List of practice Questions

According to Cahn-Ingold-Prelog sequence rules, the correct order of priority for the given groups is

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 $(h = 6.62 \times 10^{-34} \, J-s, c = 3 \times 10^8 \, m/s)$

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

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

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 $E$)

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 $f : R \rightarrow R$ 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 $f: R \rightarrow R$ 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 $\overline{ M _{ W }}$ 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:

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

In the adiabatic compression, the decrease in volume is associated with

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

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

Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is

The bond length of $HCl$ molecule is $1.275\,?$ and its dipole moment is $1.03\, D$. The ionic character of the molecule (in percent) (charge of the electron $= 4.8 \times 10^{-10}$ esu) is

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

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

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

The orbit of geo-stationary satellite is circular, the time period of satellite depends on - (i) mass of the satellite (ii) mass of the earth (iii) radius of the orbit (iv) height of the satellite from the surface of earth Which of the following is correct?

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

The surface tension of soap solution is $0.03\, N/m$. The work done in blowing to form a soap bubble of surface area $40 \, cm^2, (in\, J)$ is

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

There is some change $W$ length when a $ 33000 \, N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \, m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} N/m^2$ and the coefficient of linear expansion of steel is $ 1.1 \times 10^{-5} /^{\circ} C)$.

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