1
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $\alpha, \beta$ and $\gamma$ be real numbers. Consider the following system of linear equations
$$ \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=11 \\\\ & 2 x-3 y+\beta z=\gamma \end{aligned} $$
Match each entry in List-I to the correct entries in List-II.
The correct option is:
$$ \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=11 \\\\ & 2 x-3 y+\beta z=\gamma \end{aligned} $$
Match each entry in List-I to the correct entries in List-II.
List - I | List - II |
---|---|
(P) If $\beta=\frac{1}{2}(7 \alpha-3)$ and $\gamma=28$, then the system has | (1) a unique solution |
(Q) If $\beta=\frac{1}{2}(7 \alpha-3)$ and $\gamma \neq 28$, then the system has | (2) no solution |
(R) If $\beta \neq \frac{1}{2}(7 \alpha-3)$ where $\alpha=1$ and $\gamma \neq 28$, then the system has | (3) infinitely many solutions |
(S) If $\beta \neq \frac{1}{2}(7 \alpha-3)$ where $\alpha=1$ and $\gamma=28$, then the system has | (4) $x=11, y=-2$ and $z=0$ as a solution |
(5) $x=-15, y=4$ and $z=0$ as a solution |
The correct option is:
2
JEE Advanced 2022 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
If $M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of the
following matrices is equal to $M^{2022} ?$
following matrices is equal to $M^{2022} ?$
3
JEE Advanced 2022 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $$p, q, r$$ be nonzero real numbers that are, respectively, the $$10^{\text {th }}, 100^{\text {th }}$$ and $$1000^{\text {th }}$$ terms of a harmonic progression. Consider the system of linear equations
$$$ \begin{gathered} x+y+z=1 \\ 10 x+100 y+1000 z=0 \\ q r x+p r y+p q z=0 \end{gathered} $$$
List-I | List-II |
---|---|
(I) If $$\frac{q}{r}=10$$, then the system of linear equations has | (P) $$x=0, \quad y=\frac{10}{9}, z=-\frac{1}{9}$$ as a solution |
(II) If $$\frac{p}{r} \neq 100$$, then the system of linear equations has | (Q) $$x=\frac{10}{9}, y=-\frac{1}{9}, z=0$$ as a solution |
(III) If $$\frac{p}{q} \neq 10$$, then the system of linear equations has | (R) infinitely many solutions |
(IV) If $$\frac{p}{q}=10$$, then the system of linear equations has | (S) no solution |
(T) at least one solution |
The correct option is:
4
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$M = \left[ {\matrix{
{{{\sin }^4}\theta } \cr
{1 + {{\cos }^2}\theta } \cr
} \matrix{
{ - 1 - {{\sin }^2}\theta } \cr
{{{\cos }^4}\theta } \cr
} } \right] = \alpha I + \beta {M^{ - 1}}$$,
where $$\alpha $$ = $$\alpha $$($$\theta $$) and $$\beta $$ = $$\beta $$($$\theta $$) are real numbers, and I is the 2 $$ \times $$ 2 identity matrix. If $$\alpha $$* is the minimum of the set {$$\alpha $$($$\theta $$) : $$\theta $$ $$ \in $$ [0, 2$$\pi $$)} and {$$\beta $$($$\theta $$) : $$\theta $$ $$ \in $$ [0, 2$$\pi $$)}, then the value of $$\alpha $$* + $$\beta $$* is
where $$\alpha $$ = $$\alpha $$($$\theta $$) and $$\beta $$ = $$\beta $$($$\theta $$) are real numbers, and I is the 2 $$ \times $$ 2 identity matrix. If $$\alpha $$* is the minimum of the set {$$\alpha $$($$\theta $$) : $$\theta $$ $$ \in $$ [0, 2$$\pi $$)} and {$$\beta $$($$\theta $$) : $$\theta $$ $$ \in $$ [0, 2$$\pi $$)}, then the value of $$\alpha $$* + $$\beta $$* is
Questions Asked from Matrices and Determinants (MCQ (Single Correct Answer))
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced 2023 Paper 1 Online (1)
JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2022 Paper 1 Online (1)
JEE Advanced 2019 Paper 1 Offline (1)
JEE Advanced 2017 Paper 2 Offline (1)
JEE Advanced 2016 Paper 2 Offline (1)
IIT-JEE 2012 Paper 2 Offline (1)
IIT-JEE 2012 Paper 1 Offline (1)
IIT-JEE 2011 Paper 1 Offline (3)
IIT-JEE 2011 Paper 2 Offline (1)
IIT-JEE 2009 Paper 1 Offline (3)
IIT-JEE 2008 Paper 1 Offline (1)
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