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# Exam Test Sets :: eLitmus

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## Important Formulas:

1. Series:
1. Sum of first n natural numbers, $$1+2+3+4+....n=\frac{n(n+1)}{2}$$
2. Sum of squares of first n natural numbers, $$1^2+2^2+....n^2=\frac{n(n+1)(2n+1)}{6}$$
3. Sum of cubes of first n natural numbers, $$1^3+2^3+....n^3=\left(\frac{n(n+1)}{2}\right) ^2$$
4. Sum of first n terms of AP., $$S_n =\frac{n}{2}[2a+(n-1)d]$$
5. Sum of first n terms of G.P., $$S_n =\frac{a(1-r^n)}{1-r}$$,Sum of first n terms of G.P., $$S_n =\frac{a(1-r^n)}{1-r}$$, when $$r\neq1$$
2. Area and Volume:
1. surface area of Sphere = $$4 \pi r^2$$
2. Volume of Sphere = $$\frac{4}{3}\pi r^3$$
3. Curved Surface area of Cone = $$\pi r l$$
4. Slant Height of Cone, $$l= \sqrt{(r^2+h^2)}$$
5. Total surface area of Cone, $$= \pi r(r+1)$$
6. Volume of Cone, $$= \frac{1}{3} \pi r^2h$$
7. Curved Surface area of the Cylinder$$= 2 \pi rh$$
8. Volume of the Cylinder$$= \pi r^2h$$
9. Total Surface area of the Cylinder$$= 2 \pi r(r+h)$$
10. Area of the Rhombus$$=\frac{product of its diagonals}{2}$$
11. Rhombus diagonals are at right angles.
12. Area of trianngle with sides a,b and c,$$\sqrt{s(s-a)(s-b)(s-c)} s=\frac{(a+b+c)}{2}$$
3. Trigonometry/Geometry:
1. Sin 90 =1;$$Sin 60=\frac{\sqrt{3}}{2};sin45=\frac{1}{\sqrt{2}};sin30=\frac{1}{2}$$
2. In right angle triangle, $$(hypotenuse)^2=(side1)^2+(side2)^2$$
4. Equations/Polynomials/Maxima/Minima:
1. Roots of a Quadratic equation $$ax^2+bx+c=0$$ are $$x=\frac{-b+-\sqrt{b^2-4ac}}{2a}$$
2. A function of $$y=f(x)$$ will have maxima or minima when $$\frac{dy}{dx}=0$$
5. Logarithm:
1. log b + log c =log(bc)
2. log b - log c =$$log(\frac{b}{c})$$
3. $$log b^a=a logb$$
4. If $$log_ab=c,$$ then $$b=a^c$$
5. log is to base 10 unless specified otherwise.
6. Algebra:
1. $$a^3+b^3=(a+b)(a^2-ab+b^2)$$
2. $$a^3-b^3=(a-b)(a^2+ab+b^2)$$
7. Permutation and Combination:
1. $$n_{c0}+n_{c1}+n_{c2}+............+n_{cn}=2^n$$