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QJEE MAIN 2025
If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right) \cdot{ }^{11} C_{r+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}$, then $\alpha$ is equal to :
JEE MainMathematicsMedium
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QJEE MAIN 2025
A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $\mathrm{P}: y^2=x-2$ at the point $B$ in the first quadrant. The area, of the region...
JEE MainMathematicsMedium
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QJEE MAIN 2025
If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$, then $\sum_{k=1}^3\left(z_k-z_0\right)^2$ is equal to
JEE MainMathematicsMedium
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QJEE MAIN 2025
Match List - I with List - II. Choose the correct answer from the options given below : JEE MainChemistryEasy
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QJEE MAIN_2025
Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10 . If its eccentricity is the minimum value of the function $...
JEE MainPhysicsEasy
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QJEE MAIN 2025
Which one of the following reactions will not lead to the desired ether formation in major proportion? (iso- $\mathrm{Bu} \Rightarrow$ isobutyl, sec $-\mathrm{Bu} \Rightarrow$ sec-butyl,...
JEE MainChemistryEasy
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QJEE MAIN 2025
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of...
JEE MainMathematicsEasy
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QJEE MAIN 2025
If the sum of the first 20 terms of the series $$ \frac{4 \cdot 1}{4+3 \cdot 1^2+1^4}+\frac{4 \cdot 2}{4+3 \cdot 2^2+2^4}+\frac{4 \cdot 3}{4+3 \cdot 3^2+3^4}+\frac{4...
JEE MainMathematicsEasy
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QJEE MAIN 2025
The correct order of basicity for the following molecules is :
JEE MainChemistryEasy
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QJEE MAIN_2025
Let the system of equations $$ \begin{aligned} & x+5 y-z=1 \\ & 4 x+3 y-3 z=7 \\ & 24 x+y+\lambda z=\mu \end{aligned} $$ $...
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