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JEE MAIN_2026_
210126_S1
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Consider the following equation:
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Showing 18 questions
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Let $S=S_1 \cap S_2 \cap S_3$, where $$ \begin{aligned} & S_1=\{z \in C:|z|<4\}, S_2=\left\{z \in C: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}\right]>0\right\} \text...
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Let $f(x)=x \sin \pi x, x>0$. Then for all natural numbers $n, f^{\prime}(x)$ vanishes at
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Let $P Q R$ be a triangle of area $\triangle$ with $a=2, b=\frac{7}{2}$ and $c=\frac{5}{2}$, where $a, b$ and $c$...
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The synthesis of 3 – octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an...
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A line $l$ passing through the origin is perpendicular to the lines $$ \begin{aligned} & l_1:(3+\mathrm{t}) \hat{\mathrm{i}}+(-1+2 \mathrm{t}) \hat{\mathrm{j}}+(4+2 \mathrm{t})...
JEE AdvanceMathematicsEasy
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QJEE Advance 20132013
Let $P Q$ be a focal chord of the parabola $y^2=4 a x$. The tangents to the parabola at $P$...
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QJEE Advance 20132013
Let $S_n=\sum_{k=1}^{4 n}(-1)^{\frac{k(k+1)}{2}} k^2$. Then $S_n$ can take value(s)
JEE AdvanceMathematicsEasy
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QJEE Advance 20132013
Let $P Q$ be a focal chord of the parabola $y^2=4 a x$. The tangents to the parabola at $P$...
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QJEE Advance 20132013
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8: 15$ is converted into an...
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QJEE Advance 20132013
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
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QJEE Advance 20132013
Let $f:\left[\frac{1}{2}, 1\right] \rightarrow R$ (the set of all real numbers) be a positive, non-constant and differentiable function such that...
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QJEE Advance 20122012
If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{b}$,...
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A curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be...
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QJEE Advance 20122012
The equation of a plane passing through the line of intersection of the planes $x+2 y+3 z=2$ and $x-y+z=3$ and...
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The function $f(x)=2|x|+|x+2|-||x+2|-2| x| |$ has a local minimum or a local maximum at $x=$
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QJEE Advance 20132013
The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $\left[0, \frac{\pi}{2}\right]$ is
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QJEE Advance 20132013
Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $\mathrm{P}=\left[\mathrm{p}_{\mathrm{ij}}\right]$ be a $\mathrm{n} \times \mathrm{n}$...
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