1
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1
Change Language

If $$\overrightarrow a = 2\widehat i + \widehat j + 3\widehat k$$, $$\overrightarrow b = 3\widehat i + 3\widehat j + \widehat k$$ and $$\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k$$ are coplanar vectors and $$\overrightarrow a \,.\,\overrightarrow c = 5$$, $$\overrightarrow b \bot \overrightarrow c $$, then $$122({c_1} + {c_2} + {c_3})$$ is equal to ___________.

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2
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1
Change Language

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be ($$\alpha$$, $$\beta$$). Then, the value of 7$$\alpha$$ + 3$$\beta$$ is equal to ____________.

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3
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to ___________.

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4
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1
Change Language

Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 < a1 < a2 < ....... < a18 < 77.

Let the set A + A = {x + y : x, y $$\in$$ A} contain exactly 39 elements. Then, the value of a1 + a2 + ...... + a18 is equal to _____________.

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