List of practice Questions

One hundred identical coins, each with probability p, of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

For two given events $A$ and $B, P(A \cap B) $ is

The equations of the tangents drawn from the origin to the circle $x^2 + y^2 + 2 rx + 2hy + h^2 = 0, $ are

The value of the expression $\sqrt{3} cosec 20^\circ -sec 20^\circ $is equal to

Prove that the value of the integral, $\int\limits_0^{2a} [f(x)/ f(x) + f(2a-x)] dx$ is equal to a

If the first and the $ (2n - 1)th$ term of an $AP, GP$ and $HP$ are equal and their nth terms are $a, b$ and $c$ respectively, then

If $ y^2 = P (x) $ is a polynomial of degree 3, then $2 \frac{d}{dx} \bigg(y^3 \frac{d^2 \, y}{ dx^2}\bigg) $ equals

If one mole of a monoatomic gas ($\gamma$ = 5/ 3) is mixed with one mole of a diatomic gas ($\gamma$ = 7 / 5), the value of $\gamma$ for the mixture is

The orbital diagram in which Aufbau principle is violated is

A cylinder of radius R made of a material of thermal conductivity $K_1$, is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K$_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

The wavelength of a spectral line for an electronic transition is inversely related to

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends the white ammonium chloride ring first formed will be

A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

Water potential is equal to

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to

The coefficient of restitution $e$, for a perfectly elastic collision is

The molecule that has linear structure is

When mercuric iodide is added to the aqueous solution of potassium iodide

A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is

The IUPAC name of the compound $CH_2=CH-CH(CH_3)_2 $ is

The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$, then $P (\bar A) +P(\bar B)$ is

Which of the following oxides of nitrogen is a coloured gas ?

Bromine can be liberated from potassium bromide solution by the action of

If two compounds have the same empirical formula but different molecular formulae, they must have

If $z_1$ and $z_2$ are two non-zero complex numbers such that $| z_1+ z_2| = | z_1| + | z_2|$ , then $arg (z_1 ) - arg (z_2)$ is equal to