The sunlight is allowed to fall on a pinhole of diameter \( 10^{-4} \text{ mm} \) and thus a diffraction pattern is obtained. How will the size and intensity of the diffraction pattern be affected if the diameter of the pinhole is slightly increased?

An electric dipole of length 2 cm is placed at an angle of \(30^\circ\) with an electric field \(3 \times 10^5 \text{ N C}^{-1}\). If the dipole experiences a torque of \(9 \times 10^{-3} \text{ N m}\), the magnitude of either charge of the dipole is

A series LCR circuit is connected to a 220 V variable frequency (a.c) supply. If L = 20 mH, \( C = 800/\pi^2 \, \mu \text{F} \) and R = 110 \( \Omega \). The frequency of the source, for which the average power absorbed by the circuit is maximum will be:

Consider two different hydrogen atoms. The electron in each atom is in first excited state. According to Bohr's model, electrons will have :

A parallel plate capacitor having area A and separated by distance d is filled by copper plate of thickness b. The new capacitance is:

Which of the following are explained in Rutherford's model of an atom?
(A) An atom consists of a core called nucleus.
(B) The nucleus occupies a very small space as compared to the size of atom.
(C) The stability of an atom.
(D) The electrons revolve around the nucleus in various orbits.
Choose the correct answer from the options given below:

Two large plane parallel sheets with equal but opposite surface charge densities +\(\sigma\) and -\(\sigma\). A point charge q placed at points \(P_1, P_2,\) and \(P_3\) experiences forces \(F_1, F_2,\) and \(F_3\) respectively. Then :

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
Alfred Russel Wallace, a naturalist, arrived at conclusions similar to Darwin while working in:

The set of values of \(x\) satisfying \(26 \equiv 5(\bmod x)\) is __________ .

The ratio of shortest wavelength of lines in Balmer and Paschen series is :

The electric field vector associated with electromagnetic wave in free space is given by \(E=40 \cos \left(6 \times 10^8 t-k x\right) V m ^{-1}\). The value of \(k\) in SI unit is :

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis.
Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Animal starch is popularly known as

Which one among the following shows particle nature of light?