The capacitance of a parallel plate capacitor with air as medium between the plates is 1 nF. When a material of dielectric constant 5 is filled between the plates, the new capacitance becomes -

Choose the phenomenon from the following, which shows that light is a transverse wave.

Match List-I with List-II

List-I (Electric Field)	List-II (Expression)
(A) Field due to an infinitely long straight uniformly charged wire	(I) \(\sigma\left(2 \varepsilon_0\right)^{-1}\)
(B) Field due to a uniformly charged thin spherical shell (inside the shell)	(II)\(q\left(4 \pi \varepsilon_0 r^2\right)^{-1}\)
(C) Field due to a uniformly charged infinite plane sheet	(III) \(\lambda\left(2 \pi \varepsilon_0 r\right)^{-1}\)
(D) Field due to a uniformly charged thin spherical shell (outside the shell)	(IV) zero

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Which of the following gives the correct expression for potential gradient in terms of the resistivity ( \(\rho\) ) of the wire?

The induced e.m.f in a coil rotating in a uniform magnetic field will increase if
A. Total number of turns in the coil decreases
B. Magnetic field increases
C. Speed of rotation of coil decreases
D. Area of the coil increases
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A straight wire of length 2 m and mass 50 g carrying a current of 4 A is balanced in air with the force due to uniform magnetic field acting perpendicular to the length of the wire. The magnitude of magnetic field is:

A capacitor of unknown capacitance is connected with a battery of V volts. The charge stored in it is \( 200 \, \mu\text{C} \). When the potential of the capacitor is reduced by 100 volts, the charge stored in it becomes \( 150 \, \mu\text{C} \). The unknown capacitance is:

Three resistors of resistance \(15 \Omega\) each are to be connected in combination. The ratio of maximum equivalent resistance to the minimum equivalent resistance is :

Match List - I with List - II.

List - I	List - II
(A) Genetic diversity	(I) Mangroves and Coral reef
(B) Species diversity	(II) Rauwolfia vomitoria in different Himalayan ranges
(C) Ecological diversity	(III) Amphibians in Western Ghats
(D) Biodiversity loss	(IV) Dodo in Mauritius

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If a line makes angle π/3 and π/4 with the positive directions of x-axis and y-axis respectively, then the acute angle made by the line with positive direction of z-axis is

2-Bromopentane is heated with alcoholic KOH. Which is the correct statement for this reaction?
A. Only pent-2-ene is formed.
B. Only pent-1-ene is formed.
C. Both pent-2-ene and pent-1-ene are formed.
D. pent-2-ene will be major product as it is more stable.
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Which of the following is not correct about the Central Limit Theorem?

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 \(E^{\circ}\left(M^{2+} / M\right)\) ?