Learn Mathematics Binomial Theorem, NDA Exam Mathematics Binomial Theorem Exercise, Free Online Binomial Theorem Lessons

NDA Exam Mathematics Study Material

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Binomial Theorem

If a, b ∈ R and n ∈ N, then (a+b)∧n = ____________ .

a) NC0 a∧n b∧0 + nC1 a∧n-1 b∧1 + …………. + nCn a∧0 b∧n
b) NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 - …………. - nCn a∧0 b∧n
c) NC0 a∧n b∧0 + nC1 a∧n-1 b∧1 - …………. + nCn a∧0 b∧n
d) NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. - nCn a∧0 b∧n

✔Answer

Correct Answer Is : NC0 a∧n b∧0 + nC1 a∧n-1 b∧1 + …………. + nCn a∧0 b∧n

Solution Is :

If the index of the binomial is n then the expansion contains ________ term.

a) N
b) N - 1
c) N + 1
d) ( - n )

✔Answer

Correct Answer Is : N + 1

Solution Is :

In each term the sum of indices a and b is ___________ n.

a) Not equal to
b) Equal to
c) Some times
d) Always

✔Answer

Correct Answer Is : Always

Solution Is :

True or false: in (a + b)∧2 if n is even then the number of terms in the expansion is odd.

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : TRUE

Solution Is :

Coefficients of the term in the binomial expansion equidistant from both the ends are?

a) Equal
b) Opposite
c) Not equal
d) Different

✔Answer

Correct Answer Is : Equal

Solution Is :

If a, b ∈ R and n ∈ N, then (a-b)∧n = ____________ .

a) NC0 a∧n b∧0 + nC1 a∧n-1 b∧1 + …………. + nCn a∧0 b∧n
b) NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. + (-1)∧n nCn a∧0 b∧n
c) NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. - (-1)∧n nCn a∧0 b∧n
d) NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. + nCn a∧0 b∧n

✔Answer

Correct Answer Is : NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. - (-1)∧n nCn a∧0 b∧n

Solution Is :

Expand: ( x∧2 + 3y)∧5

a) X∧10 + 15x∧8y + 90x∧6y∧2 + 270x∧4y∧3 + 405x∧2y∧4 + 243y∧5
b) X∧10 + 15x∧8y + 90x∧6y∧2 + 270x∧4y∧3 + 405x∧2y∧4
c) 15x∧8y + 90x∧6y∧2 + 270x∧4y∧3 + 405x∧2y∧4 + 243y∧5
d) X∧10 - 15x∧8y - 90x∧6y∧2 - 270x∧4y∧3 - 405x∧2y∧4 - 243y∧5

✔Answer

NDA Exam Mathematics Study Material

Binomial Theorem

If a, b ∈ R and n ∈ N, then (a+b)∧n = ____________ .

Correct Answer Is : NC0 a∧n b∧0 + nC1 a∧n-1 b∧1 + …………. + nCn a∧0 b∧n

Solution Is :

If the index of the binomial is n then the expansion contains ________ term.

Correct Answer Is : N + 1

Solution Is :

In each term the sum of indices a and b is ___________ n.

Correct Answer Is : Always

Solution Is :

True or false: in (a + b)∧2 if n is even then the number of terms in the expansion is odd.

Correct Answer Is : TRUE

Solution Is :

Coefficients of the term in the binomial expansion equidistant from both the ends are?

Correct Answer Is : Equal

Solution Is :

If a, b ∈ R and n ∈ N, then (a-b)∧n = ____________ .

Correct Answer Is : NC0 a∧n b∧0 - nC1 a∧n-1 b∧1 + …………. - (-1)∧n nCn a∧0 b∧n

Solution Is :

Expand: ( x∧2 + 3y)∧5

Correct Answer Is : X∧10 + 15x∧8y + 90x∧6y∧2 + 270x∧4y∧3 + 405x∧2y∧4 + 243y∧5

Solution Is :

Evaluate: ( √5 + √3)∧4

Correct Answer Is : 124 + 32 √15

Solution Is :

By using binomial theorem, find the value of (99)∧4.

Correct Answer Is : 96059601

Solution Is :

Evaluate: ( √2 + 1) ∧5 - ( √2 - 1)∧5

Correct Answer Is : 82

Solution Is :

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