1

JEE Main 2021 (Online) 17th March Evening Shift

Numerical

+4

-1

Let $$A = \left[ {\matrix{
a & b \cr
c & d \cr
} } \right]$$ and $$B = \left[ {\matrix{
\alpha \cr
\beta \cr
} } \right] \ne \left[ {\matrix{
0 \cr
0 \cr
} } \right]$$ such that AB = B and a + d = 2021, then the value of ad $$-$$ bc is equal to ___________.

Your input ____

2

JEE Main 2021 (Online) 17th March Evening Shift

Numerical

+4

-1

If 1, log

_{10}(4^{x}$$-$$ 2) and log_{10}$$\left( {{4^x} + {{18} \over 5}} \right)$$ are in arithmetic progression for a real number x, then the value of the determinant $$\left| {\matrix{ {2\left( {x - {1 \over 2}} \right)} & {x - 1} & {{x^2}} \cr 1 & 0 & x \cr x & 1 & 0 \cr } } \right|$$ is equal to :Your input ____

3

JEE Main 2021 (Online) 17th March Morning Shift

Numerical

+4

-1

If $$A = \left[ {\matrix{
2 & 3 \cr
0 & { - 1} \cr
} } \right]$$, then the value of det(A

^{4}) + det(A^{10}$$-$$ (Adj(2A))^{10}) is equal to _____________.Your input ____

4

JEE Main 2021 (Online) 16th March Evening Shift

Numerical

+4

-1

Let $$A = \left[ {\matrix{
{{a_1}} \cr
{{a_2}} \cr
} } \right]$$ and $$B = \left[ {\matrix{
{{b_1}} \cr
{{b_2}} \cr
} } \right]$$ be two 2 $$\times$$ 1 matrices with real entries such that A = XB, where

$$X = {1 \over {\sqrt 3 }}\left[ {\matrix{ 1 & { - 1} \cr 1 & k \cr } } \right]$$, and k$$\in$$R.

If $$a_1^2$$ + $$a_2^2$$ = $${2 \over 3}$$(b$$_1^2$$ + b$$_2^2$$) and (k

$$X = {1 \over {\sqrt 3 }}\left[ {\matrix{ 1 & { - 1} \cr 1 & k \cr } } \right]$$, and k$$\in$$R.

If $$a_1^2$$ + $$a_2^2$$ = $${2 \over 3}$$(b$$_1^2$$ + b$$_2^2$$) and (k

^{2}+ 1) b$$_2^2$$ $$\ne$$ $$-$$2b_{1}b_{2}, then the value of k is __________.Your input ____

Questions Asked from Matrices and Determinants (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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