Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative:If nC4, nC5, nC6 are in AP the value of n can be - Mathematics


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


  • 14

  • 11

  • 9

  • 5




Concept: Combinations
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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.5 [Page 198]


Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.5 | Q 24 | Page 198


How many chords can be drawn through 21 points on a circle?

How many triangles can be formed by joining the vertices of a hexagon?

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.

In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?

  1. There is no restriction on the selection.
  2. A particular player is always chosen.
  3. A particular player is never chosen.

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?

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

The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:

The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5) is:

If nC12 = nC9 find 21Cn

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

If nPr = 720 and nCr = 120, find n, r

Prove that 15C3 + 2 × 15C4 + 15C5 = 17C5

Prove that `""^(2"n")"C"_"n" = (2^"n" xx 1 xx 3 xx ... (2"n" - 1))/("n"!)`

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?

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

A trust has 25 members. In how many ways can a President, Vice President and a Secretary be selected?

How many different selections of 5 books can be made from 12 different books if, Two particular books are never selected?

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?

In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?

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

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of at most 3 women?

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?

Choose the correct alternative:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines

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 a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

Choose the correct alternative:
The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is


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