Class 12th

In how many different ways can four different books on Chemistry and three different books on Maths be arranged so that any two Chemistry books are not together?

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Contributor-Level 10

(d):The three different Maths books can be arranged in 3! ways. Now there are four places created for the Chemistry books such that they are not together.

The four Chemistry books can be arranged in the available four places in 4! ways.

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5 months ago

A questions paper which is divided into two groups containing three and four questions respectively carries the note that it is not necessary to answer all the questions. One question must be answered from each group. In how many ways can an examinee select the questions?

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Contributor-Level 9

In the first group, one question can be selected or can be rejected; so three questions can be dealt with in 2 * 2 * 2 ways, but this includes the case when all three questions have been left; so they can be selected in 23 – 1 = 7 ways. Similarly four questions of the second group can be selected in 24 – 1 = 15 ways. Thus all seven questions can be selected in 15 * 7 = 105 ways; but this includes the case when all questions have been solved; hence leaving that case, total number of ways required is 105 – 1 = 104

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Class 12th Maths

How many numbers lying between 1000 and 2000 and divisible by 5 can be made with the digits 1, 2, 3, 5, 7 and 9? (Digits are not to be repeated in any number).

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Contributor-Level 9

Every number between 1000 and 2000, which is divisible by five and which can be formed by the given digits, must contains 5 in unit's place and 1 in thousand's place. Thus we are left with four digits out of which we are to place two between 1 and 5, which can be done in 4P2 = 12 ways. Hence, 12 numbers can be formed.

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5 months ago

A shop selling books offers 3 % discount on all cash purchases. What cash amount does a customer pay for books with marked price Rs. 650?

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Contributor-Level 10

(c):Discount = 3%

Price = 650.

S.P = .97 * 650 = 630.5

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5 months ago

A rectangular box of internal base dimensions 2r, 3r and internal height 9r is filled with spheres of radius r. Find the maximum number of spheres that can be fitted into the box.

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Contributor-Level 9

Let L be the vertical distance between the centers of two adjacent balls.

$L = \sqrt[]{[{(2 r)}^{2} - r^{2}]} = r \sqrt[]{3}$

Also, if the box can hold n sphere then (n – 1) L + 2r

≤ 9r [ the last ball height = 2r]

$(n - 1) \sqrt[]{3} r \leq 7 r$

$n \leq \frac{7}{\sqrt[]{3}} + 1$

n ≤ 5.04

Since, n is a natural number.

n = 5

So, the box can hold maximum of 5 spheres.

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5 months ago

An pipe can fill a tank in 3 hours. Because of a leak in the tank it was taking 3.5 hrs to fill the tank. Find the time in which the leak can drain all the water of the tank when full.

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Contributor-Level 10

(b):Total time required to empty it =

$\frac{1}{(\frac{1}{3} - \frac{1}{3.5})} = 21 hours.$

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5 months ago

Answer the questions based on the following information.

Mr. John has 5 girls and 9 boys. He decides to give them a present on the occasion of Christmas. He takes 200 one-rupee coins and puts them in 2 bags which he closes. One of the bags contains more coins than the other. He asks his boys to choose one of the bags. They chose the bag with more money. When money is divided equally among boys they are left with Rs. 3. When money is divided equally among girls (not necessarily the same amount as given to boys), Rs. 4 was left. No girl gets less than a boy.

The total number of coins in the bag with fewer coins is

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Contributor-Level 9

9B + 3 + 5G + 4 = 200 9B + 5G = 193

The positive integer solutions are (B, G) = (2, 35) (7, 25) (12, 17) (17, 8)

Only one of the (B, G) gives G > B and 9B + 3 > 100, i.e. (B, G) = (12, 17)

17 * 5 = 85

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5 months ago

I can row at the rate of 8 miles per hour in still water. It takes twice as long to row up a river as to row down the river. Find the speed at which the river flows.

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