De Morgan laws Questions

If p, 1 and q are in AP and p and 2 q are in GP, then which of the following statements is/are correct? I. p, 4, q are in HP.

 II. 1p, 1/4 ,1/q  are in AP.

 Select the answer using the code given below:

If p^x = q^y = rz, where x, y and z are in GP, then consider the following statements:

I. p, q and r are in AP.

II. ln p, ln q and ln r are in GP.

Which of the statements given above is/are correct?

If A and B are non-empty subsets of a set, and A^c and B^c represent their complements, then which of the following is/are correct?

 I. A - B = B^c - A^c

II. A - B^c = A^c - B

 Select the answer using the code given below.

Let y = x! and z = (2x)!. If (z/y) = 120, then what is the value of (3x)!?

If (10 + log₁₀x), (10 + log₁₀ y) and (10 + log₁₀ z) are in AP, then consider the following statements:

 I. The GM of x and z is y².

II. The AM of log₁₀ x and log₁₀ z is log₁₀ y.

 Which of the statements given above is/are correct?

How many terms of the series 1 + 3 + 5 + 7 +... amount to a sum equal to 12345678987654321?

How many terms are identical in the two APS 19, 21, 23,... up to 110 terms and 19, 22, 25, 28,... up to 75 terms?

If then what is the value of (1 + α¹⁹ - α³⁵)100 - (1 - 3α²⁵ + α³⁸)⁵⁰?

What is the remainder when 5⁹⁹ is divided by 13?

What is the number of rational terms in the expansion of (3^1/2 +5^1/4)¹²?