If the eccentricity of a hyperbola is $\sqrt{3}$,then the eccentricity of its conjugate hyperbola is:

If the axes are rotated through an angle $\alpha$,then the number of values of $\alpha$ such that the transformed equation of $x^2+y^2+2x+2y-5=0$ contains no linear terms is

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is $3.2 \ V$. If a second light having wavelength twice of first light is used, the stopping potential drops to $0.7 \ V$. The wavelength of first light is . . . . . . $m$.
$(h = 6.63 \times 10^{-34} \ J.s, e = 1.6 \times 10^{-19} \ C, c = 3 \times 10^8 \ m/s)$

Which of the following is a worker bee in a honeybee colony?

If the length of a stretched string is shortened by $40 \%$ and the tension is increased by $44 \%$,then the ratio of the final and initial fundamental frequencies is :