JEE PYQ: Functions Question 1
Question 1 - 2021 (16 Mar Shift 1)
The number of roots of the equation, $(81)^{\sin^2 x} + (81)^{\cos^2 x} = 30$ in the interval $[0, \pi]$ is equal to:
(1) 3
(2) 4
(3) 8
(4) 2
Type: MCQ
Show Answer
Answer: (2) 4
Solution
Let $(81)^{\sin^2 x} = t$
$t + \frac{81}{t} = 30$
$(t - 3)(t - 27) = 0$
$(81)^{\sin^2 x} = 3^1$ or $(81)^{\sin^2 x} = 3^3$
$3^{4\sin^2 x} = 3^1$ or $3^{4\sin^2 x} = 3^3$
$\sin^2 x = \frac{1}{4}$ or $\sin^2 x = \frac{3}{4}$
Total solutions in $[0, \pi]$ = 4
BETA
