Question

,.JEE MAINS MATHS QUESTION SEPTEMBER 2020..

Answer 1

Step-by-step explanation:

.....BE and CF are two Equal altitudes of a triangle ABC. using RHS congruence rule , prove that the triang

le ABC is isosceles

Answer 2

The function $f(x)=\left\{\begin{array}{cc}k_1(x-\pi)^2-1\quad x\leq\pi\\k_2cosx\quad x>\pi\end{array}\right$ is twice differentiable function.

To find : The ordered pair (k₁ , k₂) is ....

solution : f(x) is differentiable so it is also continuous finction in given conditions.

i.e., $\displaystyle\lim_{x\to\pi^-}f(x)=\displaystyle\lim_{x\to\pi^+}=f(\pi)$

⇒k₁(π - π)² - 1 = k₂cos(π) = -1

⇒-1 = -k₂

⇒k₂ = 1

now differentiating function two times we get,

$f"(x)=\left\{\begin{array}{cc}2k_1\quad x\leq\pi\\-k_2cosx\quad x>\pi\end{array}\right$

for differentiable,

$f"(\pi^-)=f"(\pi^+)$

⇒2k₁ = k₂

so, k₁ = 1/2

therefore the value of ordered pair (k₁ , k₂) is (1/2, 1)