Factorisation

Factorize: a³ + b³ + 8c³ - 6abc

factorization

Factorize: a³ – 27b³ + c³ + 9abc

Factorization

Factorize: a (b² + c² – a²) + b(a² + c² – b²)

Factorization

Factorize: m³ – n³ –(x² –mn)(m – n)

factorization

Factorize:

3x² – 2ab – x (b – 6a)

Factorization

Factorize: ab(x² + 1) – x(a² + b²)

Algebra

If x³ + y³ = 280 and x²y + y²x = 240, then find the ratio of x and y.

Arithmetic Progression

If p times the p^th term of an AP is q times the q^th term. Then show that the (p + q)^th term of the AP must be zero.

Quadratic equation - interesting way to solve

Solve for x:

(x + 5)² + (x + 3)² = 12

Divisibility

Show that  3¹ + 3² +... 3²⁰¹⁰ is divisible by 363.

algebra

 If x² + y² = 74 and xy = 35, find the value of x and y.

Remainder theorem

Show that: (c + a - 2b)d²+ (a + b - 2c) d + (b + c - 2a) is exactly divisible by (d - 1).

algebra

By means of the formula  (a + b)(a - b) = a² - b²

find the value of the expression
2117 x 1883 - 1113 x 887

Algebra

show that (y² - 3y)( y² - 3y + 2)+ 1 is a perfect square and find the square root.

Simultaneous equation

If 6x + 4y - 2z - 5 = 3x -2y + 4z + 10 = 5x - 2y + 6z + 13 = 0, then find x, y and z

Simultaneous equation

If p/x + q/y = 0 and px + qy = r then find the value of x and y.

simultaneous equation

if m/x + n/y = a and n/x + m/y = b, then find x and y

math for fun

 

(If you wish to know more about carbon dating, why don’t you take a peep at:

http://mathcentral.uregina.ca/beyond/articles/ExpDecay/Carbon14.html)

2-variations

The pressure of gas under constant heat condition is found to vary inversely with the volume raised to the power of γ, where γ is the ratio of specific heat of the gas under constant pressure to constant volume, and is found to be 1.14. A student observes that a certain gas occupies a volume of 22.4 litres under 3 kg /cm² pressure. What will be the pressure of gas if the same quantity of gas is reduced to 11.2 litres?

variation

For a free falling body, the instantaneous velocity is proportional to square of time taken. In 3.3 sec. the velocity of the body is 100 m/s. What will be the velocity after 10 sec.?