For all twice differentiable functions f : R $$ \to $$ R,
with f(0) = f(1) = f'(0) = 0

Let f : R $$ \to $$ R be a function defined by
f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable. Then :

Let $$\theta = {\pi \over 5}$$ and $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$.

If B = A + A⁴ , then det (B) :

The common difference of the A.P.
b₁, b₂, … , b_m is 2 more than the common
difference of A.P. a₁, a₂, …, a_n. If
a₄₀ = –159, a₁₀₀ = –399 and b₁₀₀ = a₇₀, then b₁ is equal to :