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Byju's Answer

Standard XI

Mathematics

Proof by mathematical induction

Consider the ...

Question

Consider the following statements :
A number $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}$ is divisible by 11 if
1. $(a_{1} + a_{3} + a_{5}) - (a_{2} + a_{4} + a_{6}) = 0$
2. $(a_{2} + a_{4} + a_{6}) - (a_{1} + a_{3} + a_{5}) = 0$
Which of these statements is/are correct?

1 alone

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2 alone

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Both 1 and 2

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Neither 1 nor 2

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Solution

The correct option is C Both 1 and 2
A number $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}$ is divisible by 11 when
$(a_{2} + a_{4} + a_{6}) - (a_{1} + a_{3} + a_{5}) = 0$
or
$(a_{1} + a_{3} + a_{5}) - (a_{2} + a_{4} + a_{6}) = 0$
So both the given statements are correct.
Hence C is the correct option.

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Similar questions

Q. Consider the following statements:
A number

a_{1} a_{2} a_{3} a_{4} a_{5}

is divisible by

9

if
1.

a_{1} + a_{2} + a_{3} + a_{4} + a_{5}

is divisible by

9

.
2.

a_{1} - a_{2} + a_{3} - a_{4} + a_{5}

is divisible by

9

.
Which of the above statements is/are correct?

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

Q. A number

a_{1} a_{2} a_{3} a_{4} a_{5}

is divisible by 9 if
(i)

a_{1} + a_{2} + a_{3} + a_{4} + a_{5}

is divisible by

9.

(ii)

a_{1} - a_{2} + a_{3} - a_{4} + a_{5}

is divisible by

9.

Which of the above statements is/are correct?

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} a n d a_{6}

are consecutive odd natural numbers such that

a_{6} > a_{1}, a_{1} + a_{2} + a_{3} + a_{4} + a_{5} + a_{6} = p^{3} a n d a_{5} = 39

, then the value of

(a_{3} + a_{4} - 12 p)

is equal to

If $a_{1}$ < $a_{2}$ < $a_{3}$ < $a_{4}$ < $a_{5}$ < $a_{6}$ , then the equation $(x - a_{1}) (x - a_{3}) (x - a_{5}) + 2 (x - a_{2}) (x - a_{4}) (x - a_{6})$ = 0 has

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Consider the following statements :A number a1a2a3a4a5a6 is divisible by 11 if 1. (a1+a3+a5)−(a2+a4+a6)=02.(a2+a4+a6)−(a1+a3+a5)=0Which of these statements is/are correct?

The correct option is C Both 1 and 2A number a1a2a3a4a5a6 is divisible by 11 when(a2+a4+a6)−(a1+a3+a5)=0 or (a1+a3+a5)−(a2+a4+a6)=0So both the given statements are correct.Hence C is the correct option.

Consider the following statements :
A number $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}$ is divisible by 11 if
1. $(a_{1} + a_{3} + a_{5}) - (a_{2} + a_{4} + a_{6}) = 0$
2. $(a_{2} + a_{4} + a_{6}) - (a_{1} + a_{3} + a_{5}) = 0$
Which of these statements is/are correct?

The correct option is C Both 1 and 2
A number $a_{1} a_{2} a_{3} a_{4} a_{5} a_{6}$ is divisible by 11 when
$(a_{2} + a_{4} + a_{6}) - (a_{1} + a_{3} + a_{5}) = 0$
or
$(a_{1} + a_{3} + a_{5}) - (a_{2} + a_{4} + a_{6}) = 0$
So both the given statements are correct.
Hence C is the correct option.