$$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$$ is equal to :

For some $$\theta \in \left( {0,{\pi \over 2}} \right)$$, if the eccentricity of the
hyperbola, x²–y²sec²$$\theta $$ = 10 is $$\sqrt 5 $$ times the
eccentricity of the ellipse, x²sec²$$\theta $$ + y² = 5, then the length of the latus rectum of the ellipse, is :

A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, –2, 2 and 2, 3, –1 respectively. If this plane also passes through the point ($$\alpha $$, –3, 5), then $$\alpha $$ is equal to:

Which of the following is a tautology ?