List of practice Questions

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

Two wires are made of the same material and have the same volume. However wire $1$ has cross sectional area A and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?

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?

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

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

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 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

A frictionless wire $A B$ is fixed on a sphere of radius $R$. A very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

Based on data provided, the value of electron gain enthalpy of fluorine would be :

A perfectly elastic ball of mass $m$ moving with velocity $u$ hits a wall moving with velocity $v$ in the opposite direction. After the collision the ball will rebound back with speed

The volume thermal expansion coefficient of an ideal gas at constant pressure is

Unlike electric force and gravitational forces, nuclear force has limited range. Nuclear force do not obey inverse square law.

The effective resistance between $P$ and $Q$ of the electrical circuit shown in the figure is

The one electron species having ionization energy of $54.4\, eVs$