1
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
Consider the matrix $f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$.

Given below are two statements :

Statement I : $f(-x)$ is the inverse of the matrix $f(x)$.

Statement II : $f(x) f(y)=f(x+y)$.

In the light of the above statements, choose the correct answer from the options given below :
A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are false
C
Both Statement I and Statement II are true
D
Statement I is true but Statement II is false
2
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
Out of Syllabus
Let the determinant of a square matrix A of order $m$ be $m-n$, where $m$ and $n$

satisfy $4 m+n=22$ and $17 m+4 n=93$.

If $\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(m A)))=3^{a} 5^{b} 6^{c}$ then $a+b+c$ is equal to :
A
96
B
84
C
109
D
101
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1
Out of Syllabus

Let for $$A = \left[ {\matrix{ 1 & 2 & 3 \cr \alpha & 3 & 1 \cr 1 & 1 & 2 \cr } } \right],|A| = 2$$. If $$\mathrm{|2\,adj\,(2\,adj\,(2A))| = {32^n}}$$, then $$3n + \alpha$$ is equal to

A
11
B
9
C
12
D
10
4
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

If the system of equations

$$2 x+y-z=5$$

$$2 x-5 y+\lambda z=\mu$$

$$x+2 y-5 z=7$$

has infinitely many solutions, then $$(\lambda+\mu)^{2}+(\lambda-\mu)^{2}$$ is equal to

A
916
B
912
C
920
D
904
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