Exam Test Sets :: eLitmus

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. \(n_{c0}+n_{c1}+n_{c2}+............+n_{cn}=2^n\)