1
JEE Main 2021 (Online) 16th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
If n is the number of irrational terms in the
expansion of $${\left( {{3^{1/4}} + {5^{1/8}}} \right)^{60}}$$, then (n $$-$$ 1) is divisible by :
A
30
B
8
C
7
D
26
2
JEE Main 2021 (Online) 16th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let [ x ] denote greatest integer less than or equal to x. If for n$$\in$$N,

$${(1 - x + {x^3})^n} = \sum\limits_{j = 0}^{3n} {{a_j}{x^j}}$$,

then $$\sum\limits_{j = 0}^{\left[ {{{3n} \over 2}} \right]} {{a_{2j}} + 4} \sum\limits_{j = 0}^{\left[ {{{3n - 1} \over 2}} \right]} {{a_{2j}} + 1}$$ is equal to :
A
2n $$-$$ 1
B
n
C
2
D
1
3
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
The maximum value of the term independent of 't' in the expansion
of $${\left( {t{x^{{1 \over 5}}} + {{{{(1 - x)}^{{1 \over {10}}}}} \over t}} \right)^{10}}$$ where x$$\in$$(0, 1) is :
A
$${{10!} \over {\sqrt 3 {{(5!)}^2}}}$$
B
$${{2.10!} \over {3\sqrt 3 {{(5!)}^2}}}$$
C
$${{10!} \over {3{{(5!)}^2}}}$$
D
$${{2.10!} \over {3{{(5!)}^2}}}$$
4
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :
A
$${{n(2n + 1)(3n + 1)} \over 6}$$
B
$${{n(n + 1)(2n + 1)} \over 6}$$
C
$${{n{{(n + 1)}^2}(n + 2)} \over {12}}$$
D
$${{n(n - 1)(2n + 1)} \over 6}$$
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
© ExamGOAL 2024