List of practice Questions

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

On a surface, if photon of wavelength $\lambda$ is incident, the stopping potential is $3.2$ V. If the wavelength incident is $2\lambda$, stopping potential is $0.7$ V. Find $\lambda$.

An electron makes transition from higher energy orbit to lower energy orbit in $Li^{2+}$ ion such that $n_1 + n_2 = 4$ and $n_2 - n_1 = 2$. Determine the wavelength of emitted photon in transition (in cm).

In a vernier calipers 50 VSD are equal to 48 MSD. 1 MSD is equal to $0.05$ mm. Find least count of this vernier calipers.

In YDSE, slit separation $d = 2$ mm, distance between slits and screen $D = 10$ m. Wavelength of light is $\lambda = 6000$\AA. If intensity of light through each slit is $I_0$, find intensity at point directly in front of one of the slits.

0.18 M HQ solution has molar conductivity $\frac{1}{30}$ times the molar conductivity of 0.02 M HZ solution. Find the value of pK$_a$(HQ) − pK$_a$(HZ).
[Given that $\alpha$ is very less than 1]

The half-life of radioactive isotope Zn$^{65}$ is 245 days. Find the time after which activity of Zn sample remains 75% of its initial value.

Two moles each of the gases P$_2$, Q$_2$ and PQ are present in a vessel at equilibrium. If 1 mole each of P$_2$ and Q$_2$ is added at equilibrium, then determine the composition (in mole) of each species at the new equilibrium.

Correct order of 2$^{nd}$ ionisation energy is:

Element X is the lightest element of group 7 of periodic table which forms oxo-anion in +6 oxidation state. The colour of potassium salt of the oxo-anion is:

In general tests of Ba$^{2+}$ and Ca$^{2+}$ give the respective tests as:

Select incorrect option:

Statement-I: Two different aldehydes on cross aldol condensation always give four products.
Statement-II: Among benzaldehyde and acetophenone, only acetophenone reacts with semicarbazide.

Let $f(x)=|\log_e x|-|x-1|+5$. Statement 1: $f(x)$ is differentiable for all $x\in(0,\infty)$
Statement 2: $f(x)$ is increasing in $(1,\infty)$
Statement 3: $f(x)$ is decreasing in $(0,1)$
Which of the following is correct?

An \( \alpha \)-particle with KE 7.9 MeV is projected towards a stationary target nucleus of \( Z = 79 \). Find the distance of closest approach.

Statement-I: Fluid exerts pressure on the surface of a solid in contact with it. Statement-II: The excess potential energy of molecules at the surface of a liquid leads to surface tension. Which of the following is correct?

Statement-I: Sucrose is dextrorotatory and upon hydrolysis, it becomes laevorotatory. Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the laevorotation of glucose is more than dextrorotation of fructose. Which of the following is correct?

Which of the following statement is correct regarding the nature and directive influence of \( \text{NO}_2 \) group in nitrobenzene?

Bohr’s radius of H-atom is \( 2.12 \times 10^{-10} \) m. Calculate the energy of electron at this level.

Which of the following statement is correct regarding an element having atomic number 79?

Sodium extract of organic compound of 0.1 g is treated with chlorine water and \( \text{CCl}_4 \) which dissolves in organic solvent to produce a violet colour. Upon treatment with \( \text{AgNO}_3 \), a yellow ppt. of 0.12 g is produced. Calculate the percentage of halide in the organic compound.

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{1}{\left\lfloor x \right\rfloor + 4} \, dx \] where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function, is: