1
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If vectors $$\overrightarrow {{a_1}} = x\widehat i - \widehat j + \widehat k$$ and $$\overrightarrow {{a_2}} = \widehat i + y\widehat j + z\widehat k$$ are collinear, then a possible unit vector parallel to the vector $$x\widehat i + y\widehat j + z\widehat k$$ is :
A
$${1 \over {\sqrt 3 }}\left( {\widehat i - \widehat j + \widehat k} \right)$$
B
$${1 \over {\sqrt 2 }}\left( { - \widehat j + \widehat k} \right)$$
C
$${1 \over {\sqrt 2 }}\left( {\widehat i - \widehat j} \right)$$
D
$${1 \over {\sqrt 3 }}\left( {\widehat i + \widehat j - \widehat k} \right)$$
2
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :
A
$${1 \over 7}$$
B
$${4 \over 7}$$
C
$${6 \over 7}$$
D
$${3 \over 7}$$
3
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Change Language
The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.
Your input ____
4
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Change Language
If the matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 2 & 0 \cr 3 & 0 & { - 1} \cr } } \right]$$ satisfies the equation

$${A^{20}} + \alpha {A^{19}} + \beta A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & 0 \cr 0 & 0 & 1 \cr } } \right]$$ for some real numbers $$\alpha$$ and $$\beta$$, then $$\beta$$ $$-$$ $$\alpha$$ is equal to ___________.
Your input ____
JEE Main Papers
2023
2021
EXAM MAP