To get eight images of a single object one should have two plane mirror at an angle of :

If \( \lambda_1 \) and \( \lambda_2 \) are the longest wavelengths of the Lyman and Paschen series respectively, then \( \lambda_1 : \lambda_2 \) is:

In Young's double slit experiment, the light has a frequency \( 12 \times 10^{14} \text{ Hz} \) and the distance between the centres of adjacent fringes is 0.8 mm. If the screen is 1.6 m away, what is the distance between the slits? (Take speed of light \( c = 3 \times 10^8 \text{ m s}^{-1} \))

Which of the following statements is correct for a charged metallic shell?

The electric field vector of a plane electromagnetic wave oscillates sinusoidally at a frequency of \(4.5 \times 10^{10} \text{ Hz}\) in a medium with permittivity \(\epsilon_0\) and permeability \(\mu_0\). The wavelength of the wave is

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
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What would be the effective mass of a photon, if the frequencies of radiation is \(6 \times 10^{14} Hz\) ?

Choose the statements that are valid for the molecularity of a reaction
(A) Molecularity is equal to the number of reacting species involved in the overall reaction
(B) Decomposition of ammonium nitrite is an example of unimolecular reaction
(C) Reactions with the molecularity three are very rare
(D) Molecularity can only be determined experimentally
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Match List I with List II

List I	List II
A. Commensalism	Balanus and Chthamalus
B. Mutualism	Mycorrhizae and legume plants
C. Parasitism	Cuscuta on hedge plants
D. Competition	Sea anemone and clownfish

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The corner points of the feasible region determined by the following system of linear inequalities :
\(2 x+y \leq 10, \quad x+3 y \leq 15, \quad x, y \geq 0\) are \((0,0),(5,0),(3,4)\) and \((0,5)\).
Let \(z=p x+q y\), where \(p, q>0\).
Condition on \(p\) and \(q\) so that maximum of \(z\) occurs at both \((3,4)\) and \((0,5)\) is :

Which one of the given assisted reproductive technologies (ART) involves transfer of fertilized egg into the fallopian tube?

Arrange the following in the increasing order of their boiling points
(A) \(n- C _4 H _6 NH _2\)
(B) \(\left( C _2 H _5\right)_2 NH\)
(C) \(n- C _4 H _9 OH\)
(D) \(C _2 H _5 N\left( CH _3\right)_2\)
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Arrange the following radiations in the decreasing order of their energy
(A) Microwaves
(B) \( \gamma \)- rays
(C) AM radio waves (D) Infrared waves
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