11th Maths Weekly Test-4 ( Combinatorics and Mathematical Induction )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-4 ( Combinatorics and Mathematical Induction )-Aug 2020

Time : 1.00 Hours

Part - A

Generic 3 - Answer All Question

An exam paper contains 8 questions, 4 in Part A and 4 in Part B. Examiners are required to answer 5 questions. In how many ways can this be done if
(i) There are no restrictions of choosing a number of questions in either parts.
(ii) At least two questions from Part A must be answered.

Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85^th string?

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabets.

Prove that n!(n+2)=n!+(n+1)!

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

How many different words can be formed by using all the letters of the word "ALLAHABAD"? and in how many of them vowels occupy the even positions?

By using the digits 0, 1, 2, 3, 4 and 5 (repetition not allowed) numbers are formed by using any number of digits. Find the total number of non-zero numbers that can be formed.

If 9P₅+5.9P₄=10P_r , find r.

Find the number of strings of 5 letters that can be formed with the letters of the word PROPOSITION.

If ¹⁵C_2r-1=¹⁵C_2r+4, find r.

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11th Maths Weekly Test-4 ( Combinatorics and Mathematical Induction )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-4 ( Combinatorics and Mathematical Induction )-Aug 2020

Part - A

Generic 3 - Answer All Question

An exam paper contains 8 questions, 4 in Part A and 4 in Part B. Examiners are required to answer 5 questions. In how many ways can this be done if (i) There are no restrictions of choosing a number of questions in either parts. (ii) At least two questions from Part A must be answered.

Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabets.

Prove that n!(n+2)=n!+(n+1)!

Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?

How many different words can be formed by using all the letters of the word "ALLAHABAD"? and in how many of them vowels occupy the even positions?

By using the digits 0, 1, 2, 3, 4 and 5 (repetition not allowed) numbers are formed by using any number of digits. Find the total number of non-zero numbers that can be formed.

If 9P5+5.9P4=10Pr , find r.

Find the number of strings of 5 letters that can be formed with the letters of the word PROPOSITION.

If 15C2r-1=15C2r+4, find r.

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An exam paper contains 8 questions, 4 in Part A and 4 in Part B. Examiners are required to answer 5 questions. In how many ways can this be done if
(i) There are no restrictions of choosing a number of questions in either parts.
(ii) At least two questions from Part A must be answered.

Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85^th string?

If 9P₅+5.9P₄=10P_r , find r.

If ¹⁵C_2r-1=¹⁵C_2r+4, find r.