Question 1: Palette 1/10

BITSAT 2025 MCQ

If ${ }^n C_{n-r}+3 \cdot{ }^n C_{n-r+1}+3 \cdot{ }^n C_{n-r+2} +{ }^n C_{n-r+3}={ }^x C_r$, then the value of $x$ is

A

$n+3$

B

$n-3$

C

$n+1$

D

$n-2$

Question 2: Palette 2/10

BITSAT 2025 MCQ

What is the coefficient of $x^{50}$ in $(1+x)^{41}\left(1-x+x^2\right)^{40}$.

A

0

B

40

C

41

D

50

Question 3: Palette 3/10

BITSAT 2024 MCQ

The coefficient of $ x^{2} $ term in the binomial expansion of $ \left(\frac{1}{3} x^{\frac{1}{2}}+x^{\frac{-1}{4}}\right)^{10} $ is

A

$ \frac{70}{243} $

B

$ \frac{60}{423} $

C

$ \frac{50}{13} $

D

None of these

Question 4: Palette 4/10

BITSAT 2023 MCQ

The sum of the coefficients of all odd degree terms in the expansion of $\left(x+\sqrt{x^3-1}\right)^5 +\left(x-\sqrt{x^3-1}\right)^5, x>1$ is

A

1

B

3

C

2

D

4

Question 5: Palette 5/10

BITSAT 2023 MCQ

$\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j$ is equal to

A

$2^{2 n}-{ }^{2 n} C_n$

B

$2^{2 n-1}-{ }^{2 n-1} C_{n-1}$

C

$2^{2 n}-\frac{1}{2}\left({ }^{2 n} C_n\right)$

D

$2^{n-1}+2\left({ }^{2 n-1} C_n\right)$

Question 6: Palette 6/10

BITSAT 2022 MCQ

The number of terms in the expansion of ${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$ is

A

5

B

7

C

9

D

10

Question 7: Palette 7/10

BITSAT 2022 MCQ

If the sum of the coefficients in the expansion of (x + y)ⁿ is 1024, then the value of the greatest coefficient in the expansion is

A

356

B

252

C

210

D

120

Question 8: Palette 8/10

BITSAT 2021 MCQ

${{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} = $

A

120

B

260

C

210

D

180

Question 9: Palette 9/10

BITSAT 2020 MCQ

The value of ${}^{47}{C_4} + \sum\limits_{r = 1}^5 {{}^{52 - r}{C_3}} $ is equal to

A

${}^{47}{C_6}$

B

${}^{52}{C_5}$

C

${}^{52}{C_4}$

D

None of these

Question 10: Palette 10/10

BITSAT 2020 MCQ

The coefficient of x⁸ in the polynomial (x $-$ 1) (x $-$ 2) ..... (x $-$ 10)

A

2640

B

1320

C

1370

D

2740