1
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the tangent at a point P on the parabola $$y^2=3x$$ is parallel to the line $$x+2y=1$$ and the tangents at the points Q and R on the ellipse $$\frac{x^2}{4}+\frac{y^2}{1}=1$$ are perpendicular to the line $$x-y=2$$, then the area of the triangle PQR is :

A
$$\frac{9}{\sqrt5}$$
B
$$3\sqrt5$$
C
$$5\sqrt3$$
D
$$\frac{3}{2}\sqrt5$$
2
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region $$A = \left\{ {(x,y):\left| {\cos x - \sin x} \right| \le y \le \sin x,0 \le x \le {\pi \over 2}} \right\}$$ is

A
$$\sqrt 5 + 2\sqrt 2 - 4.5$$
B
$$1 - {3 \over {\sqrt 2 }} + {4 \over {\sqrt 5 }}$$
C
$$\sqrt 5 - 2\sqrt 2 + 1$$
D
$${3 \over {\sqrt 5 }} - {3 \over {\sqrt 2 }} + 1$$
3
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\overrightarrow a = 4\widehat i + 3\widehat j$$ and $$\overrightarrow b = 3\widehat i - 4\widehat j + 5\widehat k$$. If $$\overrightarrow c $$ is a vector such that $$\overrightarrow c .\left( {\overrightarrow a \times \overrightarrow b } \right) + 25 = 0,\overrightarrow c \,.(\widehat i + \widehat j + \widehat k) = 4$$, and projection of $$\overrightarrow c $$ on $$\overrightarrow a $$ is 1, then the projection of $$\overrightarrow c $$ on $$\overrightarrow b $$ equals :

A
$$\frac{3}{\sqrt2}$$
B
$$\frac{1}{\sqrt2}$$
C
$$\frac{1}{5}$$
D
$$\frac{5}{\sqrt2}$$
4
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of the integral $$\int_1^2 {\left( {{{{t^4} + 1} \over {{t^6} + 1}}} \right)dt} $$ is

A
$${\tan ^{ - 1}}{1 \over 2} - {1 \over 3}{\tan ^{ - 1}}8 + {\pi \over 3}$$
B
$${\tan ^{ - 1}}2 - {1 \over 3}{\tan ^{ - 1}}8 + {\pi \over 3}$$
C
$${\tan ^{ - 1}}2 + {1 \over 3}{\tan ^{ - 1}}8 - {\pi \over 3}$$
D
$${\tan ^{ - 1}}{1 \over 2} + {1 \over 3}{\tan ^{ - 1}}8 - {\pi \over 3}$$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12