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...

                                                                  New Syllabus Course Title: Scientific Communication                                                                   Full Marks:50 Course No: SC 101                                                   ...

 1. Read the following passage and answer the questions given below briefly: [10] There is a considerable scientific disagreement about the medical hazards of the new pollutants; about the effects of DDT now found in human bodies, about the diseases due to smog, or about the long range effects of fallout. But the crucial point is that the disagreements exists, for they reveal that we have risked these hazards before we know what harm they might do. Unwittingly we have loaded the air with substances that interfere with the functioning of the blood. Because we wanted to build nuclear bombs and kill mosquitoes; we have burdened our bodies with strontium-90 and DDT, with consequences that no one can now predict. We are, in effect, conducting a high experiment ourselves. A generation hence-too late to help-public health statistics may reveal what hazards are associated with these pollutants. ('Science and Survival,' Barry commoner) a) What are the three pollutants with which man has...

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...