List of practice Questions

For a crystal, the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a d value of $2.28\,?$. The wavelength (in $?$) of $X$- rays used for Bragg's diffraction is

One litre of oxygen at a pressure of $1 \,atm$ and two litres of nitrogen at a pressure of $0.5\, atm$, are introduced into a vessel of volume $1\, L$. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is

Identify $A$ and $B$ in the following reaction $CH _{3}- CH _{3} \stackrel{B}{\leftarrow}{B} CH _{3} COOH \xrightarrow{A} CH _{3} CH _{2} OH$

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6} $ and $P(A \cap B) = \frac{1}{3}$, then $P(A)$ is equal to (Here, $E$ is the complement of the event $E$)

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$, then the equation of the circle is

The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$, is

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y -11 = 0$ is

The radius of the circle with the polar equation $r^2 - 8r( \sqrt{3} \, \cos \, \theta + \sin \, \theta) + 15 = 0$ is

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

If $\overline{ M _{ W }}$ is the weight average molecular weight and $\overline{ M _{ n }}$ is the number average molecular weight of a polymer, the poly dispersity index (PDI) of the polymer is given by:

The velocities of two particles $A$ and $B$ are $0.05$ and $0.02\, ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de- Broglie's wavelength is

Two particles $A$ and $B$ initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of $A$ is $v$ and speed of $B$ is $2v$, the speed of center of mass $(CM)$ is

Which of the following correspond $(s)$ has '$Z$' configuration?

Which one of the following graphs represents "Freundlich adsorption isotherm'' ?

Which of the following is true in the case of an adiabatic process, where $\gamma = C_{p} / C_{v} $ ?

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20\, cm$ and $40\, cm$ and carry $0.2\, A$ and $0.3\, A$. current respectively in opposite directions. The magnetic induction (in tesla) at the center is

Which of the following statements are correct for alkali metal compounds? (i) Superoxides are paramagnetic in nature. (ii) The basic strengths of hydroxides increases down the group. (iii) The conductivity of chlorides in their aqueous solutions decreases down the group. (iv) The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2}?$. The maximum energy of a photon in the radiation in $eV $ is $(h = 6.62 \times 10^{-34} \, J-s, c = 3 \times 10^8 \, m/s)$

In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to

The magnetised wire of moment $M$ and length $l$ is bent in the form of semicircle of radius $r$. Then its magnetic moment is

In a certain code ROAD is written as URDG. How is SWAN written in that code?