1
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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
Change Language

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
Change Language

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
Change Language

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
JEE Main Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12