An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is (in $\%$)

$A$ thin prism $P_1$ with angle $4^o$ and made from a glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of the prism $P_2$ is.....$^o$

The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ is:

What is the scientific name of modern man?

Starting with a sample of pure $^{66}Cu$,$\frac{7}{8}$ of it decays into $Zn$ in $15 \ min$. The corresponding half-life is .......... $min$.

If a point $P$ moves such that its distances from the point $A(1,1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is