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NDA Exam Mathematics Study Material

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Binomial Theorem

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

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

✔Answer

Correct Answer Is : FALSE

Solution Is :

Expand: ( 2x∧2 + 3)∧4

a) 16x∧8 - 96x∧6 - 216x∧4 - 216x∧2 - 81
b) 16x∧8 + 96x∧6 + 216x∧4 + 216x∧2
c) 16x∧8 + 96x∧6 + 216x∧4 + 216x∧2 + 81
d) 16x∧8 - 96x∧6 - 216x∧4 - 216x∧2 - 81

✔Answer

Correct Answer Is : 16x∧8 + 96x∧6 + 216x∧4 + 216x∧2 + 81

Solution Is :

Evaluate: ( √3 + √2)∧4

a) 49
b) 20
c) 49 + √6
d) 49 + 20 √6

✔Answer

Correct Answer Is : 49 + 20 √6

Solution Is :

By using binomial theorem, find the value of (102)∧4.

a) 108243216
b) 243216
c) 108243
d) 10824321

✔Answer

Correct Answer Is : 108243216

Solution Is :

Find the value of ( 1 . 02 )∧6 , correct upto four places of decimals.

a) ( 1 . 1262 )
b) ( 11 . 262 )
c) ( 112 . 62 )
d) ( 1126 . 2 )

✔Answer

Correct Answer Is : ( 1 . 1262 )

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is __________ .

a) Even
b) Odd
c) Even or odd
d) Even and odd

✔Answer

Correct Answer Is : Odd

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is odd. So how many middle terms are there?

a) Zero
b) One
c) Two
d) Three

✔Answer

Correct Answer Is : One

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is odd. So which middle term is there?

a) ( n + 1 / 2 )th
b) ( n + 2 / 2 )th
c) ( n + 3 / 2 )th
d) All of these

✔Answer

Correct Answer Is : ( n + 2 / 2 )th

Solution Is :

True or false: if n is any real number, a = 1, b = x and |x | < 1 then , (1+x)∧n = 1 + nx + (n(n-1) / 2!)x∧2 + ………….

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

✔Answer

Correct Answer Is : TRUE

Solution Is :

In (a + b)∧2 if n is odd then the number of terms in the expansion is __________ .

a) Even
b) Odd
c) Even or odd
d) Even and odd

✔Answer

Correct Answer Is : Even

Solution Is :

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NDA Exam Mathematics Study Material

Binomial Theorem

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

Correct Answer Is : FALSE

Solution Is :

Expand: ( 2x∧2 + 3)∧4

Correct Answer Is : 16x∧8 + 96x∧6 + 216x∧4 + 216x∧2 + 81

Solution Is :

Evaluate: ( √3 + √2)∧4

Correct Answer Is : 49 + 20 √6

Solution Is :

By using binomial theorem, find the value of (102)∧4.

Correct Answer Is : 108243216

Solution Is :

Find the value of ( 1 . 02 )∧6 , correct upto four places of decimals.

Correct Answer Is : ( 1 . 1262 )

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is __________ .

Correct Answer Is : Odd

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is odd. So how many middle terms are there?

Correct Answer Is : One

Solution Is :

In (a + b)∧2 if n is even then the number of terms in the expansion is odd. So which middle term is there?

Correct Answer Is : ( n + 2 / 2 )th

Solution Is :

True or false: if n is any real number, a = 1, b = x and |x | < 1 then , (1+x)∧n = 1 + nx + (n(n-1) / 2!)x∧2 + ………….

Correct Answer Is : TRUE

Solution Is :

In (a + b)∧2 if n is odd then the number of terms in the expansion is __________ .

Correct Answer Is : Even

Solution Is :

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