SSC (Marathi Semi-English) 9th Standard [इयत्ता ९ वी] - Maharashtra State Board Question Bank Solutions for Algebra

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.

The mean of 5 observations is 50. One of the observations was removed from the data, hence the mean became 45. Find the observation which was removed.

There are 40 students in a class, out of them 15 are boys. The mean of marks obtained by boys is 33 and that for girls is 35. Find out the mean of all students in the class.

If `barx` is the mean of x₁, x₂ ............x_n and `bary` is the mean of y₁, y₂, …….y_n and `barz` is the mean of x₁, x₂ ............x_n, y₁, y₂, ……….y_n then `barz` =?

The mean of five numbers is 50, out of which mean of 4 numbers is 46, find the 5^th number: