Question
Represent these numbers on the number line.
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Answer
$\frac{7}{4}$ can be represented on the number line as follows.
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Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
$402$
→$402$
Find the area enclosed by the following figures as the sum of the areas of a rectangle and a trapezium:
Find ten rational numbers between $\frac{3}{5}\ \text{and}\ \frac{3}{4}$
→For each of the following numbers, find the smallest whole number by which it should
be divided so as to get a perfect square. Also find the square root of the square
number so obtained.$396$
→be divided so as to get a perfect square. Also find the square root of the square
number so obtained.$396$
A train starts from station $A$ with a certain number of passengers. At station $B$, the train drops one third of the passengers and takes in 96 more. At the next station $C$ one half of the passengers on board get down while 12 new passengers get on board. At station $D$, a quarter of the passengers get down and 20 new passengers board the train. It then reaches its final destination-station $E$-with 200 passengers.
(1) How many passengers were on board when the train left station $A$ ?
(a) 460$\quad$(b) 520$\quad$(c) 540$\quad$(d) 560
(2) How many passengers were on board when the train left station $B$ ?
(a) 428$\quad$(b) 436$\quad$(c) 444$\quad$(d) 456
(3) How many passengers were on board when the train left station $C$ ?
(a) 228$\quad$(b) 240$\quad$(c) 256$\quad$(d) 264
(4) Had the train started with 720 passengers from station $A$, how many passengers would have got down at station $E$ ?
(a) 228$\quad$(b) 236$\quad$(c) 245$\quad$(d) 256
→(1) How many passengers were on board when the train left station $A$ ?
(a) 460$\quad$(b) 520$\quad$(c) 540$\quad$(d) 560
(2) How many passengers were on board when the train left station $B$ ?
(a) 428$\quad$(b) 436$\quad$(c) 444$\quad$(d) 456
(3) How many passengers were on board when the train left station $C$ ?
(a) 228$\quad$(b) 240$\quad$(c) 256$\quad$(d) 264
(4) Had the train started with 720 passengers from station $A$, how many passengers would have got down at station $E$ ?
(a) 228$\quad$(b) 236$\quad$(c) 245$\quad$(d) 256
Find the square root of the following decimal numbers.$7.29$
→Write five rational numbers which are smaller than $2.$
→Mohanlal bought a shop to start a hardware store. The shop is 12 m long, 4 m wide and 3 m high. Mohanlal paid for it at the rate of ₹ 3500 per sq metre floor area and had to pay 8% of the total cost as stamp duty. To make the shop ready for use, he has to get it painted and the fabrication work done.
1. How much did Mohanlal pay for the shop?
(a) ₹ 168000$\quad$(b) ₹ 181440$\quad$(c) ₹ 504000$\quad$(d) ₹ 544320$\quad$
2. If Mohanlal utilizes one third of the shop to store paint boxes of dimensions 12 cm x 8 cm x 4 cm, how many boxes can he store?
(a) 37500 $\quad$(b) 75000 $\quad$(c) 105000 $\quad$(d) 125000 $\quad$
3. Mohanlal gets the two long side walls and the rear wall of the shop painted. How much will he pay for it at the rate of 96 per sq metre?
(a) ₹ 8064$\quad$(b) ₹ 9216$\quad$(c) ₹ 10368$\quad$(d) ₹ 13824$\quad$
4. To serve his customers and passers-by, Mohanlal installed a cylindrical water cooler tank in front of his shop. If the tank is 1 m high and 28 cm wide, how many litres of water it can hold?
(a) 38.5 $\quad$(b) 61.5 $\quad$(c) 77 $\quad$(d) 92.4 $\quad$
→1. How much did Mohanlal pay for the shop?
(a) ₹ 168000$\quad$(b) ₹ 181440$\quad$(c) ₹ 504000$\quad$(d) ₹ 544320$\quad$
2. If Mohanlal utilizes one third of the shop to store paint boxes of dimensions 12 cm x 8 cm x 4 cm, how many boxes can he store?
(a) 37500 $\quad$(b) 75000 $\quad$(c) 105000 $\quad$(d) 125000 $\quad$
3. Mohanlal gets the two long side walls and the rear wall of the shop painted. How much will he pay for it at the rate of 96 per sq metre?
(a) ₹ 8064$\quad$(b) ₹ 9216$\quad$(c) ₹ 10368$\quad$(d) ₹ 13824$\quad$
4. To serve his customers and passers-by, Mohanlal installed a cylindrical water cooler tank in front of his shop. If the tank is 1 m high and 28 cm wide, how many litres of water it can hold?
(a) 38.5 $\quad$(b) 61.5 $\quad$(c) 77 $\quad$(d) 92.4 $\quad$
A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 h to clean all the rooms.
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
The area of a trapezium is $91cm^2$ and its height is $7\ cm$. If one of the parallel sides is longer than the other by $8\ cm$, find the two parallel sides.
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