1

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

For real numbers $$\alpha$$ and $$\beta$$, consider the following system of linear equations :

x + y $$-$$ z = 2, x + 2y + $$\alpha$$z = 1, 2x $$-$$ y + z = $$\beta$$. If the system has infinite solutions, then $$\alpha$$ + $$\beta$$ is equal to ______________.

x + y $$-$$ z = 2, x + 2y + $$\alpha$$z = 1, 2x $$-$$ y + z = $$\beta$$. If the system has infinite solutions, then $$\alpha$$ + $$\beta$$ is equal to ______________.

Your input ____

2

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

Let $$f(x) = \left| {\matrix{
{{{\sin }^2}x} & { - 2 + {{\cos }^2}x} & {\cos 2x} \cr
{2 + {{\sin }^2}x} & {{{\cos }^2}x} & {\cos 2x} \cr
{{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \cos 2x} \cr
} } \right|,x \in [0,\pi ]$$. Then the maximum value of f(x) is equal to ______________.

Your input ____

3

JEE Main 2021 (Online) 25th July Morning Shift

Numerical

+4

-1

Let $$M = \left\{ {A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right):a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} } \right\}$$. Define f : M $$\to$$ Z, as f(A) = det(A), for all A$$\in$$M, where z is set of all integers. Then the number of A$$\in$$M such that f(A) = 15 is equal to _____________.

Your input ____

4

JEE Main 2021 (Online) 22th July Evening Shift

Numerical

+4

-1

Let $$A = \left[ {\matrix{
0 & 1 & 0 \cr
1 & 0 & 0 \cr
0 & 0 & 1 \cr
} } \right]$$. Then the number of 3 $$\times$$ 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is ____________.

Your input ____

Questions Asked from Matrices and Determinants (Numerical)

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