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

What is the class-mark of class 25-35?

If the classes are 0-10, 10-20, 20-30... then in which class should the observation 10 be included?

The monthly maximum temperature of a city is given in degree celcius in the following data. By taking suitable classes, prepare the grouped frequency distribution table

29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0, 30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4, 30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2

From the table, answer the following questions.

1. For how many days the maximum temperature was less than 34^oC?
2. For how many days the maximum temperature was 34^oC or more than 34^oC?

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

(x² − 7x + 9) ; (x + 1)

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`.