*Average value of a quantity
*Average value of a quantity
If a quantity y varies with x, then its average value in the interval x e [a, b] is defined as,
Average value for one complete cycle
- of sinθ & cosθ is zero.
- of sin2 θ & cos2θ is half.
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*Inverse function
*Inverse function
Function of the form, 
have the shown variation. All the curves pass through the point (1, 1). For n > 1 the graph lies above the rectangular hyperbola
(n =1) in the region
0 < x < 1 and then lies below it in the region x > 1. For 0 < n < 1 the graph first lies below the hyperbola in the region 0 < x < 1 and then lies above the hyperbola in the region x > 1.
*Point slope form
*Point slope form
Equation of a straight line having slope m and passing through a point A (x1, y1) is 
2 point form
Equation of a straight line passing through two point A (x1, y1) and B (x2, y2) is 
*Arithmetic progression
*Arithmetic progression
*Logarithms Let a is an arbitrary positive real number except 0. If ax = y, then logay = x
*Logarithms
Let a is an arbitrary positive real number except 0. If ax = y, then logay = x
Conversely, the antilogarithm of x is the number y i.e. y = antilogax.
Here ax = y is called arbitrary exponential function and loga y = x is read is log of y to the base a is equal to x. If a = 10, log is called common & if it is e, then called natural.
*Cramer’s rule For two simultaneous equations, a1 x + b1 y = c1 & a2 x + b2 y = c2
*Cramer’s rule
For two simultaneous equations,
a1 x + b1 y = c1 & a2 x + b2 y = c2
*Property of supplementary angles.
*Property of supplementary angles.
If α + β = 1800, then:
sinα= sinβ,cosα = -cosβ & tanα= – tanβ
>Trigonometric series
>Trigonometric series
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m.
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m. The separation between the two wires so that the upper wire is just supported by the magnetic repulsion is
