1
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1
Out of Syllabus

Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm{A}| \neq 0$$ and $$\mathrm{|A-d(A d j A)|=0}$$. Then

A
$$1+\mathrm{d}^{2}=\mathrm{m}^{2}+\mathrm{q}^{2}$$
B
$$1+d^{2}=(m+q)^{2}$$
C
$$(1+d)^{2}=m^{2}+q^{2}$$
D
$$(1+d)^{2}=(m+q)^{2}$$
2
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1
Out of Syllabus

The set of all values of $$\mathrm{t\in \mathbb{R}}$$, for which the matrix

$$\left[ {\matrix{ {{e^t}} & {{e^{ - t}}(\sin t - 2\cos t)} & {{e^{ - t}}( - 2\sin t - \cos t)} \cr {{e^t}} & {{e^{ - t}}(2\sin t + \cos t)} & {{e^{ - t}}(\sin t - 2\cos t)} \cr {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr } } \right]$$ is invertible, is :

A
$$\left\{ {k\pi ,k \in \mathbb{Z}} \right\}$$
B
$$\mathbb{R}$$
C
$$\left\{ {(2k + 1){\pi \over 2},k \in \mathbb{Z}} \right\}$$
D
$$\left\{ {k\pi + {\pi \over 4},k \in \mathbb{Z}} \right\}$$
3
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Let $$\alpha$$ and $$\beta$$ be real numbers. Consider a 3 $$\times$$ 3 matrix A such that $$A^2=3A+\alpha I$$. If $$A^4=21A+\beta I$$, then

A
$$\alpha=1$$
B
$$\alpha=4$$
C
$$\beta=8$$
D
$$\beta=-8$$
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Consider the following system of equations

$$\alpha x+2y+z=1$$

$$2\alpha x+3y+z=1$$

$$3x+\alpha y+2z=\beta$$

for some $$\alpha,\beta\in \mathbb{R}$$. Then which of the following is NOT correct.

A
It has a solution for all $$\alpha\ne-1$$ and $$\beta=2$$
B
It has no solution if $$\alpha=-1$$ and $$\beta\ne2$$
C
It has no solution for $$\alpha=-1$$ and for all $$\beta \in \mathbb{R}$$
D
It has no solution for $$\alpha=3$$ and for all $$\beta\ne2$$
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12