A cell of emf E and internal resistance r gives current of 0.5 A with external resistance of 12 \(\Omega\) and a current of 0.25 A with an external resistance 25 \(\Omega\). What is the value of internal resistance?

An \(\alpha\)-particle moves in a circular paths of radius 0.83 cm in the presence of a magnetic field \( 0.25 \text{ Wb/m}^2 \). The de-Broglie wavelength associated with the particle would be approximately :

A ray of light incident at 25° on one refracting surface of a prism of angle 60° suffers a deviation of 50°. What will be the angle of emergence?

An inductor of reactance 100 \( \Omega \) and resistor of resistance 100 \( \Omega \) are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is:

The least distance of distinct vision of a person is 50 cm. He wants to read a book placed at 25 cm. The focal length of the spectacles would be :

In a Young's double slit experiment, two slits are separated by 3 mm and the screen is placed 1.5 m away. The distance between two consecutive minima for a light of wavelength 420 nm is

A uniform electric field of 16 N/C exists in the vertically downward direction. The increase in electric potential as one goes up through a height of 75 cm.

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The transition metals and their compounds are known for their catalytic activity. This activity is ascribed to their ability to adopt multiple oxidation states and to form complexes. Vanadium(V) oxide (in Contact Process), finely divided iron, and nickel (in Catalytic Hydrogenation) are some of the examples. Catalysts at a solid surface involve the formation of bonds between reactant molecules and atoms of the surface of the catalyst (first row transition metals utilise 3d and 4s electrons for bonding). This has the effect of increasing the concentration of the reactants at the catalyst surface and also weakening of the bonds in the reacting molecules (the activation energy is lowering). Also because the transition metal ions can change their oxidation states, they become more effective as catalysts. Reaction between iodide and persulphate ions takes place as follows: \(2I^- + S_2O_8^{2-} \rightarrow I_2 + 2SO_4^{2-}\)
Which of the following catalyses the above reaction?

If v is the frequency of ac mains, then the frequency of sonometer wire at resonance is :

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In the formation of coordination complexes, if the inner \(d\) orbital \((n-1)d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital \((nd)\) in hybridisation (like \(sp^3d^2\)), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu = \sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton \((BM)\). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
\([Co(NH_3)_6]^{3+}\) and \([Ni(NH_3)_6]^{2+}\) respectively are

Which of the following is/are not considered as transition elements?
Ag, Mo, Zn, Hg, W

Which of the following does not have any place in the ecological pyramids?

If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below: