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In ax² + bx + c= 0

(a) If c= 0 one root is zero and other root is -b/a



(b) If b= 0 roots are equal in magnitude and opposite in sign

    

(c) If a= c roots are reciprocals to each other

    

(d) If a,b,c are of same sign then both roots are negative

    

(e) If a&c are of same sign & b is of opposite sign both roots are +ve.

    

(f)  If a&c are of different sign roots are of different signs.

rate if twaz useful!!

Power = force X velocity

g vatue at a depth of 'h' = g ( 1 - h / R )

If w is a cube root of unity then:

a) w³ = 1

b) 1 + w+ w²= 0

sin(A+B) =sinAcosB +sinB cosA

sin(A-B) =sinAcosB -sinB cosA

cos(A+B) =cosAcosB-sinAsinB

cos(A-B) =cosAcosB+sinAsinB

1. Number of diagonals of a ploygon of n sides= ⁿC₂- n  =  n(n−3) / 2

2.  ⁿC_r + ⁿC_r−1 =  ⁽ⁿ⁺¹⁾C_r

molarity=no. of moles volume of solution  in l

molality=no. of moles  mass of solvent in kg

CIRCULAR MOTION

Car taking a turn on level road: v = √(μsrg)

Overloaded truck:

(a) Radius of inner wheel < Radius of outer wheel

(b) maximum safe velocity on turn, v = √(gdr/2h)

1. Let Δx be an error in the variable, then Δx/x is called the relative error and  (Δx/x) X 100



    is called the percentage error in x.

2. If θ is the angle between the two curves at a point of intersection (x₁,y₁) then

                            tanθ = |m₁−m₂ / 1+m₁m₂| and m₁= [dydx]_(x1,y1)  for y = f(x)