11th Standard Syllabus & Materials

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11th Standard Maths Chapter 4 Combinations and Mathematical Induction One Mark Question and Answer

Published on: 27/08/2019

Combinations and Mathematical Induction

Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 11th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

10 x 1 = 10

If 15C_3r= 15 C_r+3 , then r is equal to _________

(a)

(b)

(c)

(d)

The product of r consecutive positive integers is divisible by _________

(a)

(b)

r!+1

(c)

(r+1)

(d)

none of these

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is _________

(a)

(b)

(c)

125

(d)

100

The number of ways to arrange the letters of the word CHEESE are _________

(a)

120

(b)

240

(c)

720

(d)

The number of different signals which can be given from 6 flags of different colours taking one or more at a time is _________

(a)

1958

(b)

1956

(c)

(d)

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

(b)

(c)

(d)

If ^a2-a \(C_2 = ^{a^2-a}\) C₄ then the value of 'a' is

(a)

(b)

(c)

(d)

The product of r consecutive positive integers is divisible by

(a)

(b)

(r-1)!

(c)

(r+1)!

(d)

r^r

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

(a)

30⁴\(\times\) 29²

(b)

30³\(\times\) 29³

(c)

30²\(\times\) 29⁴

(d)

30\(\times\)29⁵

10.

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

(a)

432

(b)

108

(c)

(d)

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Answers Key:

Multiple Choice Question

10 x 1 = 10

(a)
r!

(a)
24

(a)
120

(b)
1956

\(\text { No. of lines }{ }^{10} \mathrm{C}_{2}-{ }^{4} \mathrm{C}_{2}+1=45-6+1=40\)

\(a^{2}-a^{a} C_{2} =a^{2}-a^{a} C_{4} \)
\(a^{2}-a^{a} C_{2} =a^{2}-a^{a} C_{a-a-4}\left(\because^{n} C_{r}={ }^{n} C_{n-r}\right) \)
\(a^{2}-a-4 =2 \)
\(a^{2}-a-6 =0 \)
\((a-3)(a+2) =0 \)
\(a=3 \text { or } a=-2 \text { which is impossible }\)

Product of r consecutive positive integers is divisible by r! (by theorem).

First in Maths = 30 ways
Second in Maths - 29 ways
Similarly for other subjects
30 \(\times\) 29 \(\times\) 30 \(\times\) 29 \(\times\) 30 \(\times\)30 = 30⁴ \(\times\)29²