BoardMaths

Binomial Theorem

4 Board Maths previous year questions on Binomial Theorem — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.

Q1 FREE PREVIEW
PYQ

The remainder when 32022 is divided by 5 is:

[JEE Main 2022, 24 Jun (Shift 1)]

a

1

b

2

c

3

d

4

✓ Correct answer: d)

4

Explanation

\((3\times 3\times 3\times \ldots .2022\text{ times })\div 5\\ \text{ Remainder }=((-1)(-1)(-1)\ldots .1011\text{ times })\\ \Rightarrow \text{ Remainder }=-1+5=4\)

Q2
PYQ

The coefficient of the term independent of \(\ x \) in the expansion of \(\ \left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10} \) is

a

\(\ \frac{5}{4} \)

b

\(\ \frac{7}{4} \)

c

\(\ \frac{9}{4} \)

d

None of these

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Q3
PYQ

The coefficient of \(x^{301}\) in \((1+x)^{500}+x(1+x)^{499}\) \(+x^2(1+x)^{498}+\ldots+x^{500}\) is:

[JEE Main 2023, 30 Jan (Shift 1)]

a

\({ }^{501} C _{302}\)

b

\({ }^{500} C _{301}\)

c

\({ }^{500} C _{300}\)

d

\({ }^{501} C _{200}\)

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Q4
PYQ

If the greatest value of the term independent of '\( x \)' in the expansion of \( \left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10} \) is \( \frac{10 \text { ! }}{(5 !)^{2}} \), then the value of '\( a \)' is equal to

a

\( -1 \)

b

1

c

\( -2 \)

d

2

🔒
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