Science (English Medium) Class 11 - CBSE Question Bank Solutions

All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.

The straight lines l₁, l₂ and l₃ are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l₂, k points on l₃. The maximum number of triangles formed with vertices at these points are ______.

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

How many committee of five persons with a chairperson can be selected from 12 persons.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.

There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.

A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw

If ⁿC_{r – 1} = 36, ⁿC_r = 84 and ⁿC_{r + 1} = 126, then find ^rC₂.

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?

In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.

A convex polygon has 44 diagonals. Find the number of its sides.

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.

In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?

In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.

If ⁿC₁₂ = ⁿC₈, then n is equal to ______.