The number of points in $(-\infty, \infty)$,for which $x^2-x \sin x-\cos x=0$,is

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. The maximum value of $\lambda$ to produce a maxima at $D$ is given by

The de-Broglie wavelength of a particle moving with a velocity of $2.25 \times 10^8 \ m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the kinetic energy of the photon is: (in $/8$)

Let $C$ be the centre of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. The tangent at any point $P$ on this hyperbola meets the straight lines $bx - ay = 0$ and $bx + ay = 0$ at points $Q$ and $R$ respectively. Then $CQ \cdot CR = $

If an electron in a hydrogen atom jumps from an orbit of level $n=3$ to an orbit of level $n=2$,then the emitted radiation frequency is (where $R=$ Rydberg's constant,$C=$ velocity of light).

If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec b = \frac{1}{7}(2 \hat{i} + 3 \hat{j} - 6 \hat{k})$,then the value of $(2\vec a - \vec b) \cdot [(\vec a \times \vec b) \times (\vec a + 2\vec b)]$ is