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  • NDA Exam Mathematics Study Material

Digitization help student to explore and study their academic courses online, as this gives them flexibility and scheduling their learning at their convenience. Kidsfront has prepared unique course material of Mathematics Binomial Theorem for NDA Exam student. This free online Mathematics study material for NDA Exam will help students in learning and doing practice on Binomial Theorem topic of NDA Exam Mathematics. The study material on Binomial Theorem, help NDA Exam Mathematics students to learn every aspect of Binomial Theorem and prepare themselves for exams by doing online test exercise for Binomial Theorem, as their study progresses in class. Kidsfront provide unique pattern of learning Mathematics with free online comprehensive study material and loads of NDA Exam Mathematics Binomial Theorem exercise prepared by the highly professionals team. Students can understand Binomial Theorem concept easily and consolidate their learning by doing practice test on Binomial Theorem regularly till they excel in Mathematics Binomial Theorem.


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

a) 124
b) 124 + √15
c) 124 - 32 √15
d) 124 + 32 √15



Answer
Correct Answer Is : 124 + 32 √15
Solution Is :
By using binomial theorem, find the value of (99)∧4.

a) 96059601
b) 96059602
c) 96059603
d) 96059604



Answer
Correct Answer Is : 96059601
Solution Is :
Evaluate: ( √2 + 1) ∧5 - ( √2 - 1)∧5

a) 2
b) 8
c) 28
d) 82



Answer
Correct Answer Is : 82
Solution Is :