If $x:32::4:16$, then value of $x$ is:

Q. If $x:32$ and $4:16$ are equivalent ratio, then find the value of x.

Q. If $(1-y)(1+2x+4x^2+8x^3+16x^4+32x^5)=1-y^6,$ where $y\ne 1,x\ne \frac{1}{2}$, then the value of $\frac{y}{x}$ is

Q. If 4 cos⁻¹ x + sin⁻¹ x = π, then the value of x is
(a) $\frac{3}{2}$

(b) $\frac{1}{\sqrt{2}}$

(c) $\frac{\sqrt{3}}{2}$

(d) $\frac{2}{\sqrt{3}}$

Q. Assertion :Let $2^{1/14}{.4}^{1/8}{.8}^{1/16}{.16}^{1/32}...\infty =2^x$ then the value of $x$ is equal to 1. Reason: The sum of series $\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+\frac{4}{32}=...\infty$ is equal to 1.

Q. If $4^{2x}=\frac{1}{32}$, then the value of x is