1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region enclosed between the parabolas y2 = 2x $$-$$ 1 and y2 = 4x $$-$$ 3 is

A
$${1 \over {3}}$$
B
$${1 \over {6}}$$
C
$${2 \over {3}}$$
D
$${3 \over {4}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The coefficient of x101 in the expression $${(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}$$, x > 0, is

A
501C101 (5)399
B
501C101 (5)400
C
501C100 (5)400
D
500C101 (5)399
3
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :

A
$${{2\,.\,{3^{12}} + 10} \over 4}$$
B
$${{19\,.\,{3^{10}} + 1} \over 4}$$
C
$$5\,.\,{3^{10}} - 2$$
D
$${{9\,.\,{3^{10}} + 1} \over 2}$$
4
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let p be the plane passing through the intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 5$$ and $$\overrightarrow r \,.\,\left( {2\widehat i - \widehat j + \widehat k} \right) = 3$$, and the point (2, 1, $$-$$2). Let the position vectors of the points X and Y be $$\widehat i - 2\widehat j + 4\widehat k$$ and $$5\widehat i - \widehat j + 2\widehat k$$ respectively. Then the points :

A
X and X + Y are on the same side of P
B
Y and Y $$-$$ X are on the opposite sides of P
C
X and Y are on the opposite sides of P
D
X + Y and X $$-$$ Y are on the same side of P
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