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QJEE MAIN 2025
Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Let $\hat{c}$ be a unit vector in the plane of the vectors $\vec{a}$ and $\vec{b}$ and be perpendicular to...
JEE MainMathematicsMedium
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QJEE MAIN 2023
The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$
JEE MainMathematicsEasy
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QJEE MAIN 2025
20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide...
JEE MainChemistryEasy
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QJEE MAIN 2025
If $y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right)$, then $(x-y)^2+3 y^2$ is equal to
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let $A(4,-2), B(1,1)$ and $C(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram $A F D E$, formed...
JEE MainMathematicsHard
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QJEE MAIN 2025
The equilibrium constant for decomposition of $\mathrm{H}_2 \mathrm{O}$ (g) $\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ is $8.0 \times 10^{-3}$ at 2300 K and...
JEE MainChemistryHard
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QJEE MAIN 2025
$
\begin{aligned}
& \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots \infty=\frac{\pi^4}{90} \\
& \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots \infty=\alpha, \\
& \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots \infty=\beta
\end{aligned}
$
then $\frac{\alpha}{\beta}$ is equal to
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let $\left(1+x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}$. If $\left(a_1+a_3+a_5+\ldots+a_{19}\right)-11 a_2=121 k$, then $k$ is equal to $\_\_\_\_$
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$...
JEE MainMathematicsEasy
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QJEE MAIN 2025
If the equation of the hyperbola with foci $(4,2)$ and $(8,2)$ is $3 x^2-y^2-\alpha x+\beta y+\gamma=0$, then $\alpha+\beta+\gamma$ is equal to $\_\_\_\_$ .
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