Directions : Read the following questions carefully and choose the right answer.
Important for :
1
In the new  budget, the price of Refined oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
» Explain it
B
Where R ⇒ the rose price of refined oil = 25%

 Reduction in consumption  = [ R × 100 ] %. (100 + R)

 ⇒ ( 25 × 100 ) % = 20%. 125

Hence, option (B) is correct.
2
The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the centre (in cm) is
» Explain it
B

Given, Common chord AB = 24 cm

Then, AD = DB = 12 cm

Diameter of circle of centre O = 30 cm, Then radius OA = 15 cm

And, Diamter of circle of centre O' = 26 cm, Then radius O'A = 13 cm

 = 152 – 122 = 81 = 9 cm

 = 132 – 122 = 25 = 5 cm

∴  OO' = OD + O'D = 9 + 5 = 14 cm

Hence, option B is correct.

3
Three planets revolve round the Sun once in 200, 250 and 300 days, respectively in their own orbits. When do they all come relatively to the same position as at a certain point of time in their orbits?
» Explain it
A
Given that, three planets revolves the Sun once in 200, 250 and 300 days, respectively in their own orbits.

∴     Required time = LCM of (200, 250 and 300) = 3000 days

Hence, after 3000 days they all come relatively to the same position as at a certain point of time in their orbits.

Hence, option A is correct.

4
The length of canvas 75 cm wide required to build a conical tent of height 14 m and the floor area 346.5 m2 is:
» Explain it
D

Given, h = 14 m and πr2 = 346.5

 = 3465 ⇒ r2 = 3465 × 7 ⇒ r2 = 441 10 10 22 4

 r = 21 2

Therefore, slant height (l) =
 r2 + h2

 441 + 196 4
=
 1225 4
=  35
2

Area of tent (which is a cone)= Area of canvas (which is a rectangle)

πrl = length of canvas × 0.75 m (breadth)

 ⇒ 22 × 21 × 35 = 3 × length 7 2 2 4

On solving the equation, we get

Length of canvas = 770 m.

Hence, option D is correct.

5
From a point P on the ground the angles of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45° Find the length of the flagstaff.
 (Take 3 = 1.732)
» Explain it
D

AC = Flag,  AB = building = 10 m

∠APB = 30°; ∠CPB = 45°

In Δ APB,

 tan 30° = AB PB

 ⇒ 1 = 10 3 PB

 ⇒   PB =  10 3 m

In ΔPBC,

 tan 45° = BC PB

 ⇒  1 = AB + AC PB

 ⇒  PB = AB + AC   ⇒   10 3 = 10 + AC

 ⇒  AC = 10 3 – 10

⇒  10(  3 – 1) m
 = 10( 1.732 – 1) m

= 10 × 0.732 = 7.32 m.

Hence, option D is correct.

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