English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

If `2^x xx3^yxx5^z=2160,` find x, y and z. Hence, compute the value of `3^x xx2^-yxx5^-z.`

If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.

Simplify:

`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`

Simplify:

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

Show that:

`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`

If `a=x^(m+n)y^l, b=x^(n+l)y^m` and `c=x^(l+m)y^n,` Prove that `a^(m-n)b^(n-l)c^(l-m)=1`

If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`

Evaluate the following using identities:

`(2x+ 1/x)^2`

Evaluate the following using identities:

(2x + y) (2x − y)

Evaluate the following using identities:

`(a^2b - b^2a)^2`

Evaluate following using identities:

(a - 0.1) (a + 0.1)

Evaluate the following using identities:

(1.5x² − 0.3y²) (1.5x² + 0.3y²)

Evaluate the following using identities:

(399)²

Evaluate following using identities:

991 ☓ 1009

Evaluate the following using identities:

117 x 83

Evaluate the following using identities:

(0.98)²

Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25

Simplify the following:

322 x 322 - 2 x 322 x 22 + 22 x 22

Simplify the following:

0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24

Simplify the following

`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`