38. The least number by which 81 be divided
to make a perfect cube is
(A) 1 (B) 3
(C) 2 (D) 4
39. The standard form of 12300000 is -
(A) 1.23 x 10^8 (B) 12.3 * 10^4
(C) 1.23 x 10^7 (D) 1.23 10^9
1. If a family of 10 persons purchases ration
for 15 days and five guests join the family
from the first day. How long will the ration
last?
(A) 15 days (B) 12 days
(C) 10 days (D) 8 days
If the distance travelled by a rickshaw in
one hour is 10 km, the distance covered by
the same rickshaw with the same speed in
one minute will be:
(A) 250/9 m (B) 500/9 m
(C) 1000 m (D) 50Q/3 m
Answers
1. (b) 3
2. (c) 1.23 × 10^7
3. (c) 10 days
4. (d) 500/3 m
1. The least number by which 81 can be divided to make a perfect cube is option (B), 3.
2. The standard form of 12300000 is - (C) 1.23 x 10⁷
3. The ration will last for 15 days for the family. Hence option (C) is correct.
4. The distance travelled by the car is 500 / 3 m. Hence, option (D) is correct.
1. A cube of a number is formed by multiplying the number thrice by itself.
• The factors of 81 are 3 × 3 × 3 × 3. Here, if one 3 three is removed, then 3 × 3 × 3 forms a perfect cube.
• To remove one 3, the factors have to be divided by one 3. Therefore, ( 3 × 3 × 3 × 3 ) / 3 = 3 × 3 × 3 = 27 (perfect cube).
• Hence, 3 is the correct answer.
2. The standard form of 12300000 is - (C) 1.23 x 10⁷
• The number 12300000 can be represented as 12300000.00.
• To represent the number in a smaller form, the decimal has to be shifted seven places towards the left. For this, 12300000.00 has to be divided by 10⁷. To keep the value of the number unchanged, the number must also be multiplied by 10⁷.
• Therefore, (12300000.00 / 10⁷) × 10⁷ = 1.23. The zeros after a decimal point are omitted.
∴ 12300000 = 1.23 x 10⁷
3. Given,
Number of people in a family = 10
Number of days for which the ration is bought = 15
• If the ration lasts for 15 days for 10 people, then it will last longer for 1 person.
Therefore, for 1 person, the ration will last for 15 × 10 days = 150 days.
• Number of persons added to the family since day 1 = 5
Total number of persons in the family = 10 + 5 = 15
• Number of days for which the ration will last for 15 persons = 150 days / 15 = 10 days (option C)
4. Given,
Distance travelled by a car in 1 hour = 10 km
Speed of the car = Distance travelled / Time taken
=> Speed of the car = 10 km / 1 hr = 10 km / hr
• Distance travelled by the car at the same speed in 1 minute = ?
1 hour = 60 mins.
=> 1 min = (1 / 60) hr
• Distance travelled by the car in (1 / 60) hr = Speed × Time
= (10 km / hr) × (1 / 60) hr
= 1 / 6 km
• All the options are given in 'm', so, we have to convert the unit of distance from km to m.
We know that, 1 km = 1000 m
∴ (1 / 6) km = (1 / 6) × 1000 m
=> (1 / 6) km = (1 × 1000 m) / 6
=> (1 / 6) km = (500 / 3) m [ option D ]