NCERT

To understand this, Assume you have a bucket that has infinite number of apples and if your mother asks "give me the apple". How will you figure out which one is "The Apple", she is asking for.

Similarly any inversre trigonometric functions behaves like a Many-one Function; which means,

For Example $\sin^ {-1}\left (\frac {2} {3}\right)$ can have many solutions, we need to fix one solutions which can be used as standerd value for the function.

• A standerd value (Angles) of any inverse trigonometric value lies between a fiexed range is known as principal value. 

For Ex; The value of $\sin^ {-1}\left (\frac {2} {3}\right)$ will always lie between –? /2 to? /2.

$y={\sin }^{?1}\left(\frac{2}{3}\right)?\sin \left(y\right)=\frac{2}{3}?y?[?\frac{?}{2},\frac{?}{2}]$  

NCERT textbooks for Classes 11 and 12 are crucial for CUET UG 2025, as they cover fundamental concepts and the exam's prescribed syllabus. However, to score well in the exam, students should also refer to additional books that offer advanced problems and varied practice exercises, especially for subjects like Physics and Chemistry.

Reference books like H.C. Verma's Concepts of Physics and OP Tandon's Organic Chemistry provide additional questions that help students practice for higher difficulty levels that might be covered in CUET Science paper.

As per the NCERT Textbooks

“An integrated Chip consists of many passive and active components fabricated on a single chip of silicon. these ICs are compact, low-cost, and highly reliable. They consume less power and have high speed.”

These ICs are used in majority of our daily use electronics and all advance electronics. 

Nuclear Binding Energy is the amount of energy required to completely dismantle a nucleus into its individual protons and neutrons which is equivalent to the amount of energy to form a nucleous from its constituent nucleons (protons and neutrons).

Binding energy is calculated using Einstein's mass-energy equivalence relation:

$B.E. = \Delta m \cdot c^2$Where:

• $\Delta m$ = mass defect (in kg or amu)

• $c$ = speed of light $(3 \times 10^8 \, \text {m/s})$ (3*108m/s)

The compound microscope comprises two convex lenses - the eyepiece (lower power) and the objective (high power, short focal length). The objective forms a magnified, inverted, and real image of a small object placed just beyond its focal point. Magnifying power is M = (L/f? ) * (D/f? ), where f? is the objective's focal length, L is the tube length, and f? is the eyepiece's focal length. This image acts as the object for the eyepiece.

The formula says that for a thin lens, the focal length (f) to its refractive index (? ) and radii of curvature (R? , R? ). Let a thin lens with surfaces of radii R? (first surface) and R? (second surface). We can use the refraction formula to calculate the image formation by the first surface. Following is the formula -? /v -? /u = (? -? )/R. Then we can combine both refractions and assume a lens in air (? = 1).

For mirrors and lenses, the Cartesian sign convention is used. For lenses: For convex lenses, the focal length is positive and for concave lenses, it is negative. Distances to the right of the optical center are positive.
For mirrors: For concave mirrors, the focal length is positive and for convex, it is negative. The distances to the right of the optical center are positive. The sign convention allows for consistent calculations for formulas like mirror and lens formulas, and for ray diagrams.

Diffraction leads to the formation of patterns of varying intensity. When around obstacles, waves bend and spread through the narrow opening, it is called diffraction. The interference results in a new wave pattern and involves the superposition of two or more coherent waves. Both these phenomena produce patterns of light and dark regions; the interference results from the combination of multiple waves and the diffraction arises from a single wave interacting with an aperture or obstacle. When the size of the aperture or obstacle is comparable to the wavelength of the wave, diffraction patterns are typically observed.

A coherent light source in Young's Double Slit Experiment illuminates two closely spaced slits, and produces two overlapping light waves. The interference of these waves constructively or destructively based on their phase difference lead to a pattern of bright and dark fringes on a screen, When the path difference is an integral multiple of the wavelength, it is constructive interference (bright fringes) and when the path difference is an odd multiple of half the wavelength, it is destructive interference (dark fringes). Through observable interference patterns, Young's Double Slit Experiment, shows the wave nature of light.