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

The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :

A
125
B
150
C
225
D
120
2
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the six numbers $$\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}$$, be in A.P. and $$\mathrm{a_1+a_3=10}$$. If the mean of these six numbers is $$\frac{19}{2}$$ and their variance is $$\sigma^2$$, then 8$$\sigma^2$$ is equal to :

A
220
B
210
C
105
D
200
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is

A
$$ - {1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
B
$$ - {1 \over 2}\left( {\sqrt 3 - i} \right)$$
C
$${1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
D
$${1 \over 2}\left( {\sqrt 3 + i} \right)$$
4
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$f(x) = {x^3} - {x^2}f'(1) + xf''(2) - f'''(3),x \in \mathbb{R}$$, then

A
$$2f(0) - f(1) + f(3) = f(2)$$
B
$$f(1) + f(2) + f(3) = f(0)$$
C
$$f(3) - f(2) = f(1)$$
D
$$3f(1) + f(2) = f(3)$$
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