1
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
2
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
$${{105} \over 16}$$
3
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)
4
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

If the constant term in the expansion of

$${\left( {3{x^3} - 2{x^2} + {5 \over {{x^5}}}} \right)^{10}}$$ is 2k.l, where l is an odd integer, then the value of k is equal to:

A
6
B
7
C
8
D
9
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