1
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+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)
2
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

The term independent of x in the expansion of

$$(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \right)^{11}},\,x \ne 0$$ is :

A
$${7 \over {40}}$$
B
$${33 \over {200}}$$
C
$${39 \over {200}}$$
D
$${11 \over {50}}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

If

$$\sum\limits_{k = 1}^{31} {\left( {{}^{31}{C_k}} \right)\left( {{}^{31}{C_{k - 1}}} \right) - \sum\limits_{k = 1}^{30} {\left( {{}^{30}{C_k}} \right)\left( {{}^{30}{C_{k - 1}}} \right) = {{\alpha (60!)} \over {(30!)(31!)}}} }$$,

where $$\alpha$$ $$\in$$ R, then the value of 16$$\alpha$$ is equal to

A
1411
B
1320
C
1615
D
1855
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12