(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.

If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`

If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`

If a, b, c, d are in continued proportion, prove that:
(a² + b² + c²) (b² + c² + d²) = (ab + bc + cd)².

If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`

If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.

If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.

Using a graph paper, drawn an Ogive for the following distribution which shows a record of the weight in kilograms of 200 students.

Use your ogive to estimate the following:
(i) The percentage of students weighing 55kg or more.
(ii) The weight above which the heaviest 30% of the students fall.
(iii) The number of students who are:
(1) under-weight and
(2) over-weight, if 55·70 kg is considered as standard weight.

The frequency distribution of scores obtained by 230 candidates in a medical entrance test is as ahead:

Draw a cummulative polygon (ogive) to represent the above data.

Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:

(i) Calculate the cumulative frequencies.
(ii) Draw the cumulative frequency curve and form it determine the median weights of the potatoes.

Find the value of x in the following proportions : 10 : 35 = x : 42

Find the value of x in the following proportions : 3 : x = 24 : 2

Find the value of x in the following proportions : 2.5 : 1.5 = x : 3

Find the value of x in the following proportions : x : 50 :: 3 : 2

Find the fourth proportional to 3, 12, 15

Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`

Find the fourth proportional to 1.5, 2.5, 4.5

Find the fourth proportional to 9.6 kg, 7.2 kg, 28.8 kg

Find the third proportional to 5, 10

Find the third proportional to 0.24, 0.6