11th Maths Weekly Test- 3 (Combinatorics and Mathematical Induction)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test- 3 (Combinatorics and Mathematical Induction)-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

If p(n):49ⁿ + 16ⁿ + \(\lambda \) is divisible by 64 for n \(\in \) N is true, then the least negative integral value of \(\lambda \) is

-3
-2
-1
-4

If 7 points out of 12 are in the same straight line then the number of triangles formed is

The number of ways in which we can arrange 4 letters of the word "MATHEMATICS" is given by

136
2454
1680
192

The number of squares which can form on a chess a board is

For all n \(\in \) N, 3\(\times\) 5²ⁿ⁺¹+2³ⁿ⁺¹ is divisible by

Everybody in a room shakes hands with everybody else. The total number of handshakes is 91. The total number of persons in the room is

The number of 10 digit number that can be written by using the digits 2 and 3 is

¹⁰C₂+⁹C₂
2¹⁰
2¹⁰-2
10!

In 3 fingers, the number of ways four rings can be worn is ways.

4³-1
3⁴
68
64

The number of five digit telephone numbers having at least one of their digits repeated is

90000
10000
30240
69760

There is a letter lock with 3 rings each marked with 5 letters and do not know the keyword. The total number of attempts can be made to know the keyword is

3⁵
5³
124
5

If (a²-a)C₂=(a²-a)C₄, then a =

2
3
4
none of these

The number of diagonals that can be drawn by joining the vertices of an octagon is

5C₁+5C₂+5C₃+5C₄+5C₅ is equal to

If ⁿC₄, ⁿC₅ and ⁿC₅ are in A.P., the value of n =

Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is

There are 15 points in a plane of which exactly 8 are collinear. The number of straight lines obtained by joining these points is

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

10²
1023
2¹⁰
10!

A candidate is required to answer 7 question out of 12 questions, which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

If n+1 C₃=2.nC₂₁ then n =

If ⁿP_r=k x ^n-1P_r-1 what is k:

If ⁿC₁₀ = ⁿC₆, then ⁿC₂ =

The product of first n odd natural numbers equals

²ⁿC_n\(\times\)ⁿP_n
\({ \left( \frac { 1 }{ 2 } \right) }^{ n }\)²ⁿC_n\(\times\)ⁿP_n
\({ \left( \frac { 1 }{ 4 } \right) }^{ n }\times \)²ⁿC_n\(\times\)²ⁿP_n
ⁿC_n\(\times\)ⁿP_n

How many words can be formed using all the letters of the word ANAND:

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

2 \(\times\) ¹¹ C₇+¹⁰C₈
¹¹C₇+¹⁰C₈
¹²C₈-¹⁰C₆
¹⁰C₆+2!

The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

⁵²C₅
⁴⁸C₅
⁵²C₅ + ⁴⁸C₅
⁵²C₅ - ⁴⁸C₅

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 without repetition

The sum of the digits at the 10^th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

How many arrangements can be made out of letters of words "ENGINEERING"

11!
\({{11!}\over{{(3!)}^{2}{(2!)}^{2}}}\)
\({{11!}\over{3!2!}}\)
\({{11!}\over{3!}}\)

If ⁿP_t = 720 nCr, then the value of r =

If ⁽ⁿ⁺⁵⁾P_(n+1)=\(\frac { 11(n-1) }{ 2 } \).⁽ⁿ⁺³⁾P_n, then the value of n are

7 and 11
6 and 7
2 and 11
2 and 6

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

30⁴\(\times\) 29²
30³\(\times\) 29³
30²\(\times\) 29⁴
30\(\times\)29⁵

The number of 4 digit numbers, that can be formed by the digits 3, 4, 5, 6, 7, 8, 0 and no digit is being repeated is

If ¹⁰⁰C_r = ¹⁰⁰C_3r then r is:

The number of different 4 letters words with or without meaning that can be formed from the letters of the word "SURYA" is

The number of ways in which we can post 5 letters in 10 letter boxes is

50
5¹⁰
10⁵
1

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11th Maths Weekly Test- 3 (Combinatorics and Mathematical Induction)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test- 3 (Combinatorics and Mathematical Induction)-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

If p(n):49n + 16n + \(\lambda \) is divisible by 64 for n \(\in \) N is true, then the least negative integral value of \(\lambda \) is

If 7 points out of 12 are in the same straight line then the number of triangles formed is

The number of ways in which we can arrange 4 letters of the word "MATHEMATICS" is given by

The number of squares which can form on a chess a board is

For all n \(\in \) N, 3\(\times\) 52n+1+23n+1 is divisible by

Everybody in a room shakes hands with everybody else. The total number of handshakes is 91. The total number of persons in the room is

The number of 10 digit number that can be written by using the digits 2 and 3 is

In 3 fingers, the number of ways four rings can be worn is ways.

The number of five digit telephone numbers having at least one of their digits repeated is

There is a letter lock with 3 rings each marked with 5 letters and do not know the keyword. The total number of attempts can be made to know the keyword is

If (a2-a)C2=(a2-a)C4, then a =

The number of diagonals that can be drawn by joining the vertices of an octagon is

5C1+5C2+5C3+5C4+5C5 is equal to

If nC4, nC5 and nC5 are in A.P., the value of n =

Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is

There are 15 points in a plane of which exactly 8 are collinear. The number of straight lines obtained by joining these points is

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

A candidate is required to answer 7 question out of 12 questions, which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

If n+1 C3=2.nC21 then n =

If nPr=k x n-1Pr-1 what is k:

If nC10 = nC6, then nC2 =

The product of first n odd natural numbers equals

How many words can be formed using all the letters of the word ANAND:

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 without repetition

The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

How many arrangements can be made out of letters of words "ENGINEERING"

If nPt = 720 nCr, then the value of r =

If (n+5)P(n+1)=\(\frac { 11(n-1) }{ 2 } \).(n+3)Pn, then the value of n are

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

The number of 4 digit numbers, that can be formed by the digits 3, 4, 5, 6, 7, 8, 0 and no digit is being repeated is

If 100Cr = 100C3r then r is:

The number of different 4 letters words with or without meaning that can be formed from the letters of the word "SURYA" is

The number of ways in which we can post 5 letters in 10 letter boxes is

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If p(n):49ⁿ + 16ⁿ + \(\lambda \) is divisible by 64 for n \(\in \) N is true, then the least negative integral value of \(\lambda \) is

For all n \(\in \) N, 3\(\times\) 5²ⁿ⁺¹+2³ⁿ⁺¹ is divisible by

If (a²-a)C₂=(a²-a)C₄, then a =

5C₁+5C₂+5C₃+5C₄+5C₅ is equal to

If ⁿC₄, ⁿC₅ and ⁿC₅ are in A.P., the value of n =

If n+1 C₃=2.nC₂₁ then n =

If ⁿP_r=k x ^n-1P_r-1 what is k:

If ⁿC₁₀ = ⁿC₆, then ⁿC₂ =

The sum of the digits at the 10^th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

If ⁿP_t = 720 nCr, then the value of r =

If ⁽ⁿ⁺⁵⁾P_(n+1)=\(\frac { 11(n-1) }{ 2 } \).⁽ⁿ⁺³⁾P_n, then the value of n are

If ¹⁰⁰C_r = ¹⁰⁰C_3r then r is: