Q18. By What smallest number 29160 be divided so that the quotient
becomes a perfect cube ?
Q19.A box contains cards numbered 6 to 50.A card is drawn at random from
the box. Find the probability that the drawn card has a number which is a
perfect square. pls its urgent
Answers
Answer:
(18)Firstly we need to factorize the number 29160
After factorization we get,
⇒29160=
2∗2∗2 ∗3∗3∗3 ∗3∗3∗3 ∗5
We need to group the expanded numbers in a group of three since it has to be a perfect cube.
The number 5 does not form a triplet. Hence the number 5 has to be divided so that the quotient becomes a perfect cube.
(19) Total number of cards = 45 numbered 6 to 50.
Square numbers in the range of 6 to 50 are - (9,16,25,36,49)
Probability of drawing a square number = 5/45 = 1/9
Answer 18 :- The number 5 does not form a triplet. Hence the number 5 has to be divided so that the quotient becomes a perfect cube.
Answer 19 :- a) No. of perfect square between 1 to 50 =7 (from 1² to 7² )
Therefore the probability that the card is drawn is a perfect square = 7 / 50
(b) No.of integers divisible by 6 between 1 to 50 =8 (from 6×1→6×8)
Therefore the probability that the card is drawn is divisible by 6 = 8 / 50 = 4 / 25