Previous Year Paper year:2019 : ICSE-X-Mathematics

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ICSE-X-Mathematics

Previous Year Paper year:2019

with Solutions - page 3

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#5

#5-a
There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box.

Find the probability that the number on the disc is :
[3]

Ans : Sample space = 25 discs numbered from 1 to 25.

#5-a-i
an odd number
Ans : Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Probability (an odd number) = ``\frac{13}{25}`` .

#5-a-ii
divisible by 2 and 3 both
Ans : Numbers divisible by 2 and 3 both are 6, 12, 18, 24

Probability (divisible by 2 and 3 both) = ``\frac{4}{25}`` .

Numbers less than 16 are 1 to 15

#5-a-iii
a number less than 16.
Ans : Probability (a no. less than 16) = ``\frac{15}{25}`` or ``\frac{3}{5}``

#5-b
Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives 441 as interest at the time of maturity. Find the amount Rekha deposited each month.
Ans : Here, n = 20, R = 9% p.a., Interest = ₹ 441

Let the monthly deposit be of ₹ x.

Hence, the monthly deposit is ₹ 280.

#5-c
Use a graph sheet for this question.
[4]

Take 1 cm = 1 unit along both x and y axis.

#5-c-i
Plot the following points :

A(0, 5), B(3, 0), C(1, 0) and D(1, -5)

Ans : and(ii)

#5-c-ii
Reflect the points B, C and D on the y-axis and name them as B’, C’, D’ respectively.
Ans :

#5-c-iii
Write down the coordinates of B’, C’ and D’.
Ans : B’ (- 3, 0), C’ (- 1, ) and D’ (- 1, - 5)

#5-c-iv
Join the points A, B, C, D, D’, C’, B’, A in order and give a name to the closed figure ABCDD’C’B’.
Ans : Arrow Head.

#6

#6-a
In the given figure,∠PQR = ∠PST = 90°, PQ = 5 cm and PS = 2 cm.

#6-a-i
Prove that△PQR ∼ APST.
Ans :

#6-a-ii
Find Area of △PQR : Area of quadrilateral SRQT.

Ans :