Height of the cone = Total height – Height of the cylinder = 15 – 10 = 5 cm

Radius of the cone = Radius of the cylinder = 50 m

Total volume of tent = Volume of cylinder + Volume of cone

⇒ πr²H + 1/3 × πr²h

⇒ π50² × 10 + 1/3 × π50² × 5

⇒ 50² × π × (10 + 5/3)

⇒ 2500 × 35/3 × π

⇒ 87500π/3 cm³

When a rectangle is formed into a cylinder, the length of the rectangle becomes the circumference of base and breadth becomes the height.

For first rectangle

2πr = 4π

∴ r = 2

h = 2π

Volume = π r² h

⇒ π × 2² × 2π = 8π²

For second rectangle

2πr = 5π

∴ r = 5/2

h = π

Volume = π r² h

⇒ π × (5/2)² × π = 6.25π²

Maximum possible volume = 8π²

Since they are in a plane (Let us consider XY plane) all line is of form y = mx + c

Let the slopes of the lines A, B and C be a, b and c respectively

Lines are parallel if their slopes are equal and perpendicular if the product of their slopes is -1

Statement 1:

A and C are parallel

∴ a = c

B and C are parallel

∴ b = c

Comparing both the equations

⇒ a = b

∴ A and B are parallel too. Statement 1 is true

Statement II:

A and C are perpendicular

∴ ac = -1 or a = -1/c

B and C are perpendicular

∴ bc = -1 or b = -1/c

Comparing both the equations

a = b

∴ A is parallel to B

∴ Statement II is true

Statement III:

Statement III need not be true because the lines A and B can be on either side of line C forming same angle but are not parallel

Angle subtended by full circle at center = 2π

Angle subtended by the given arc = π

∴ The arc is a semi-circle

Arc length of a semi-circle = π r = 22

⇒ 22/7 × r = 22

∴ r = 7 cm

Each pair can have one intersection point

Number of pairs in 8 lines = ⁸C₂ = 8! / (2! × 6!) = 28

Let the equal angles be x and the larger angle be x + 30

Sum of angles = 5x + x + 30 = 6x + 30

Sum of angles of a six sides polygon = (n – 2) × 180 = (6 – 2) × 180 = 720

⇒ 6x + 30 = 720

⇒ 6x = 690

∴ x = 115° 

Point of intersection of the perpendicular bisector is the circumcenter of the triangle.

It is possible for three chords to form a triangle but do not include the center when it is an obtuse angled triangle

∴ Statement 1 is possible

In a right triangle the perpendicular drawn from two vertices of the hypotenuse are the sides themselves. They meet on the vertex and lie on the side

∴ Statement 2 is possible

∴ Both 1 and 2 true

Frequency density is the ratio of the class frequency to the class width of the particular class.

Total amount of money spent as salary = Salary for category A worker + Salary for category B workers + Salary for category C workers

⇒ 65000 + 3 × 25000 + 5 × 20000 = 240000

Average salary = Total salary/Total number of workers

⇒ 240000/9 = 26666. 67

All B and C category workers get salary less than mean salary

∴ The number of workers earning less than the mean salary = 5 + 3 = 8

Total time taken = Time taken at a speed of 4 km/h + Time taken at a speed of 5 km/h

⇒ 12/4 + 10/5 = 5 hours [∵ Time = Distance/Speed]

Average speed = Total distance/Total time

⇒ (12 + 10) /5 = 22/5 = 4.4 km/h