Question

16 Write one rational and one irrational number lying between 0.25 and 0.32 1
17 In the figure, if ACB = CDA,AC = 6 cm and AD = 3 cm, then find the length of AB
C
A B
D
1
18 If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’
and centre O is 600, then find the length of OP.
OR
If the radii of two concentric circles are 4 cm and 5 cm, then find the length of each
chord of one circle which is tangent to the other circle.
1
19 If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c 1
20 Find the value(s) of for which the quadratic equation + 2√2 + 18 = 0 has equal
roots
1
Section – B
21 Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5
both.
2
22 Prove that the rectangle circumscribing a circle is a square. 2
6
23 In the given figure, DEFG is a square and BAC = 900. Show that FG2= BG x FC
OR
In an equilateral triangle, prove that three times the square of one side is equal to four
times the square of one of its altitudes.
2
24 ‘Skysails’ is that genre of engineering science that uses extensive utilization of wind
energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towing
kite to gain a height of anything between 100 metres – 300 metres.
The sailing kite is made in such a way that it can be raised to its proper elevation and
then brought back with the help of a ‘telescopic mast’ that enables the kite to be raised
properly and effectively.
Based on the following figure related to sky sailing, answer the questions:
(i) In the given figure, if sin = cos (3 − 30), where and 3 − 30 are acute
angles, then find the value of .
(ii) What should be the length of the rope of the kite sail in order to pull the ship at
the angle (calculated above) and be at a vertical height of 200 m?
2
7
25 Jayanti throws a pair of dice and records the product of the numbers appearing on the
dice. Pihu throws 1 dice and records the squares the number that appears on it. Who
has the better chance of getting the number 36? Justify?
OR
An integer is chosen between 70 and 100, Find the probability that it is
(a) a prime number
(b) divisible by 7
2
26 Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy
as she got first position in the class. While coming back to their home, Isha asked for a
treat from her father as a reward for her success. They went to a juice shop and asked
for two glasses of juice.
Aisha, a juice seller, was serving juice to her customers in two types of glasses.
Both the glasses had inner radius 3cm. The height of both the glasses was 10cm.
First type: A Glass with hemispherical raised bottom.
Second type: A glass with conical raised bottom of height 1.5 cm.
Isha insisted to have the juice in first type of glass and her father decided to have the
juice in second type of glass. Out of the two, Isha or her father Suresh, who got more
quantity of juice to drink and by how much?

Answer 1

Answer

16. Rational 0.26

Irrational 0.27070070007...

17. Step-by-step explanation:

Given,

AC = 8 cm,

AD = 3 cm and ∠ACB = ∠CDA

From figure,

∠CDA = 90°

∴ ∠ACB = ∠CDA = 90°

In right angled ∆ADC,

AC2 = AD2 + CD2

⇒ (8)2 = (3)2 + (CD)2

CD2 = 64 – 9 = 55

⇒ CD = √55 cm

In ∆CDB and ADC.

∠BDC = ∠AD [each 90°]

∠DBC = ∠DCA [each equal to 90°-∠A]

∴ ∠CDB ∼ ∆ADC

Then,

⇒ CD2 = AD × BD

18. In pic OR in pic

19.It is given that first three terms of an A.P are b, c and 2b. Divide both sides by c. Now divide both sides by 3. Therefore, the ratio of b and c is 2:3.

20.in pic