SSC (English Medium) ९ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Algebra

Find the factor of the polynomial given below.

`1/2x^2 - 3x + 4`

Factorize the following polynomial.

(x² – x)² – 8 (x² – x) + 12

Factorize the following polynomial.

(x – 5)² – (5x – 25) – 24

Factorize the following polynomial.

 (x² – 6x)² – 8 (x² – 6x + 8) – 64

Factorize the following polynomial.

(x² – 2x + 3) (x² – 2x + 5) – 35 

Factorize the following polynomial.

(y + 2) (y – 3) (y + 8) (y + 3) + 56 

Factorize the following polynomial.

 (y² + 5y) (y² + 5y – 2) – 24

Factorize the following polynomial.

(x – 3) (x – 4)² (x – 5) – 6

Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.

If (a + b + c) (a - b + c) = a² + b² + c² show that a, b, c are in continued proportion.

If `a/b = b/c` and  `a , b , c > 0` then show that, (a + b + c) (b - c) = ab - c² 

If `a/b = b/c` and a, b, c > 0 then show that, `[a^2 + b^2]/(ab) = (a+c)/b`

If a, b, c are in continued proportion, then prove that 

`a/[ a + 2b] = [a - 2b]/[ a - 4c]`

If a, b, c are in continued proportion, then prove that 

`b/[b+c] = [a-b]/[a-c]` 

If a, b, c, d are in proportion, then prove that

`[11a^2 + 9ac]/[ 11b^2 + 9bd] = [ a^2 + 3ac]/[ b^2 + 3bd]`

If a, b, c, d are in proportion, then prove that 

`sqrt[( a^2 + 5c^2)/( b^2 + 5d^2)] = a/b`

If a, b, c, d  are in proportion, then prove that 

`[a^2 + ab + b^2]/[a^2 - ab + b^2] = [c^2 + cd + d^2 ]/[ c^2 - cd + d^2 ]`

The calculated mean of 50 observations was 80. It was later discovered that observation 19 was recorded by mistake as 91. What was the correct mean?

The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observation is 25. Find the 18^th observation.