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

How many liters of water will flow out of a pipe having a cross sectional area 6 cm² in one hour, if the speed of water in the pipe is 30 cm/sec?

State the axis on which the following points lie: J(0, -7), M(5, 0), P(-4, 0), R(0, 6) and W(2, 0)

Plot the points O (0, 0), P (6, 0) and R (0, 5) on a graph. Find the coordinates of the point Q such that OPQR is a rectangle.

Plot the points A (3, 4) and C (-3, -2) on a graph. Find the coordinates of the point B and D such ABCD is a square. Also find the area of the square.

Plot the points (-2, 3), (3, 3), (5, -2) and (-5, -2) on a graph and join them in order. Name the figure you get.

Rationalise the denominators of : `3/sqrt5`

Rationalise the denominators of : `(2sqrt3)/sqrt5`

Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`

Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`

Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`

Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`

Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`

Rationalise the denominators of:

`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`

Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`

Simplify :
` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`

Simplify:

`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`

Rationalise the denominator of `1/[ √3 - √2 + 1]`

If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`

Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`

In the following figure, ABCD is a rhombus and DCFE is a square.

If ∠ABC =56°, find:
(i) ∠DAE
(ii) ∠FEA
(iii) ∠EAC
(iv) ∠AEC