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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Disinformation is when false or misleading information is spread on purpose to trick or confuse people. It is like someone telling a lie or making up stories to make others believe something that isn't true. Disinformation can be found in many places, like social media, news articles, or even on online videos. Sometimes, people create disinformation to make others think a certain way or to cause trouble to others.  It's important to be careful and not believe everything we see or hear. We should always try to verify information from reliable sources before accepting it as true. A critical thinker will always ask the questions in different way to verify whether the information is true or false. The questioning technique used by them are, they ask why, what, who, where, when, and how. They inquiry the information from different perspectives. In the recent days, with the advancement in information, the case of disinformation is increasing rapidly. Let's see an example where Sa...

Have you ever thought what are the most commonly used Mathematics Formulae? Yes, many of you have. Let me convert your imagination into reality. Here are some of the most commonly used mathematics formulas: 1. Quadratic Formula:  $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ where a, b, and c are coefficients of quadratic equation. 2. Pythagoras Theorem: $$a^2+b^2=c^2$$ where a, b, and c are the length of the sides of a right-angle triangle. 3. Distance Formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinate of two points in a plane. 4. Area of a Circle: $$A=\pi{r^2}$$ where r is the radius of the circle. 5. Volume of a Sphere: $$V=\frac{4}{3}\pi{r^3}$$ where r is the radius of the sphere. 6. Volume of a Cylinder: $$V=\pi{r^2}h$$ where r is the radius and h is the height of the cylinder. 7. Area of a Triangle: $$A=\frac{1}{2}bh$$ where b is the base of the triangle and h is the height. 8. Slope-intercept formula: $$y=mx+c$$ where m is the slope o...