Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation on the set $\{1,2,3,4\}$. The minimum number of ordered pairs that must be added to $R$ so that it becomes an equivalence relation is:
Previous 10 Questions — JEE Main 2025 (23 January Morning Shift)
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If A, B and $\big(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1})\big)$ are non-singular matrices of the same ord…
Topic: JEE Main 2025 (23 January Morning Shift)
Let the area of $\triangle$ PQR with vertices P(5,4), Q(-2,4) and R(a,b) be 35 square units. If its orthocenter and cen…
Topic: JEE Main 2025 (23 January Morning Shift)
Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC divides the arc AC such …
Topic: JEE Main 2025 (23 January Morning Shift)
If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four…
Topic: JEE Main 2025 (23 January Morning Shift)
If the line 3x - 2y + 12 = 0 intersects the parabola 4y = 3x2 at the points A and B, then at the vertex of the parabola…
Topic: JEE Main 2025 (23 January Morning Shift)
Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\f…
Topic: JEE Main 2025 (23 January Morning Shift)
Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, z \in C$, be the equation of a circle with center at $C$. …
Topic: JEE Main 2025 (23 January Morning Shift)
Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. T…
Topic: JEE Main 2025 (23 January Morning Shift)
The value of $\int_{e^2}^{e^4} \frac{1}{x}\left(\frac{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}}{e^{\left(\left(…
Topic: JEE Main 2025 (23 January Morning Shift)
If the system of equations
$(\lambda-1)x+(\lambda-4)y+\lambda z=5$
$\lambda x+(\lambda-1)y+(\lambda-4)z=7$
$(\lambd…
Topic: JEE Main 2025 (23 January Morning Shift)
