Real Numbers and Logarithms

If p = logabc, q = logbca and r = logcab, then which of the following is true?

1. pqr = 2
2. p + q = 2r
3. p + q + r + 2 = pqr
4. pqr =1

Answer: (c) p + q + r + 2 = pqr

If log10Cos72o. log10Cos73o…......log10cos121o = log10a, then find the value of a.

1. 2
2. -1
3. 0
4. 1

Answer: (d) 1

An integer, X, written as a product of its prime factors is a² x 7b+2. An integer, Y, written as a product of its prime factors is a³ x 72. The highest common factor (HCF) of X and Y is 1225. The lowest common multiple (LCM) of X and Y is 42875. Find the sum of the values of X and Y.

1. 14700
2. 21000
3. 15698
4. 12512

Answer: (a) 14700

The sum of two natural numbers is 17402. One of the two numbers is divisible by 10. If the unit digit of that number is erased, the other number is obtained. What is the difference between these two numbers?

1. 10,000
2. 14,238
3. 12,654
4. 11,890

Answer: (b) 14,238

If ax, bx and cx are in GP, then which of the following is/are true? (A) a, b, c are in GP. (B) log a, log b, log c are in GP. (C) log a, log b, log c are in AP. (D) a, b, c are in AP.

1. Only B
2. A and C
3. A and B
4. Only A

Answer: (b) A and C

Anna and Robert run around a circular track and they take 120 seconds and 200 seconds respectively to complete one revolution. If they start together at 8 am from the same point, how long will it take for them to meet again for the first time at the starting point?

1. 8:50 AM
2. 9:00 AM
3. 7:50 AM
4. 8:10 AM

Answer: (d) 8:10 AM

Find the value of the given expression:

1. 1/2
2. log1/2
3. 1
4. 1/2 + log31/2

Answer: (d) 1/2 + log31/2

Solve the given expression and choose the correct answer.

1. Exactly one solution
2. Exactly three real solutions
3. Atleast two are irrational numbers
4. No real solution

Answer: (b) Exactly three real solutions

What is the value of logp(q), if log4 (x4/4) + 3 log44x4 = p + q log4x.

1. 4
2. 6
3. -1
4. 0

Answer: (a) 4

What is the value of the given expression?

1. 2
2. 3
3. 4
4. 0

Answer: (c) 4