
Choose the correct option. is divisible by
A) 15
B) 17
C) 19
D) 21
Answer
461.1k+ views
Hint: In the given question, we have been asked that the given expression is divisible by which number. In order to solve the question, first we need to rewrite the equation to make it possible to have a common factor. Later by applying the combination, we will need to expand the given expression by using the commutation formula i.e. . Then, by taking out the common factor we will observe that the given expression is divisible by any number which is given as the option.
Complete step-by-step solution:
We have given that,
Rewritten the above expression as,
Now, applying the combinations, we get
As we know that,
Therefore,
Solving the above, we obtained
Taking out the common term from both the brackets, we get
As we can see that 19 is the common factor of both the numbers i.e. 114 and 95.
Thus,
Taking out 19 as a common factor, we get
Thus, the given expression is divisible by 19.
Hence, the option (C) is the correct answer.
Note:In mathematics, a permutation is known as the choice of ‘r’ things from the given set of ‘n’ things without the replacement. In permutation, order matters.
The formula of permutation is given by;
And a combination is known as the choice of ‘r’ things from the given set of ‘n’ things without the replacement and where the order does not matter.
The formula of combination is given by;
.
Complete step-by-step solution:
We have given that,
Rewritten the above expression as,
Now, applying the combinations, we get
As we know that,
Therefore,
Solving the above, we obtained
Taking out the common term from both the brackets, we get
As we can see that 19 is the common factor of both the numbers i.e. 114 and 95.
Thus,
Taking out 19 as a common factor, we get
Thus, the given expression is divisible by 19.
Hence, the option (C) is the correct answer.
Note:In mathematics, a permutation is known as the choice of ‘r’ things from the given set of ‘n’ things without the replacement. In permutation, order matters.
The formula of permutation is given by;
And a combination is known as the choice of ‘r’ things from the given set of ‘n’ things without the replacement and where the order does not matter.
The formula of combination is given by;
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

What is the technique used to separate the components class 11 chemistry CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
