Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

The value of n, when np2 = 20 is: - Business Mathematics and Statistics


The value of n, when np2 = 20 is:


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Concept: Combinations
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Chapter 2: Algebra - Exercise 2.7 [Page 45]


If nPr = 1680 and nCr = 70, find n and r.

There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?

If a polygon has 44 diagonals, find the number of its sides.

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

  1. atleast two ladies are included.
  2. atmost two ladies are included.

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters

  1. cannot be repeated
  2. can be repeated
  3. cannot be repeated but must begin with E
  4. cannot be repeated but end with CAB.

From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?

Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?

The number of diagonals in a polygon of n sides is equal to

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:

There are 10 true or false questions in an examination. Then these questions can be answered in

If `""^15"C"_(2"r" - 1) = ""^15"C"_(2"r" + 4)`, find r

Prove that `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4` = 40C5

A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?

How many chords can be drawn through 20 points on a circle?

In a parking lot one hundred, one-year-old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?

How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?

Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular student is excluded?

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination

How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, the number of straight lines that can be obtained from the pairs of these points?

A polygon has 90 diagonals. Find the number of its sides?

Choose the correct alternative:
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

Choose the correct alternative:
In 2nC3 : nC3 = 11 : 1 then

Choose the correct alternative:
`""^(("n" - 1))"C"_"r" + ""^(("n" - 1))"C"_(("r" - 1))` is

Choose the correct alternative:
The number of rectangles that a chessboard has ______

Choose the correct alternative:
If nC4nC5nC6 are in AP the value of n can be


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