For a medium with permittivity \( (\epsilon) \) and permeability \( (\mu) \), the speed of light \( (v) \) is given by :

In a Young's double slit experiment, interference fringes were produced on a screen placed 1.8 m from the two slits 0.3 mm apart and illuminated by light of wavelength 600 nm. The fringe width is

Wavelength of matter wave is independent of :

With the rise in temperature, the electrical resistance

If the ratio of mass number of two nuclei is 8 : 27, then the ratio of the volumes of their nuclei is :

Which of the following statements are correct?
A. Electric field lines are always perpendicular to equipotential lines.
B. A zero electric field inside a conducting sphere does not mean that the potential gradient is also zero.
C. The resultant of two electric fields is determined by vector addition of the two field strengths.
D. If the field lines get closer together at any place, it means that the field strength is decreasing.
E. The resultant potential at a point is just the sum of the individual potentials.
Choose the correct answer from the options given below:

The primary voltage and primary current of a transformer are 220 V and 10 A. The ratio of the number of turns on the secondary coil to the number of turns on the primary coil is 2:1. The values of voltage and current at the output are

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

\(\int_0^{\frac{\pi}{3}} \frac{\sin x}{(2-\cos x)^2} d x=\)

A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is

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.
Atomic number of \(\mathrm{V}, \mathrm{Mn}, \mathrm{Cu}\) and Zn is \(23,25,29\) and 30 respectively. Which of them shows a positive value for the standard electrode potential \(E^{\circ}\left(M^{2+} / M\right)\) ?

A person invested ₹ \(10000\) in a stock of a company for \(6\) years.
The value of his investment at the end of each year is given below:

2018	2019	2020	2021	2022	2023
₹11000	₹11500	₹13000	₹11800	₹12200	₹14000

The compound annual growth rate (CAGR) of his investment is:
[Given (1.4) \({ }^{\frac{1}{8}}=1.058\) ]

Match List-l with List-II

List-l	List-II
(A) Bt Cotton	(I) Functional ADA CDNA
(B) Method of Cellular defense	(II) 'A' peptide
(C) Genetically engineered insulin	(III) RNAi
(D) Gene therapy	(IV) Insecticidal protein

Choose the correct answer from the options given below: