Let $N$ denote the number that turns up when a fair die is rolled. If the probability that the system of equations $x + y + z = 1$ , $2x + Ny + 2z = 2$, $3x + 3y + Nz = 3$ . has a unique solution is $\dfrac{k}{6}$, then the sum of the value of $k$ and all possible values of $N$ is:
Previous 10 Questions — JEE Main 2023 (24 January Morning Shift)
Nearest firstNext 10 Questions — JEE Main 2023 (24 January Morning Shift)
Ascending by ID
1
2
3
4
5
6
7
8
9
10
The relation $\mathsf{R} = \{(a,b) : \gcd(a,b)=1,\ 2a \ne b,\ a,b \in \mathbb{Z}\}$ is:
Topic: JEE Main 2023 (24 January Morning Shift)
$\displaystyle \lim_{t\to 0}\left(1^{\frac{1}{\sin^2 t}}+2^{\frac{1}{\sin^2 t}}+\cdots+n^{\frac{1}{\sin^2 t}}\right)^{\…
Topic: JEE Main 2023 (24 January Morning Shift)
$\tan^{-1}\!\left(\dfrac{1+\sqrt{3}}{3+\sqrt{3}}\right) + \sec^{-1}\!\left(\sqrt{\dfrac{8+4\sqrt{3}}{6+3\sqrt{3}}}\righ…
Topic: JEE Main 2023 (24 January Morning Shift)
Let $y=y(x)$ be the solution of the differential equation
$x^{3}\,dy+(xy-1)\,dx=0,\quad x>0,$ with $y\!\left(\dfrac{1…
Topic: JEE Main 2023 (24 January Morning Shift)
Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event.
Given below are two statements:
(S1): If $…
Topic: JEE Main 2023 (24 January Morning Shift)
The area enclosed by the curves $y^2 + 4x = 4$ and $y - 2x = 2$ is:
Topic: JEE Main 2023 (24 January Morning Shift)
The equation $x^{2}-4x+[x]+3 = x[x]$, where $[x]$ denotes the greatest integer function, has:
Topic: JEE Main 2023 (24 January Morning Shift)
If $A$ and $B$ are two non-zero $n \times n$ matrices such that $A^{2}+B=A^{2}B$, then:
Topic: JEE Main 2023 (24 January Morning Shift)
For three positive integers $p, q, r$, $x^{p q^{2}} = y^{q r} = z^{p^{2} r}$ and $r = pq + 1$ such that
$3,\ 3\log_{y…
Topic: JEE Main 2023 (24 January Morning Shift)
Let $\triangle PQR$ be a triangle. The points $A, B,$ and $C$ are on the sides $QR, RP,$ and $PQ$ respectively such tha…
Topic: JEE Main 2023 (24 January Morning Shift)
