(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

If 2 log y - log x - 3 = 0, express x in terms of y.

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log60

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log1.2

If log 4 = 0.6020, find the value of each of the following: log8

If log 4 = 0.6020, find the value of each of the following: log2.5

If log 8 = 0.90, find the value of each of the following: log4

If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`

If log 27 = 1.431, find the value of the following: log 9

If log 27 = 1.431, find the value of the following: log300

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)

Simplify: log a² + log a^-1

Simplify: log b ÷ log b²

Find the value of:

`("log"sqrt(8))/(8)`

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`

The diagonals PR and QS of a quadrilateral PQRS are perpendicular to each other. A, B, C and D are mid-point of PQ, QR, RS and SP respectively. Prove that ABCD is a rectangle.

PQRS is a parallelogram. M and N are the mid-points of the adjacent sides QR and RS. O is the mid-point of the diagonal PR. Prove that MONR is a rectangle and MN is half of PR.