1
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let A be a 3 $$\times$$ 3 matrix such that $$\mathrm{|adj(adj(adj~A))|=12^4}$$. Then $$\mathrm{|A^{-1}~adj~A|}$$ is equal to

A
12
B
2$$\sqrt3$$
C
1
D
$$\sqrt6$$
2
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\overrightarrow \alpha = 4\widehat i + 3\widehat j + 5\widehat k$$ and $$\overrightarrow \beta = \widehat i + 2\widehat j - 4\widehat k$$. Let $${\overrightarrow \beta _1}$$ be parallel to $$\overrightarrow \alpha $$ and $${\overrightarrow \beta _2}$$ be perpendicular to $$\overrightarrow \alpha $$. If $$\overrightarrow \beta = {\overrightarrow \beta _1} + {\overrightarrow \beta _2}$$, then the value of $$5{\overrightarrow \beta _2}\,.\left( {\widehat i + \widehat j + \widehat k} \right)$$ is :

A
9
B
7
C
6
D
11
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$x+2y+3z=3$$

$$4x+3y-4z=4$$

$$8x+4y-\lambda z=9+\mu$$

has infinitely many solutions, then the ordered pair ($$\lambda,\mu$$) is equal to :

A
$$\left( {{{72} \over 5},{{21} \over 5}} \right)$$
B
$$\left( { - {{72} \over 5}, - {{21} \over 5}} \right)$$
C
$$\left( { - {{72} \over 5},{{21} \over 5}} \right)$$
D
$$\left( {{{72} \over 5}, - {{21} \over 5}} \right)$$
4
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the plane containing the line of intersection of the planes

P1 : $$x+(\lambda+4)y+z=1$$ and

P2 : $$2x+y+z=2$$

pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of

the point (2$$\lambda,\lambda,-\lambda$$) from the plane P2 is :

A
$$2\sqrt6$$
B
$$3\sqrt6$$
C
$$4\sqrt6$$
D
$$5\sqrt6$$
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