List of practice Questions

What will happen when $D-(+)$-glucose is treated with methanolic �$HCl$ followed by Tollens� reagent ?

Which of the followings forms the base of talcum powder?

Which of the following method gives better yield of p-nitrophenol?

Give the possible structure of $X$ in the following reaction : $C_6 H_6 + D_2 SO_4 \xrightarrow{D_2O} X$

A deuteron of kinetic energy $50 \,keV$ is describing a circular orbit of radius $0.5$ metre in a plane perpendicular to the magnetic field $B$. The kinetic energy of the proton that describes a circular orbit of radius $0.5$ metre in the same plane with the same $B$ is

Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e. $T^{2}=K r^{3}$ here $K$ is constant. If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F=\frac{G M m}{r^{2}}$ here $G$ is gravitational constant. The relation between $G$ and $K$ is described as

Find the number of photon emitted per second by a $25$ watt source of monochromatic light of wavelength $ 6600\, ??. What is the photoelectric current assuming $3\%$ efficiency for photoelectric effect ?

A ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in diagram. It undergoes partial reflection and refraction. At each reflection, $25 \%$ of incident energy is reflected. The rays $A B$ and $A^{\prime} B^{\prime}$ undergo interference. The ratio of $I_{\max }$ and $I_{\min }$ is :

A capillary tube of radius $r$ is immersed vertically in a liquid such that liquid rises in it to height $h$ (less than the length of the tube). Mass of liquid in the capillary tube is $m$. If radius of the capillary tube is increased by $50 \%$, then mass of liquid that will rise in the tube, is

A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4\, m s^{-1}$ at an angle of $60^{\circ}$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330\, ms ^{-1}$ )

If $\sum\limits^{n}_{r=0} \frac{r+2}{r+1} \,^{n}C_{r} = \frac{2^{8}-1}{6} $, then $n =$

Let $f (x) = \frac{ax+ b}{cx + d} $ , then $fof(x) = x$, provided that :

The average kinetic energy of an ideal gas per molecule in SI unit at $25^{\circ} C$ will be

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance $d(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres, as:

A ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The co-ordinates of the point $A$ is

At an extreme point of a function $f (x)$, the tangent to the curve is

The curve $y = xe^x$ has minimum value equal to

The equation $x^2 - 2 \sqrt{3} xy + 3y^2 - 3x + 3 \sqrt{3} y - 4 = 0 $ represents

The line joining $(5,0)$ to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $q$ varies, then the locus of $P$ is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0 $ is the equation of a circle whose radius cannot exceed $5$, is

The lengths of the tangent drawn from any point on the circle $15x^2 +15y^2 - 48x + 64y = 0$ to the two circles $5x^2 + 5y^2 - 24x + 32y + 75 = 0$ and $5x^2 + 5y^2 - 48x + 64y + 300 = 0$ are in the ratio of

The length of the chord $x + y = 3$ intercepted by the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ is

The locus of the point of intersection of two tangents to the parabola $y^2 = 4ax$, which are at right angle to one another is

The parabola having its focus at $(3, 2)$ and directrix along the $y$-axis has its vertex at