SSC (Marathi Semi-English) इयत्ता ९ वी - Maharashtra State Board Question Bank Solutions for Algebra

Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.

(2x³ − 2x² + ax − a) ; (x − a)

Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.

(54m³ + 18m² − 27m + 5) ; (m − 3)

If the polynomial y³ − 5y² + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.

If ( x³¹ + 31) is divided by (x + 1) then find the remainder. 

Fill in the blanks of the following.

`x/7 = y/3 = (3x + 5y)/("_____") = (7x -9y)/("_____")`

Fill in the blanks of the following.

`a/3 = b/4 = c/7 = (a-2b+3c)/("______") = ("______")/ (6 - 8 +14)`

If a(y + z) = b(z + x) = c(x + y) and out of a, b, c no two of them are equal then show that,

`(y - z)/[a ( b - c )] = ( z - x)/[ b ( c - a)] = ( x - y)/[c ( a - b )]`

If `x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y]` and x + y + z ≠ 0 then show that the value of each ratio is equal to 1.

If `[ax + by]/( x + y) = ( bx + az )/(x + z) = (ay + bz)/[y + z]` and `x + y + z ≠ 0 ` then show that `[a + b]/2`.

 If `(y + z)/a = (z + x )/b = (x + y)/c` then show that `x/[b + c - a ] = y/[c + a - b] = z/(a + b - c)`

If `(3x - 5y)/(5z + 3y) = (x + 5z)/(y - 5x) = (y - z)/(x - z)`then show that every ratio = `x/y`.

Polynomials bx² + x + 5 and bx³ − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.

Solve. 

`[ 16x^2 - 20x +9]/[ 8x^2 + 12x + 21] = ( 4x - 5 )/( 2x + 3)`

Solve. 

`( 5y^2 + 40y - 12)/( 5y + 10y^2 - 4) = ( y + 8)/( 1 + 2y)`

Solve:

`[12x^2 + 18x + 42]/[ 18 x^2 + 12x +58 ] = [ 2x + 3]/[ 3x + 2]`

If `[ 2x - 3y ]/[ 3z + y] = [ z - y ]/[ z - x ] = [ x + 3z ]/[ 2y - 3x]` then prove that every ratio = `x/y`.

 If `[by + cz ]/[b^2 + c^2] = [cz + ax]/[c^2 + a^2] = [ax + by]/[a^2 + b^2]` then prove that `x/a= y/b = z/c`

Complete the following cumulative frequency table:

Complete the following Cumulative Frequency Table:

The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.

55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.

1. How many students obtained marks 40 or above 40?
2. How many students obtained marks 90 or above 90?
3. How many students obtained marks 60 or above 60?
4. What is the cumulative frequency of equal to or more than type of the class 0-10?