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)!...

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1. Read the following passage and answer the questions given below briefly. [10] To achieve a continuous improvement in the quality of the environment demands perception, education, economic strength, research, plus policies and administration graced to the right aims. A process of constant appraisal and adjustment is necessary, for as the scope of existing problems is reduced new ones will arise. Fresh discoveries will bring fresh difficulties and will always do so. As Goethe said, 'Every solution of a problem is a new problem.' Of first importance is the capacity to perceive the essentials of society's existence, to be able to analyse the factors that create and enhance the environment and to relate these to the contemporary situation. If people are to understand, they must be offered ideas which when their horizons; ideas to excite them to an awareness of a deeper purpose in their living and to a new relationship with their environment. The challenge is to find and captu...

The cow is considered a sacred animal in Nepal and holds great cultural and religious significance. It is also an important source of livelihood for many Nepalese farmers, providing milk, meat, and dung for fuel and fertilizer. In Hinduism, cows are considered sacred and are associated with the goddesses Lakshmi and Gauri, who are considered to be the embodiment of wealth, fertility, and motherhood. The cow is also a symbol of non-violence and is believed to possess healing powers. The cow is also a symbol of wealth and status in Nepal. Many families, especially in rural areas, own cows as a sign of prosperity and a source of income. Cows are considered a valuable asset, and their ownership is often used as a measure of social status. In addition, cows are often given as gifts at weddings and other important events. The cow is also considered a symbol of motherhood and is often depicted in art and religious iconography as a nurturing figure. In Hinduism, the cow is seen as a repres...