Q1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

1. 173 m
2. 200 m
3. 273 m
4. 300 m

EXPLANATION

Option 3

Q2. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

1. 120 metres
2. 180 metres
3. 324 metres
4. 150 metres

EXPLANATION

Q3. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

1. 12 cm3
2. 15 cm3
3. 16 cm3
4. 20 cm3

EXPLANATION

Q4. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

1. 720
2. 900
3. 1200
4. 2000

EXPLANATION

Option 3.

Step-1: Solve for the height of the hall 

Given: length(l) = 15 m, breadth(b) = 12 m 

Let the height be h 

According to the equation sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls 

area of floor= 1 x b 

area of ceiling= 1 x b 

area of wall= 2(l + b)h 

so, the equation will become 

= l*b+ l*b = 2(l + b) × h 

= lb = lh + bh 

= 15(12) = 15(h) + 12(h) 

=180=27h 

h = 20/3

Step-2: Solve for the volume of the height Volume of hall 1 x b x h = 15 * 12* 20/3

=1200

 Hence, the volume of hall= 1200 m3.

Q5. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

1. 4
2. 7
3. 9
4. 14

EXPLANATION

In this case, we have to find HCF with the remainder

Step

1. Find the Differences between numbers
2. Get the HCF ( that differences)

We have here 43, 91 and 183

So differences are

183 – 91 = 92,

183 – 43 = 140,

91 – 43 = 48.

Now

HCF (48, 92 and 140)

As

48 = 2 × 2 × 2 × 2 × 3,

92 =2 × 2 × 23,

140 = 2 × 2 × 5 × 7

HCF= 2 × 2 = 4.

And 4 is the required number.