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The equation of the circle which touches the circle $S \equiv x^2+y^2-10 x-4 y+19=0$ at the point $(2,3)$ internally and having radius equal to half of the radius of the circle $S=0$ is
A block of mass $\sqrt{2} \mathrm{~kg}$ is placed on a rough horizontal surface. A force ' $F$ ' acting upwards at an angle of $45^{\circ}$ with the horizontal causes the block to start motion. If the coefficient of static friction between the surface and the block is 0.25 , the magnitude of the force ' $F$ ' is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
In hydrogen atom, an electron is transferred from an orbit of radius 1.3225 nm to another orbit of radius 0.2116 nm . What is the energy (in J ) of emitted radiation?
If the circle $S=0$ intersect the three circle
$$\begin{aligned} & S_1 \equiv x^2+y^2+4 x-7=0 \\ & S_2 \equiv x^2+y^2+y=0 \text { and } S_3 \equiv x^2+y^2+\frac{3}{2} x+\frac{5}{2} y-\frac{9}{2}=0 \end{aligned}$$
orthogonally, then radical axis of $S=0$ and $S_1=0$ is
For a particle moving along a straight line path, the displacements in third and fifth seconds of its motion are 10 m and 18 m respectively. The speed of the particle at time $t=4 \mathrm{~s}$ is
Observe the following statements.
Statement -I Rutherford model of an atom cannot explain the stability of an atom.
Statement-II The wavelength of X-rays is higher than the wavelength of microwaves.
The correct answer is