1
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 receives at least 2 and at most 6 candies, is equal to :

A
205
B
615
C
510
D
430
2
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
$${11 \over {50}}$$
3
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is :

A
21
B
22
C
23
D
24
4
JEE Main 2022 (Online) 28th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let f, g : R $$\to$$ R be functions defined by

$$f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x \ge 0} \cr } } \right.$$ and $$g(x) = \left\{ {\matrix{ {{e^x} - x} & , & {x < 0} \cr {{{(x - 1)}^2} - 1} & , & {x \ge 0} \cr } } \right.$$ where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :

A
one point
B
two points
C
three points
D
four points
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