Q.1. If area of circle is equal to volume of sphere with equal radii, find the radius.

1. √3

2. √3/2

3. 1 / 2

4. 3/4

5. 1

Sol : Option 4
Let r be the radius, We have
πr^{2} = 4/3 πr^{3}
⇒ r = 3/4

Q.2. The length of a garden is thrice its breadth. A playground measuring 180 sq. m occupies 1/15th of the total area of the garden. The length of the garden is

1. 60 m

2. 30 m

3. 40 m

4. 50 m

5. 90 m

Sol : Option 5
Let L be the length and B is the breadth of the garden. We have L = 3B.
Total area of the garden = 180 x 15 = 2700 sq m. ⇒ LB = 2700
⇒ 3B^{2} = 2700 ⇒ B^{2} = 900 ⇒ B = 30m
Hence the length of the garden = 30 × 3 = 90 m

Q.3. The perimeter of an equilateral triangle is 96√3 cm. Find its height.

1. 32 cm

2. 48 cm

3. 16 cm

4. 64 cm

5. 24 cm

Sol : Option 2
Perimeter of the equilateral triangle is 96√3 cm.
Each of the side of the equilateral triangle is 96√3 / 3 = 32√3 cm.
The height of the equilateral triangle will be = (√3 / 2) x 32√3 = 48cm

Q.4. If the ratio of radius of two spheres is 4:7, the ratio of their volume is

1. 4 : 7

2. 64 : 343

3. 49 : 16

4. 16 : 49

5. None of these

Sol : Option 2
Ratio of radii of 2 spheres is 4: 7.
∴ratio of their volume =4^{3} : 7^{3} = 64: 343

Q.5. The diameter (in meter) of a sphere whose volume is 268 (4/21) m^{3} is

1. 6

2. 12

3. 8

4. 24

5. 16

Sol : Option 3
Volume of the sphere = 268 (4/21) = 5632 / 21 m^{3}. Now 4/3 π ^{3} = 5632 / 21 ⇒ r^{3} = (5632 / 21) x (3/4) x (7/22) = 64 ⇒ r = 4m Hence diameter = 8m

Q.6. The slant height of a right circular cone is 13 m and its height is 5 m. Find area of the curved surface.

1. 490.28 m^{2}

2. 288.28 m^{2}

3. 450m^{2}

4. 200 m^{2}

5. None of these

Sol : Option 1
Area of curved surface = πrl
Now r = √(13^{2} - 5^{2}) = √169 - 25 = √144 = 12m
Required Area= (22/7) x 13 x 12 = 490.28m^{2}

Q.7. Ratio of Volumes of cube and Sphere is 6/π. Find the ratio of side of cube and radius of sphere.

1. 2: 1

2. 3: 1

3. 4: 1

4. 5: 1

5. 1: 2

Sol : Option 1
Let the side of cube is 'a' and radii of sphere is 'r'.
Now Volume of cube= a^{3}
Volume of sphere= 4/3π x r^{3}
a^{3} / (4/3)π r^{3} = 6 / π
a / r = 2 / 1
Hence the answer is 2: 1.

Q8. What is the radius of a circle if its circumference is numerically equal to four times its area?

1. 1/ 2

2. 3

3. 1

4. 4

5. 5

Sol : Option 1
Let ‘r’ be the radius of the circle. We have 2πr = 4πr^{2} ⇒ r = 1/2

Q9. Find the area of an isosceles triangle whose sides are 10 cm, 6 cm and 6 cm.

1. 25√11 sq. cm.

2. √11 sq. cm.

3. 5 sq. cm.

4. 11 sq. cm.

5. 5√11 sq. cm.

Sol : Option 5
Semi perimeter of triangle s = (10 + 6 + 6) / 2 = 11.
Area of triangle = √11 x (11-10) x (11-6) x (11-6) = √11 x 5 x 5 = 5√11cm^{2}

Q10. The surface area of a sphere is 616cm^{2}. Find its radius.

1. 8cm

2. 10 cm

3. 9 cm

4. 11 cm

5. 7 cm

Sol : Option 5
Let 'r' be the radius of the sphere. We have
4πr^{2} = 616
4 × 22/7 × r^{2} = 616
r = 7