Exam Test Sets :: eLitmus

eLitmus Dashboard
Tot. Mock Test: 13+
Tot. Exam. Sec.: 3+
Important Formulas:
- Series:
- Sum of first n natural numbers, \(1+2+3+4+....n=\frac{n(n+1)}{2}\)
- Sum of squares of first n natural numbers, \(1^2+2^2+....n^2=\frac{n(n+1)(2n+1)}{6}\)
- Sum of cubes of first n natural numbers, \(1^3+2^3+....n^3=\left(\frac{n(n+1)}{2}\right) ^2\)
- Sum of first n terms of AP., \(S_n =\frac{n}{2}[2a+(n-1)d]\)
- 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 \(r\neq1 \)
- Area and Volume:
- surface area of Sphere = \(4 \pi r^2\)
- Volume of Sphere = \(\frac{4}{3}\pi r^3\)
- Curved Surface area of Cone = \(\pi r l\)
- Slant Height of Cone, \(l= \sqrt{(r^2+h^2)}\)
- Total surface area of Cone, \(= \pi r(r+1)\)
- Volume of Cone, \(= \frac{1}{3} \pi r^2h\)
- Curved Surface area of the Cylinder\(= 2 \pi rh\)
- Volume of the Cylinder\(= \pi r^2h\)
- Total Surface area of the Cylinder\(= 2 \pi r(r+h)\)
- Area of the Rhombus\(=\frac{product of its diagonals}{2}\)
- Rhombus diagonals are at right angles.
- Area of trianngle with sides a,b and c,\(\sqrt{s(s-a)(s-b)(s-c)} s=\frac{(a+b+c)}{2}\)
- Trigonometry/Geometry:
- Sin 90 =1;\(Sin 60=\frac{\sqrt{3}}{2};sin45=\frac{1}{\sqrt{2}};sin30=\frac{1}{2}\)
- In right angle triangle, \((hypotenuse)^2=(side1)^2+(side2)^2\)
- Equations/Polynomials/Maxima/Minima:
- Roots of a Quadratic equation \(ax^2+bx+c=0\) are \(x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\)
- A function of \(y=f(x)\) will have maxima or minima when \(\frac{dy}{dx}=0\)
- Logarithm:
- log b + log c =log(bc)
- log b - log c =\(log(\frac{b}{c})\)
- \(log b^a=a logb\)
- If \(log_ab=c,\) then \(b=a^c\)
- log is to base 10 unless specified otherwise.
- Algebra:
- \(a^3+b^3=(a+b)(a^2-ab+b^2)\)
- \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
- Permutation and Combination:
- \(n_{c0}+n_{c1}+n_{c2}+............+n_{cn}=2^n\)