If two soap bubbles \(A\) and \(B\) of radii \(r_1\) and \(r_2\) respectively are kept in vaccum at constant temperature, then the ratio of masses of air inside the bubbles \(A\) and \(B\) is

A small disc is on the top of a smooth hemisphere of radius ' R '. The smallest horizontal velocity ' \(V\) ' that should be imparted to the disc so that disc leaves the hemisphere surface without sliding down is (there is no friction)

The number of rotational degrees of freedom of a monatomic molecule is

A body projected with some velocity at an angle \(45^{\circ}\) with the horizontal from the origin in \(X Y\)-plane passes through a point at \((4,3) \mathrm{m}\). Its horizontal range is

At a place the horizontal component of earth's magnetic field is \(3 \times 10^{-5} \mathrm{~T}\) and the magnetic declination is \(30^{\circ}\). A compass needle of magnetic moment \(18 \mathrm{Am}^2\) pointing towards geographic north at this place experiences a torque of

Flux coming out from a unit positive charge kept in air is

The frequncy of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments \(M_1\) and \(M_2\) is \(6 \mathrm{~Hz}\) when like poles are tied and it is \(2 \mathrm{~Hz}\) when the unlike poles are tied together, then the ratio \(M_1: M_2\) is

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

Which species among the following doesn't show disproportionation reactions?

If the lines \(2 x+y+12=0, k x-3 y-10=0\) are conjugate with respect to the circle \(x^2+y^2-4 x+3 y-1=0\), then \(k=\)

For any two non-zero complex numbers \(z_1\) and \(z_2\), if \(\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2\), then

Which of the following statement is false?
1) The area of a triangle is invariant under the translation of the axes
2) The slope of a straight line is invariant under the translation of the axes
3) The shifting of origin to another point, while changing the direction of the axes, is called translation of axes.
4) If \(f(x, y)=0\) is transformed equation of a curve when the axes are translated to the point \((h, k)\) then the original equation of the curve is \(f(x-h, y-k)=0\)

$12$ balls are distributed among $3$ boxes, then the probability that the first box will contain $3$ balls is