English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

Prove that:

`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`

Prove that:

`(a^-1+b^-1)^-1=(ab)/(a+b)`

If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`

Simplify the following:

`(3^nxx9^(n+1))/(3^(n-1)xx9^(n-1))`

Simplify the following:

`(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))`

Simplify the following:

`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`

Simplify the following:

`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`

Solve the following equation for x:

`7^(2x+3)=1`

Solve the following equation for x:

`2^(x+1)=4^(x-3)`

Solve the following equation for x:

`2^(5x+3)=8^(x+3)`

Solve the following equation for x:

`4^(2x)=1/32`

Solve the following equation for x:

`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`

Solve the following equation for x:

`2^(3x-7)=256`

Solve the following equations for x:

`2^(2x)-2^(x+3)+2^4=0`

Solve the following equations for x:

`3^(2x+4)+1=2.3^(x+2)`

If 49392 = a⁴b²c³, find the values of a, b and c, where a, b and c are different positive primes.

If `1176=2^a3^b7^c,` find a, b and c.

Given `4725=3^a5^b7^c,` find

(i) the integral values of a, b and c

(ii) the value of `2^-a3^b7^c`

If `a=xy^(p-1), b=xy^(q-1)` and `c=xy^(r-1),` prove that `a^(q-r)b^(r-p)c^(p-q)=1`

Assuming that x, y, z are positive real numbers, simplify the following:

`(sqrt(x^-3))^5`