The correct answer is option 3 i.e. 3 : 1.

From the pie chart:

Percentages of the total amount won by A and C are 15% and 9% respectively.

So, The difference in amounts won by A and C

= 15% - 9%

= 6%

From the pie chart:

Percentages of the total amount won by D and F are 14% and 16% respectively.

So, The difference in amounts won by D and F

= 16% - 14%

= 2%

Hence, Required ratio

= (12500 × 6%) : (12500 × 2%)

= 3 : 1

The correct answer is option 4 i.e. 80%.

We have:

So,

Total number of tickets sold in January = 720

Total number of tickets sold in April = 400

Required percentage = {(720 - 400)/400} × 100 = 80%

The correct answer is option 2 i.e. 25%.

Total number of youth addicted to drugs and those inclined towards Yoga in state A

= 12 + 16.5 = 28.5 lakhs

And

Total number of youth addicted to drugs and those inclined towards Yoga in state C

= 20 + 18 = 38 lakhs

Hence,

Required percentage = [(38 - 28.5)/38] × 100 = 25%

The correct answer is option 3 i.e. 50°.

If AB and CD are diameters, then O is the center of the circle.

For chord AD, the angle subtended at center = ∠AOD = 80°

∴ ∠ACD = ∠AOD/2 = 40° [∵ Angle subtended by the chord on any point of the circle is half the central angle]

In triangle CAD

∠CAD = 90° [∵ Diameter subtends right angle on the circle]

∠ACD + ∠CAD + ∠ADC = 180° [∵ Angle sum property of triangle]

40° + 90° + ∠ADC = 180°

∴ ∠ADC = 50°

The correct answer is option 3 i.e. 90°.

Interior angel + Exterior angle = 180°

Convert the exterior angles given to interior angles,

Thus interior angle C = 180 - 150 = 30°

The sum of the three angles of a triangle is 180°.

Thus, A + 60° + 30° = 180°

A = 90°

Thus, the exterior angle to A = 180 - 90 = 90°

The correct answer is option 1 i.e. 288 cm³.

Let the slant height of the cone be ‘l’ cm

Curved surface area of the cone = π × r × l = 180

⇒ 3 × 6 × I = 180

⇒ I = 10 cm

Let the height of the cone be ‘h’ cm.

According to Pythagoras' theorem: r² + h² = l²

⇒ 6² + h² = 10²

⇒ h² = 100 - 36

⇒ h = √64 = 8

So, the volume of the cone = 1/3 × π × r² × h = 1/3 × 3 × 36 × 8 = 288 cm³

The correct answer is option 3 i.e. 3/5.

Here cos A cosec A + cosec A  = 2

⇒ (cos A/sin A) + (1/sin A) = 2

⇒ cos A + 1 = 2 sin A

Squaring both sides.

⇒ (cos A + 1)² = 4 sin² A

⇒ cos² A + 2 cos A + 1 = 4 (1 - cos² A)

⇒ 5 cos²A  +  2 cos A - 3 = 0

⇒ (5 cos A - 3)(cos A + 1) = 0

Cos A = 3/5, -1

(∵ A is between 0 to 90)

∴ cos A = (3/5)

The correct answer is option 1 i.e. 4312 × 10⁴ cm².

The radius of a roller, r = 49 cm

The length of the roller i.e., the height of the cylinder, h = 200 cm

[The distance covered by the roller in 1 revolution] = [Curved Surface Area of the cylinder] = 2πrh

⇒ The distance covered by the roller in 1 revolution is,

= 2 × 22/7 × 49 × 200 = 61600 cm²

Thus, the distance covered by the roller in 700 revolutions is given by,

= 700 × 61600 cm² =  4,31,20,000 cm² = 4312  × 10⁴ m²

The correct answer is option 1 i.e. 5 feet.

AB = CD

In triangle CDE, 

tan30^o = CE/DC

⇒ 1/√3 = CE/12√3

⇒ CE = 12

Hence,

BC = (BE - CE) = (17 - 12) = 5 

BC = AD = 5

Height of boy = 5 feet