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1
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
The number of elements in the set {x $$\in$$ R : (|x| $$-$$ 3) |x + 4| = 6} is equal to :
A
4
B
2
C
3
D
1
2
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
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) 16th March Morning Shift
+4
-1
The range of a$$\in$$R for which the

function f(x) = (4a $$-$$ 3)(x + loge 5) + 2(a $$-$$ 7) cot$$\left( {{x \over 2}} \right)$$ sin2$$\left( {{x \over 2}} \right)$$, x $$\ne$$ 2n$$\pi$$, n$$\in$$N has critical points, is :
A
[1, $$\infty$$)
B
($$-$$3, 1)
C
$$\left[ { - {4 \over 3},2} \right]$$
D
($$-$$$$\infty$$, $$-$$1]
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Let $$A = \{ 1,2,3,....,10\}$$ and $$f:A \to A$$ be defined as

$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$$

Then the number of possible functions $$g:A \to A$$ such that $$gof = f$$ is :
A
55
B
105
C
5!
D
10C5
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