Let the area of the triangle formed by the lines $x+2=y-1=z, \frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^2$ is equal to $\_\_\_\_$ .
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a<0$ and the parabola $y^2=9 x$ at the...
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let the area of the bounded region $\left\{(x, y): 0 \leq 9 x \leq y^2, y \geq 3 x-6\right\}$ be $A$. Then 6 A is...
JEE MainMathematicsMedium
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QJEE MAIN 2025
The product of the last two digits of $(1919)^{1919}$ is $\_\_\_\_$
JEE MainMathematicsMedium
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QJEE MAIN 2025
The number of integral terms in the expansion of $\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)^{1016}$ is
JEE MainMathematicsEasy
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QJEE MAIN 2025
Let $\alpha$ be a solution of $x^2+x+1=0$, and for some $a$ and $b$ in $...
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let $f(x)$ be a positive function and $I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x$ and $I_2=\int_{-1}^2 f(x(1-x)) d x$. Then the value of $\frac{I_2}{I_1}$...
JEE MainMathematicsMedium
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QJEE MAIN 2025
The Value of $\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2(2)}-1}{\tan (2)}\right)-\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2\left(\frac{1}{2}\right)}+1}{\tan \left(\frac{1}{2}\right)}\right)$ is equal to
JEE MainMathematicsMedium
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QJEE MAIN 2025
The sum of the squares of the roots of $|x-2|^2+|x-2|-2=0$ and the squares of the roots of $x^2-2|x-3|-5=0$, is
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