the sister of O's father, N.
Correct Answer: A — Aunt
Learn More →
Q. If M is the uncle of N and N is the daughter of O, how is M related to O? (2019)
-
A.
Brother-in-law
-
B.
Cousin
-
C.
Father
-
D.
Son
Solution
M is the uncle of N, which means M is the brother of N's parent O, making M the brother-in-law of O.
Correct Answer: A — Brother-in-law
Learn More →
Q. If M ≥ N and N > O, which of the following is true?
-
A.
M > O
-
B.
M < O
-
C.
N < M
-
D.
O = N
Solution
From M ≥ N and N > O, we can conclude M > O.
Correct Answer: A — M > O
Learn More →
Q. If Monday is the first day of the month, what day will it be on the 15th of the month? (2023)
-
A.
Monday
-
B.
Tuesday
-
C.
Wednesday
-
D.
Thursday
Solution
15 days from Monday is Wednesday.
Correct Answer: C — Wednesday
Learn More →
Q. If n=4 and l=2, what is the type of orbital?
Solution
For l=2, the orbital type is d.
Correct Answer: C — d
Learn More →
Q. If O is the father of P and Q, and Q is the sister of R, what is the relationship of O to R? (2022)
-
A.
Father
-
B.
Uncle
-
C.
Brother
-
D.
Grandfather
Solution
O is the father of Q, and since Q is the sister of R, O is also the father of R.
Correct Answer: A — Father
Learn More →
Q. If one of the resistors in a Wheatstone bridge is replaced with a variable resistor, what is the effect on the balance condition?
-
A.
It cannot be balanced
-
B.
It can be balanced by adjusting the variable resistor
-
C.
It will always be unbalanced
-
D.
It will short-circuit the bridge
Solution
The variable resistor allows for adjustment to achieve balance in the bridge.
Correct Answer: B — It can be balanced by adjusting the variable resistor
Learn More →
Q. If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?
Solution
Substituting x = 2 into the equation gives 2^2 - 3*2 + p = 0 => 4 - 6 + p = 0 => p = 2.
Correct Answer: D — 4
Learn More →
Q. If one root of the equation x^2 - 6x + k = 0 is 2, what is the value of k?
Solution
Using the root, we substitute: 2^2 - 6*2 + k = 0 => 4 - 12 + k = 0 => k = 8.
Correct Answer: A — 4
Learn More →
Q. If one root of the equation x^2 - 7x + k = 0 is 3, what is the value of k?
Solution
Using Vieta's formulas, if one root is 3, the other root is 7 - 3 = 4. Thus, k = 3 * 4 = 12.
Correct Answer: B — 9
Learn More →
Q. If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)
Solution
Using the root 2 in the equation: 2² - 6*2 + k = 0, we find k = 10.
Correct Answer: B — 10
Learn More →
Q. If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)
Solution
Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.
Correct Answer: A — 10
Learn More →
Q. If one root of the equation x² - 7x + k = 0 is 3, what is the value of k? (2020)
Solution
Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 9.
Correct Answer: D — 9
Learn More →
Showing 5341 to 5370 of 19340 (645 Pages)
