IPMAT Indore (SA) PYQs

Suppose that a, b, and c are real numbers greater than 1. Then the value of $\dfrac{1}{1+\log_{a^2 b} \frac{c}{a}} + \dfrac{1}{1+\log_{b^2 c} \frac{a}{b}} + \dfrac{1}{1+\log_{c^2 a} \frac{b}{c}}$ is

If $\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2,$ then the value of $x$ is

Let $a, b, c$ be real numbers greater than 1, and $n$ be a positive real number not equal to 1. If $log_n(log_2a) = 1; log_n(log_2b) = 2$ and $log_n(log_2c) = 3$ then which of the following is true?