A value of x satisfying the equation sin[cot⁻¹ (1+ x)] = cos [tan⁻¹ x], is :

Let E and F be two independent events. The probability that both E and F happen is $${1 \over {12}}$$ and the probability that neither E nor F happens is $${1 \over {2}}$$, then a value of $${{P\left( E \right)} \over {P\left( F \right)}}$$ is :

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :

Contrapositive of the statement

‘If two numbers are not equal, then their squares are not equal’, is :