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QJEE Advanced 2025
If $ \alpha=\int_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x $ then the value of $\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)$ is $\_\_\_\_$ ....
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Let
$
\alpha=\frac{1}{\sin 60^{\circ} \sin 61^{\circ}}+\frac{1}{\sin 62^{\circ} \sin 63^{\circ}}+\cdots+\frac{1}{\sin 118^{\circ} \sin 119^{\circ}}
$
Then the value of $\left(\frac{\operatorname{cosec} 1^{\circ}}{\alpha}\right)^2$
is $\_\_\_\_$
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(0,4)$ be functions defined by $...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi<\arg (z) \leq \pi$. Let $\omega$ be the cube...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Consider the vectors $ \vec{x}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \quad \vec{y}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \quad \text { and } \quad \vec{z}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k} $ For two...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
A factory has a total of three manufacturing units, $M_1, M_2$, and $M_3$, which produce bulbs independent of each other. The units $M_1, M_2$, and...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Let $a_0, a_1, \ldots, a_{23}$ be real numbers such that $ \left(1+\frac{2}{5} x\right)^{23}=\sum_{i=0}^{23} a_i x^i $ for every real number $x$. Let $a_r$...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Let $y(x)$ be the solution of the differential equation $ x^2 \frac{d y}{d x}+x y=x^2+y^2, \quad x>\frac{1}{e} $ satisfying $y(1)=0$. Then the value...
JEE AdvanceMathematicsEasy
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QJEE Advanced 2025
Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $...
JEE AdvanceMathematicsEasy
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QJEE-Advanced 2025
A linear octasaccharide (molar mass $=1024 \mathrm{~g} \mathrm{~mol}^{-1}$ ) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is...
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