Two identical cells each of emf E and internal resistance r are connected in parallel, their equivalent emf and equivalent internal resistance respectively will be:

A parallel plate air capacitor is charged, and then the battery is disconnected. Now on inserting a dielectric between the plates of the capacitor, which of the following change:
1. potential difference between the plates
2. charge on the plates
3. electric field between the plates
4. energy stored in the capacitor
Choose the correct answer from the options given below:

Which of the following combinations should be used for better tuning of an LCR circuit used for communication?

In Ampere-circuital law, the missing term is:

Identify the correct statements among the following.
(A) For two unlike equal charges, there is a neutral point on the middle point on the line joining the two charges.
(B) For two, unlike unequal charges, the neutral point will be outside on the line joining the two charges.
(C) For two positive equal charges, the neutral point will be at the middle point of the line joining the two charges.
(D) For two negative charges placed along a line, there will not be any neutral point.
Choose the correct answer from the options given below:

When a ray of light is incident at an angle of incidence \( 60^\circ \) on one face of an equilateral prism the angle of deviation is found to be minimum. The refractive index of the prism is :

At one place on earth, the resultant magnetic field is 0.25 G and the angle of dip is 45°. The horizontal component of earth's magnetic field will be

Helium gas is filled in a transparent balloon which is kept in air. The balloon behaves as:

If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is

In the following statements the in correct statement is :

The karyotype of an individual was found to be 44 + XXY. The individual is suffering from which of the following disorder?

\(\int\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x\) is equal to

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Metallic radii of some transition elements are as follows:
Fe: 126 pm; Co: 125 pm; Ni: 125 pm; Cu: 128 pm
Which of these elements will have highest density?