Question

Arrange A, B, C, D in ascending order
A) Maximum value of sin5x
B) Minimum value of $x+\frac{1}{x}(x>0)$
C) Minimum value of $4\times 2^{(x^2-3{)}^3+27}$
D) Minimum value of $5{\sin }^{2}x+3{\cos }^{2}x$

• A. A, B, D,C
• B. A, C, B, D
• C. A, D, B, C
• D. B, D, A, C

Answer 1

Answer: (A)

A, B, D,C

(A) $f\left(x\right)=\sin 5x$
$f(x{)}_{max}=1$
(B) Use AM & GM
$\frac{x+\frac{1}{x}}{2}\ge (1{)}^{\frac{1}{2}}$

$x+\frac{1}{x}\ge 2$

(C) $f\left(x\right)=4\times 2^{(x^2-3{)}^3}+27$

$f\left(\sqrt{3}\right)$ is minimum value
$f\left(\sqrt{3}\right)=4\times 2^{27}$
(D) $f\left(x\right)=2sin{x}^{2}x+3$
$fmi{n}^{\left(x\right)}=3$ when $sinx=0$