et $A(x,y,z)$ be a point in $xy$-plane, which is equidistant from three points $(0,3,2)$, $(2,0,3)$ and $(0,0,1)$. Let $B=(1,4,-1)$ and $C=(2,0,-2)$. Then among the statements (S1): $\triangle ABC$ is an isosceles right angled triangle, and (S2): the area of $\triangle ABC$ is $\dfrac{9\sqrt{2}}{2}$,
Next 10 Questions — JEE Main 2025 (28 January Morning Shift)
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If $f(x)=\dfrac{2^x}{,2^x+\sqrt{2},},; x\in\mathbb{R}$, then $\displaystyle \sum_{k=1}^{81} f!\left(\dfrac{k}{82}\right…
Topic: JEE Main 2025 (28 January Morning Shift)
The sum of the squares of all the roots of the equation $x^2 + |2x - 3| - 4 = 0$ is
Topic: JEE Main 2025 (28 January Morning Shift)
The relation $R={(x,y): x,y\in\mathbb{Z}\ \text{and}\ x+y\ \text{is even}}$ is:
Topic: JEE Main 2025 (28 January Morning Shift)
Let $(a_n)$ be a sequence such that $a_0=0$, $a_1=\dfrac{1}{2}$ and $2a_{n+2}=5a_{n+1}-3a_n,; n=0,1,2,\ldots$. Then $\d…
Topic: JEE Main 2025 (28 January Morning Shift)
$\displaystyle \cos\left(\sin^{-1}\frac{3}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{33}{65}\right)$ is equal to:
Topic: JEE Main 2025 (28 January Morning Shift)
If $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96 x^2 \cos ^2 x}{\left(1+e^x\right)} \mathrm{d} x=\pi\left(\alpha \pi^…
Topic: JEE Main 2025 (28 January Morning Shift)
Let $\mathrm{T}_{\mathrm{r}}$ be the $\mathrm{r}^{\text {th }}$ term of an A.P. If for some $\mathrm{m}, \mathrm{T}_{\m…
Topic: JEE Main 2025 (28 January Morning Shift)
Let $\binom{n}{r-1}=28$, $\binom{n}{r}=56$ and $\binom{n}{r+1}=70$. Let $A(4\cos t,,4\sin t)$, $B(2\sin t,,-2\cos t)$ a…
Topic: JEE Main 2025 (28 January Morning Shift)
Two numbers $k_{1}$ and $k_{2}$ are randomly chosen from the set of natural numbers. Then, the probability that the val…
Topic: JEE Main 2025 (28 January Morning Shift)
Three defective oranges are accidentally mixed with seven good ones and, on looking at them, it is not possible to diff…
Topic: JEE Main 2025 (28 January Morning Shift)
