If $$x = \sec \theta - \cos \theta $$ and $$y = {\sec ^n}\theta - {\cos ^n}\theta $$, then show
that $$\left( {{x^2} + 4} \right){\left( {{{dy} \over {dx}}} \right)^2} = {n^2}\left( {{y^2} + 4} \right)$$
Answer
Solve it.
4
IIT-JEE 1984
Subjective
If $$\alpha $$ be a repeated root of a quadratic equation $$f(x)=0$$ and $$A(x), B(x)$$ and $$C(x)$$ be polynomials of degree $$3$$, $$4$$ and $$5$$ respectively,
then show that $$\left| {\matrix{
{A\left( x \right)} & {B\left( x \right)} & {C\left( x \right)} \cr
{A\left( \alpha \right)} & {B\left( \alpha \right)} & {C\left( \alpha \right)} \cr
{A'\left( \alpha \right)} & {B'\left( \alpha \right)} & {C'\left( \alpha \right)} \cr
} } \right|$$ is
divisible by $$f(x)$$, where prime denotes the derivatives.
Answer
Solve it.
Questions Asked from Differentiation
On those following papers in Subjective
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