If Brewster's angle be θ, then the critical angle is:

A galvanometer has a resistance of 8 \( \Omega \). It is shunted by a wire of resistance 2 \( \Omega \). If the total current is 2 A, the current passing through the shunt is

The half-lives of two radioactive specimens are \(T_1=5\) years and \(T_2=7.5\) years.
The ratio of their disintegration constants \(\lambda_1\) and \(\lambda_2\) is:

Match List I with List II

LIST I	LIST II
A.Resistance	I.Property of the material
B.Super conductor	II.The capacity of supplying current in the circuit
C.Specific resistance	III.The collision of electrons while moving through the conductors.
D.Ampere-hour	IV.Motion of electrons through a conductor without any collision

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Match List I with List II

List I	List II
A. Rod rotated in uniform magnetic field	I. \( e = e_{0} \sin(\omega t) \)
B. Coil rotated in uniform magnetic field	II. \( e = Blv \)
C. Rod moved with linear velocity \( v \)	III. constant (for motional emf at constant \( v \))
D. Rectangular coil moved in magnetic field	IV. \( e = \frac{B\omega l^{2}}{2} \)

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Which of the following statements is not true with reference to a potentiometer ?

An electron of mass \( 9.11 \times 10^{-31} \text{ kg} \) is moving with velocity \( 5.4 \times 10^6 \text{ m/s} \). Its momentum will be

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
In context of the Lanthanoids, which of the following statements is/are NOT correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. Availability of \(4f\) electrons results in the formation of compounds in \(+4\) oxidation state for all the members of the series
C. Because of similar properties, the separation of lanthanoids is not easy
D. \(La(OH)_3\) is least basic among hydroxides of lanthanoids
E. Ce can act as an oxidising agent
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The value of \(\int_0^1 x e^x d x\) is :

The conductivity of 0.001 mol \(\text{L}^{-1}\) acetic acid is \(5.01 \times 10^{-5} \text{ S cm}^{-1}\).
Calculate its dissociation constant if \(\Lambda_m^{\circ}\) for acetic acid is
390.5 \(\text{S cm}^2 \text{mol}^{-1}\).

Which of the following statements are true regarding Lanthanoid elements?
i. \(\text{La}(\text{OH})_3\) is the basic hydroxide of Lanthanoids.
ii. \(\text{Zr}^{4+}\) and \(\text{Hf}^{4+}\) ions have almost similar ionic sizes.
iii. \(\text{Ce}^{4+}\) acts as an oxidising agent.
iv. Trivalent Lanthanoid ions are not coloured.
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The standard reduction potentials are given as :
\(\text{E}^{\circ}_{\text{K}^{+}/\text{K}} = -2.93 \text{ V}\)
\(\text{E}^{\circ}_{\text{Ag}^{+}/\text{Ag}} = +0.80 \text{ V}\)
\(\text{E}^{\circ}_{\text{Cu}^{2+}/\text{Cu}} = +0.34 \text{ V}\)
\(\text{E}^{\circ}_{\text{Ni}^{2+}/\text{Ni}} = -0.25 \text{ V}\)
\(\text{E}^{\circ}_{\text{Li}^{+}/\text{Li}} = -3.05 \text{ V}\)
Arrange the following metals in increasing order of their reducing power :
A. K
B. Ag
C. Cu
D. Ni
E. Li
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\(60 \%\) members of a committee favour a certain proposal and \(40 \%\) members oppose the proposal.
A member is selected and let the random variable \(X=0\) if he opposes and \(X=1\) if he is in favour.
Then the variance of the random variable \(X\) is