A proton and an alpha particle have the same de-Broglie's wavelength. What is same for both of them?

A magnetic field energy of \( 34 \times 10^{-6} \) J is stored in an inductor of inductance 1.7 mH in an LC circuit. The current flowing in the inductor is:

Which of the following statements are correct ?
(A) Electrostatic field lines form closed loops.
(B) In an electric dipole, the direction from charge to q is the direction of the dipole.
(C) Water molecule is an example of polar molecule.
(D) The electric field due to a uniformly charged thin shell is zero at some points inside the shell.
(E) Electrostatic force is conservative in nature.
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The ratio of nucleus density of nitrogen nucleus (\( {}^{14}_7\text{N} \)) to the nucleus density of oxygen nucleus (\( {}^{16}_8\text{O} \)) will be :

In the given circuit when steady current flows, the potential drop across the capacitor is:

Which of the following statements are correct?
(A) When light rays undergoes two internal reflections inside a raindrop, a secondary rainbow is formed.
(B) The angle between the emergent ray and angle of prism is called the angle of deviation.
(C) Light undergoes successive total internal reflections as it move through an optical fibre.
(D) A telescope provides angular magnification of distant objects.
(E) A simple magnifier is a diverging lens of small focal length.
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A bar magnet with pole strength m and magnetic dipole moment p is cut into two identical pieces along its length.
Then for each of the two pieces

Match List-I with List-II

List-I	List-II
(A) The vectors \(\lambda \hat{i}+\hat{j}+2 \hat{k}\) and \(\hat{i}+\lambda \hat{j}+\hat{k}\) are perpendicular if \(\lambda\) is equal to	(I) 1
(B) The vectors \(3 \hat{i}+6 \hat{j}-\hat{k}\) and \(2 \hat{i}+\lambda \hat{j}-2 \hat{k}\) are collinear if \(\lambda\) is equal to	(II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{b}=3 \hat{i}-\hat{j}+5 \hat{k}\) is	(III) \(2 / 3\)
(D) If \(|\vec{a}|=1\) and \(\vec{a}+\vec{b}=\overrightarrow{0}\), then \(|\vec{b}|\) is equal to	(IV) 2

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Read the passage carefully and answer the Questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O_H bond along with the reactions involving the complete -COOH group.
Arrange the following in the increasing order of their pK_a values:
(A) CF₃-COOH
(B) O₂N-CH₂-COOH
(C) NC-CH₂-COOH
(D) H-COOH
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The ratio of shortest wavelength of lines in Balmer and Paschen series is :

A pendulum of length 'l' having a bob of mass 'm' carrying charge 'q' is suspended from a stationary rigid support in a region of uniform electric field 'E' as shown in the figure. If the system is in equilibrium, the nature and magnitude of 'q' will be :

The current in a device varies with time 't' as I = 6 t, where I is in mA and t is in s. The amount of charge that passes through the device during t = 0 s to t = 3 s is

The term of the perpetuity is: