A resistor, a capacitor and an inductor are joined in series with an alternating current source. If the frequency of the source is slightly increased from a very low value, then :

Two lenses of focal lengths, 20 cm and - 25 cm, respectively are placed in contact with each other. The power of the combination of lenses is

A conducting wire of length 0.1 m and mass \( 3 \times 10^{-3} \text{ kg} \), carrying a current of 5 A is suspended freely in a horizontal direction in a uniform magnetic field. The magnitude of magnetic field perpendicular to the length of conductor is:

Polaroids A and B are placed with their axes perpendicular to each other. Unpolarised light of intensity \(I_0\) is incident on A. A third polaroid C is kept between A and B such that its axis makes an angle of \(30^\circ\) with that of B. The Intensity of transmitted light through B is:

In the single slit experiment of diffraction, the aperture of the slit is 2 mm. If a monochromatic light of wavelength 600 nm is incident normally on the slit, the distance between \( 2^{\text{nd}} \) order minima and the \( 4^{\text{th}} \) order maxima on the screen placed 2 m away from the slit will be:

In the given arrangement, the current in the wire XY is increasing steadily. The direction of induced current in the metal rings 1 and 2 will be, respectively.

The frequency of a photon whose energy is 66.3 eV would be
(Given \( h = 6.63 \times 10^{-34} \text{ Js} \))

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.
Among \(\mathrm{Cr}(\mathrm{Z}=24), \mathrm{Co}(\mathrm{Z}=27), \mathrm{Mn}(\mathrm{Z}=25)\) and \(\mathrm{Fe}(\mathrm{Z}=26)\); which will show the maximum variety of oxidation states?

Which of the following pairs of solutions are isotonic?

If a function \(f: R _{+} \rightarrow[-5, \infty)\) given by \(f(x)=9 x^2+6 x-5\) is one-one and onto, then \(f^{-1}(y)\) is

A bubble in glass slab (\( \mu = 1.5 \)) when viewed from one side appears at 5 cm and 2 cm from otherside, then the thickness of the glass slab is:

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function \(z=2 x+y\) is