A tiny spherical oil drop of mass 8 mg is kept suspended by applying a potential difference of 100 V between two metallic plates kept separated by a distance 1 cm. The number of electrons on the oil drop are : (Take \( g = 10 \text{ ms}^{-2} \))

A metal foil of thickness (3/4)d is introduced between two plates of a capacitor of capacitance C. The distance between the plates of the capacitor is d. The new capacitance of the capacitor will be

\( \alpha, \beta \) and \( \gamma \) rays emitted by a radioactive substance are allowed to pass through a region containing a magnetic field at right angles to their path. The energy gained will be

Match List I with List II

LIST I	LIST II
A. Brackett series	I. Visible region
B. Balmer series	II. Ultraviolet region
C. Paschen series	III. far infrared region
D. Lyman series	IV. infrared region

Choose the correct answer from the options given below:

The electric field is defined as \(\vec{E} = \lim_{q_0 \to 0} \frac{\vec{F}}{q_0}\) where \(q_0\) is the test charge and \(\vec{F}\) force on \(q_0\) due to the source charge. The meaning of \(\lim_{q_0 \to 0}\) is :

The correct sequence A, B, C, D, E with reference to atomic spectral series is :
(A) Lyman series \(\frac{1}{\lambda}=R\left(\frac{1}{A^2}-\frac{1}{n^2}\right)\)
(B) Balmer series \(\frac{1}{\lambda}=R\left(\frac{1}{B^2}-\frac{1}{n^2}\right)\)
(C) Pfund series \(\frac{1}{\lambda}=R\left(\frac{1}{C^2}-\frac{1}{n^2}\right)\)
(D) Brackett series \(\frac{1}{\lambda}=R\left(\frac{1}{D^2}-\frac{1}{n^2}\right)\)
(E) Paschen series \(\frac{1}{\lambda}=R\left(\frac{1}{E^2}-\frac{1}{n^2}\right)\)
Choose the correct answer from the options given below :

If \( +\sigma \) and \( -\sigma \) are the uniform surface charge densities of two parallel infinite thin plane sheets then the net electric field at the mid point of the two sheets will be given by (Where \( \epsilon_0 \) is the permittivity of free space, where the sheets are kept)

A radioactive nucleus M undergoes series of decays given below: M \(\xrightarrow{\beta^- decay}\) N \(\xrightarrow{\gamma decay}\) O \(\xrightarrow{\alpha decay}\) P. The mass number of M is 150 and Atomic No of M is 64. The Atomic number of P is

Answer the question on the basis of passage given below :
A colloid is a heterogeneous system in which a substance is dispersed (dispersed phase) as fine particles in another substance called dispersion medium.
Their particle size is intermediate between that of pure solutions (less than 1 nm) and suspensions (greater than 1000 nm). They are known for interesting properties such as enormous surface area, Tyndall effect, Brownian motion etc.
They are widely used in industries and day to day life.
Some prominent uses of colloids are those in smoke precipitators, purification of water, medicines, cleansers etc.
Which of the following electrolyte exhibits maximum flocculating power in the coagulation of a positive metal hydroxide sol?

The area of the triangle whose vertices are \((3,8),(-4,2)\) and \((5,1)\) is

Two photons of equal energy 8 MeV each, strikes two different metal sheets having work functions 4 MeV and 6 MeV, respectively. The ratio of maximum velocity of electrons emitted from two metal sheets respectively is :

Time reversal test is satisfied by:

The differential coefficient of \(\log _e\left[\log _e\left(\log _e x^5\right)\right]\) with respect to \(x\) is: