algebra

sum of two numbers is 80 and the sum of their reciprocal is 4/75. Find the two numbers.

AP

Find the value of the expression:

(2 + 4 + 6 +.... + 100) + (1 + 3 + 5 + 7 + ...... + 99) ÷ 101

8-indicies

Find the value of k in the expression

64 + 2.64 + 3.64 + 4.64 + 5.64 + ....49.64 = k²

7-indicies

Find the value of x for which a= 2¹⁰⁰ + (2⁵⁰)² + (2²⁵)⁴ + (2⁵)²⁰ and b = 2⁹⁹ + (2³³)³ + (2¹¹)⁹ + (2³)³³ +2⁹⁹.x are equal (a = b).

6-indicies

Show that 25ⁿ⁺¹.3ⁿ⁺¹ – 3ⁿ⁺².5²ⁿ⁺¹ + 5ⁿ.15ⁿ where n is a natural number, is completely divisible by 31.

Numbers

numbers

Find the natural number for which 2010ⁿ –n²⁰¹⁰ = 2009

number and divisibility

Prove that 2⁰ + 2¹ + 2² + 2³ + …. 2⁹⁸ is divisible by 7

5-indicies

Prove that X = 4²ⁿ⁺³.3²ⁿ⁺³ - 6²ⁿ⁺³.2²ⁿ⁺¹ is a perfect square.

numbers

If n is a Natural number, then show that 7ⁿ -3 is divisible by 2.

Numbers

If x and y are digits such that 23xy + xy23 + xyxy = 11413, then find the value of x + y.

4-indicies

If,  (x – 2)^2x-4. 2³ = 8^17. Then find the value of x

3-indicies

If A = 2²ⁿ⁺¹.3ⁿ⁺⁵, and a = 4ⁿ, and b = 3ⁿ⁺⁴

Express A in terms of a and b.

Simultaneous Equation

At a flower show which 1250 attended, outsiders were charged $1, villagers $ 0.5 and school children $ 0.05. The total receipt from the flower show was $695. There were 3 times as many villagers as outsiders. How many outsiders came to the show?

Simultaneous equation using cross multiplication technique

Use cross multiplication to solve the equation:

5x- 3y -1=0 -------------- (1)
x +2y- 12=0 --------- (2)

simultaneous equation using cross multiplication technique

Use cross multiplication to solve the simultaneous equation:
3x-2y-5=0
4x +6y+12=0

Ratio and proportion

Show that:

If,

                 ax+cy+bz=0 ---- (1)
                 cx+by+az=0 ---- (2)
                 bx+ay+cz=0 ---- (3)

Then, a³+b³+c³ = 3abc
 

Ratio and Proportion

Find the ratio x:y:z from the following set of equation:

ax+by+cz=0
lx+my+nz=0

MAKING THE SUBJECT OF THE EQUATION

 

MAKING THE SUBJECT OF THE EQUATION