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QJEE MAIN 2025
Let $a$ be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $\alpha$...
JEE MainMathematicsMedium
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QJEE MAIN 2025
$x \mathrm{mg}$ of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298...
JEE MainChemistryEasy
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QJEE MAIN 2025
Let $\vec{a}=2 \hat{i}-3 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\vec{c}$ be such that $(\vec{a}-\vec{c}) \times \vec{b}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$ and $\vec{a} \cdot \vec{c}=3$....
JEE MainMathematicsMedium
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QJEE MAIN 2025
JEE MainChemistryHard
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QJEE MAIN 2025
Let m and $\left.\mathrm{n}_{( } \mathrm{m}<\mathrm{n}\right)$, be two 2-digit numbers. Then the total numbers of pairs ( $\mathrm{m}, \mathrm{n}$ ), such that $\operatorname{gcd}(m, n)=6$, is...
JEE MainMathematicsHard
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QJEE MAIN 2025
A metal complex with a formula $\mathrm{MCl}_4 \cdot 3 \mathrm{NH}_3$ is involved in $\mathrm{sp}^3 \mathrm{~d}^2$ hybridisation. It upon reaction with excess of $\mathrm{AgNO}_3$ solution gives...
JEE MainChemistryEasy
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QJEE MAIN 2025
Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}-3 \hat{j}+3 \hat{k}, \vec{c}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{d}$ be a vector such that $\vec{b} \times \vec{d}=\vec{c} \times \vec{d}$ and $...
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let the ellipse $3 x^2+p y^2=4$ pass through the centre $C$ of the circle $x^2+y^2-2 x-4 y-11=0$ of radius $r$. Let $f_1, f_2$ be the...
JEE MainMathematicsMedium
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QJEE MAIN 2025
Sea water, which can be considered as a 6 molar $(6 \mathrm{M})$ solution of NaCl , has a density of $2 \mathrm{~g} \mathrm{~mL}^{-1}$. The concentration...
JEE MainChemistryEasy
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QJEE MAIN 2025
Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $...
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