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ICSE Class 10 Mathematics Solved Question Paper 2018

Long Answer Type

21.

A(2, 5), B(–1, 2) and C(5, 8) are the vertices of a triangle ABC, `M' is a point on AB such that AM : MB = 1 : 2. Find the co-ordinates of 'M’. Hence find the equation of the line passing through the points C and M.

22.
Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children.

Let the original number of children be x.

It is given that Rs. 7500 is divided among x children.

$\Rightarrow Money received by each child = Rs . \frac{7500}{x} If there were 20 less children, then money received by each child = Rs . \frac{7500}{x - 20}$

From the given information, we have

$\frac{7500}{x - 20} - \frac{7500}{x} = 100 \Rightarrow \frac{75}{x - 20} - \frac{75}{x} = 1 \Rightarrow \frac{75 x - 75 (x - 20)}{(x - 20) x} \Rightarrow \frac{75 x - 75 x + 1500}{x^{2} - 20 x} \Rightarrow 1500 = x^{2} - 20 x \Rightarrow x^{2} - 20 x - 1500 = 0$

$\Rightarrow x^{2} - 50 x + 30 x - 1500 = 0 \Rightarrow x (x - 50) + 30 (x - 50) = 0 \Rightarrow (x - 50) (x + 30) = 0 \Rightarrow x = 50 or x = - 30$

Since number of children cannot be negative, we reject x = - 30.

$\Rightarrow x = 50$

Thus, the original number of children = 50.

23.

If the mean of the following distribution is 24, find the value of 'a '.

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Number of students	7	a	8	10	5

24.

Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5
cm and ∠ABC = 120°

(i) Construct a circum-circle of ΔABC

(ii) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and
BC.

25.

Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.

26.

In ΔPQR, MN is parrallel to QR and $\frac{PM}{MQ} = \frac{2}{3}$

( i ) find $\frac{MN}{QR}$

( ii ) Prove that ΔOMN and ΔORQ are similar.

(iii) Find, Area of ΔOMN : Area of ΔORQ

27.

The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and cone are each of 4 cm. Find the volume of the solid.

28.

Use Remainder theorem to factorize the following polynomial:

2x³ + 3x² – 9x – 10.

29.

In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons.

30.

The angle of elevation from a point P of the top of a tower QR, 50 m high is 60⁰ and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre.