Sujit Prasad Kushwaha

This is the mathematics formulae book for class 12 students. Here, we have covered all the formulae needed to solve the questions of Mathematics. Permutation The total arrangement of total objects taken some or all at a time is called permutation. The permutation of 'n' objects taken 'r' at a time is denoted by $^np_{r}$ and is defined by; 1. $^np_{r}=\frac{n!}{(n-r)!}$ 2. Permutation of an object, all different;$$=\frac{n!}{p!\,q!\,r!}$$ where,  n=total objects p=repetition of first kind  q=repetition of second kind r=repetition of third kind 3. Circular permutation= $(n-1)!$ 4. If clockwise and anticlockwise arrangement are not distinguishable [necklace of beads and beads into bracelet]; Total number of permutation=$\frac{(n-1)!}{2}$ Combination The selection of total objects taken some or all at a time is called combination. The combination of 'n objects taken 'r' at a time is denoted by $^nc_{r} \, or \, c(n,r)$ and defined by; $$^nc_{r}=\frac{n!}{(n-r)!...

The phenomenon of bending of light and spreading into geometrical shadow after passing through obstacle or slits is called diffraction. The diffraction pattern can be obtained on the screen when width of slit is equivalent to wavelength of light. The bright and the dark fringes obtained on the screen due to diffraction are called secondary maxima and minima. Types of diffraction: On the basis of arrangement of device used, there are two types of diffraction. They are: 1. Fresnel's diffraction: The diffraction which is obtained due to the source slits and screen at a finite distance is called fresnel’s diffraction. In this diffraction, the wave front is spherical. So, diffraction pattern obtained on the screen are quite complex. 2.Fraunhoffer’s diffraction: The diffraction which is obtained due to the source slits and screen at infinite distance is called fraunhoffer’s diffraction. In this diffraction, the wave front is plane. So, diffraction pattern obtained on the sc...

Today, I am going to share three inspirations stories of Olympians who have become winner in spite of losing the game. 1. The Olympics for most sportspeople is a once in a lifetime event. Lawrence Lemieux stopped racing in an Olympic yacht race to help a fellow competitor who was in trouble. The whole world was watching. His priority of safety and concern for other people's lives was greater than his desire to win. Even though he did not win the race, he was a winner. He was honored by kings and queens all over the world because he kept the spirit of the Olympics alive. 2. Reuben Gonzales was playing the world title. The world was watching. In the final game, at match point, Gonzales played a super shot. The referee and the linesman both confirmed that the shot was good and he was declared the winner. But Gonzales hesitated and after a little pause, he went to his opponent and said, "The shot was faulty, let's play again." The service changed and he lost the match. Ev...

Life is like a melting river, That keeps flowing forever. Life is for study, That makes you steady.   Life is like a burning candle, And we are the one to handle. Life is seen to be a dazzling science, That discovers planets and mines.   Life teaches us to serve like cup, Without any type of give up. Life is the combination of sorrows and joys, Without knowledge, it is like a toy.   Life is horrible desert and land, Seem to be full of unwanted sand, Life is and administrative game, That can brighten your name and fame.   Life is like a burning cigarette, Which end with the horrible signs. Life is for hard work and labor, We are responsible as its saver. ✍Sunil Neupane

Situated just 7 kilometers north of Prithvichowk in the scenic Pokhara Valley, Mahendra Cave is a captivating natural wonder that has intrigued both travelers and locals. Located in the Batulechaur-16 area of northern Pokhara, this limestone cave offers more than just breathtaking geological formations; it's also rich in history, folklore, and spirituality. Whether you're an adventurer, a history enthusiast, or someone seeking spiritual peace, Mahendra Cave offers an unforgettable experience. The Historical Background: The story of Mahendra Cave's discovery is as fascinating as the cave itself. Local villagers, troubled by the loss of their domestic animals to wild tigers, tracked the predators back to what is now known as Mahendra Cave. This discovery, believed to have occurred in 2012 B.S., quickly made the cave a point of interest. Its significance grew even more when the late King Mahendra Bir Bikram Shah Dev visited the site in 2016 B.S. The cave was subsequently named...