Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 35

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NDA & NA EE

IMPORTANT

Earn 100

The sum of the coefficients in the expansion of ${(x + y)}^{n}$ is $4096$ . The greatest binomial coefficient in the expansion is

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Important Questions on Binomial Theorem

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 36

The value of

{}^{12}C_{2} +^{13} C_{3} +^{14} C_{4} + \dots +^{999} C_{989}

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 37

The expression

{}^{n}C_{0} + 2 \cdot {}^{n}C_{1} + 3 \cdot {}^{n}C_{1} + \dots + (n + 1) \cdot {}^{n}C_{n}

is equal to

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 38

The sum to

(n + 1)

terms of the series

\frac{C_{0}}{2} - \frac{C_{1}}{3} + \frac{C_{2}}{4} - \frac{C_{3}}{5} + \dots

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 39

If ${(1 + x - 2 x^{2})}^{6} = 1 + a_{1} x + a_{2} x^{2} + \dots + a_{12} x^{12},$ then
consider the following statements.
$I .$ $a_{2} + a_{4} + a_{6} + \dots + a_{12} = 31$
$II .$ $a_{1} + a_{3} + a_{5} + \dots + a_{11} = - 31$

Which of the above statement(s) is/are correct?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 16 - Binomial Theorem>Exercise 1>Q 40

The sum of

1 + n (1 - \frac{1}{x}) + \frac{n (n + 1)}{2!} {(1 - \frac{1}{x})}^{2} + \dots

will be