Wires $A$ and $B$ have resistivities $\rho_A$ and $\rho_B$,where $\rho_B = 2 \rho_A$,and have lengths $l_A$ and $l_B$. If the diameter of wire $B$ is twice that of $A$ and the two wires have the same resistance,then the ratio $\frac{l_B}{l_A}$ is:

$A$ telescope has an objective lens of focal length $150 \ cm$ and an eyepiece of focal length $5 \ cm$. If a $50 \ m$ tall tower at a distance of $1 \ km$ is observed through this telescope in normal setting,the angle formed by the image of the tower is $\theta$ (in degrees),then $\theta$ is close to..... (in $^{\circ}$)

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(A | B)$.

What is the reduction electrode potential (in volts) of a copper electrode when $[Cu^{2+}] = 0.01 \ M$ is in a solution at $25^{\circ} C$? ($E^{\circ}$ of $Cu^{2+}/Cu$ electrode is $+0.34 \ V$)

The angle between the tangents drawn to the parabola $y^2=4x$ from the point $(1,4)$ is