1
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1
Out of Syllabus

$$\sum\limits_{\matrix{ {i,j = 0} \cr {i \ne j} \cr } }^n {{}^n{C_i}\,{}^n{C_j}}$$ is equal to

A
$$2^{2 n}-{ }^{2 n} C_{n}$$
B
$${2^{2n - 1}} - {}^{2n - 1}{C_{n - 1}}$$
C
$$2^{2 n}-\frac{1}{2}{ }^{2 n} C_{n}$$
D
$${2^{2n - 1}} + {}^{2n - 1}{C_n}$$
2
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

The remainder when $$(11)^{1011}+(1011)^{11}$$ is divided by 9 is

A
1
B
4
C
6
D
8
3
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

For two positive real numbers a and b such that $${1 \over {{a^2}}} + {1 \over {{b^3}}} = 4$$, then minimum value of the constant term in the expansion of $${\left( {a{x^{{1 \over 8}}} + b{x^{ - {1 \over {12}}}}} \right)^{10}}$$ is :

A
$${{105} \over 2}$$
B
$${{105} \over 4}$$
C
$${{105} \over 8}$$
D
$${{105} \over 16}$$
4
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1
Out of Syllabus

Let n $$\ge$$ 5 be an integer. If 9n $$-$$ 8n $$-$$ 1 = 64$$\alpha$$ and 6n $$-$$ 5n $$-$$ 1 = 25$$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ is equal to

A
1 + nC2 (8 $$-$$ 5) + nC3 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 1 $$-$$ 5n $$-$$ 1)
B
1 + nC3 (8 $$-$$ 5) + nC4 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 2 $$-$$ 5n $$-$$ 2)
C
nC3 (8 $$-$$ 5) + nC4 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 2 $$-$$ 5n $$-$$ 2)
D
nC4 (8 $$-$$ 5) + nC5 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 3 $$-$$ 5n $$-$$ 3)
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