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JEE Advance 2009
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Let $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ be points with integer coordinates satisfying the system of homogeneous equations: $$ \begin{array}{r} 3 x-y-z=0 \\ -3 x+z=0 \\ -3 x+2 y+z=0 \end{array} $$ Then the number of such points for which $x^2+y^2+z^2 \leq 100$ is
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The value of $\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\ln 6-x^2\right)} d x$ is
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Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three sets of complex numbers as defined below $$ \begin{aligned} & A=\{z: \operatorname{Im} z \geq...
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Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$, whose projection...
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QJEE Advance 20082008
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JEE AdvanceMathematicsEasy
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