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JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Let a, b, c, d in arithmetic progression with common difference $$\lambda$$. If $$\left| {\matrix{ {x + a - c} & {x + b} & {x + a} \cr {x - 1} & {x + c} & {x + b} \cr {x - b + d} & {x + d} & {x + c} \cr } } \right| = 2$$, then value of $$\lambda$$2 is equal to ________________.
2
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let I be an identity matrix of order 2 $$\times$$ 2 and P = $$\left[ {\matrix{ 2 & { - 1} \cr 5 & { - 3} \cr } } \right]$$. Then the value of n$$\in$$N for which Pn = 5I $$-$$ 8P is equal to ____________.
3
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 ___________.
If 1, log10(4x $$-$$ 2) and log10$$\left( {{4^x} + {{18} \over 5}} \right)$$ 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 :