1
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

The sum, of the coefficients of the first 50 terms in the binomial expansion of $$(1-x)^{100}$$, is equal to

A
$${ }^{99} \mathrm{C}_{49}$$
B
$${ }^{101} \mathrm{C}_{50}$$
C
$$-{ }^{99} \mathrm{C}_{49}$$
D
$$-{ }^{101} \mathrm{C}_{50}$$
2
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

The sum of the coefficients of three consecutive terms in the binomial expansion of $$(1+\mathrm{x})^{\mathrm{n}+2}$$, which are in the ratio $$1: 3: 5$$, is equal to :

A
63
B
92
C
25
D
41
3
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

If the $$1011^{\text {th }}$$ term from the end in the binominal expansion of $$\left(\frac{4 x}{5}-\frac{5}{2 x}\right)^{2022}$$ is 1024 times $$1011^{\text {th }}$$R term from the beginning, then $$|x|$$ is equal to

A
$$\frac{5}{16}$$
B
8
C
12
D
15
4
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let the number $$(22)^{2022}+(2022)^{22}$$ leave the remainder $$\alpha$$ when divided by 3 and $$\beta$$ when divided by 7. Then $$\left(\alpha^{2}+\beta^{2}\right)$$ is equal to

A
13
B
10
C
20
D
5
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