Let (h, k) lie on the circle | ELLIPSE | JEE Main 2026

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JEE Main 2026

24-01-2026 S2

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Let (h, k) lie on the circle $\mathrm{C}: x^2+y^2=4$ and the point $(2 h+1,3 k+2)$ lie on an ellipse with eccentricity $e$. Then the value of $\frac{5}{e^2}$ is equal to

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QJEE Main 20262026

The number of elements in the set $\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}$ is $\_\_\_\_$ .

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QJEE Main 20262026

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QJEE Main 20242024

Let z=(1+i)(1+2i)(1+3i)...(1+n i), where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to

JEE MainMathematicsEasy

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QJEE Main 20262026

Let $(h, k)$ lie on the circle $\mathrm{C}: x^2+y^2=4$ and the point $(2 h+1,3 k+2)$ lie on an ellipse with...

JEE MainMathematicsEasy

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QJEE Main 20242024

If $f(x)$ satisfies the relation $f(x)=e^x+\int_0^1\left(y+x e^x\right) f(y) d y$, then $e+f(0)$ is equal to $\_\_\_\_$ .

JEE AdvanceMathematicsMedium

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QJEE Main 20262026

Let [t] denote the greatest integer less than or equal to t. If the function
$...

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QJEE Main 20262026

Let $\vec{a}=2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\vec{b}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\vec{c}$ is a vector such that $2(\vec{a} \times \vec{c})+3(\vec{b} \times \vec{c})=\overrightarrow{0}$...

JEE MainMathematicsEasy

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QJEE Main 20262026

The smallest positive integral value of $a$, for which all the roots of $x^4-a x^2+9=0$ are real and distinct, is...

JEE MainMathematicsMedium

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QJEE Main 20262026

Let $f$ be a function such that $3 f(x)+2 f\left(\frac{m}{19 x}\right)=5 x, x \neq 0$, where $m=\sum_{i=1}^9(i)^2$. Then $f(5)-f(2)$ is...

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QJEE Main 20262026

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JEE MainMathematicsEasy

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QJEE Main 20262026

Consider the following three statements for the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=\left|\log _e x\right|-|x-1|$ :
(I)...

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QJEE Main 20262026

If the domain of the function $f(x)=\sin ^{-1}\left(\frac{1}{x^2-2 x-2}\right)$, is $(-\infty, \alpha] \cup[\beta, \gamma] \cup[\delta, \infty)$, then $\alpha+\beta+\gamma+\delta$ is equal...

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QJEE ADVANCE 20062006

Match the following:

JEE AdvanceChemistryEasy

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QJEE ADVANCE 20062006

According to Bohr's theory, $\mathrm{E}_{\mathrm{n}}=$ Total energy $\mathrm{K}_{\mathrm{n}}=$ Kinetic energy $\mathrm{V}_{\mathrm{n}}=$ Potential energy $\mathrm{r}_{\mathrm{n}}=$ Radius of $\mathrm{n}^{\text {th }}$ orbit...

JEE AdvanceChemistryEasy

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QJEE ADVANCE 20062006

Match the following:

JEE AdvanceChemistryEasy

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QJEE ADVANCE 20062006

Match the extraction processes listed in Column I with metals listed in Column II:

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QJEE ADVANCE 20062006

We have taken a saturated solution of $\mathrm{AgBr} . \mathrm{K}_{\text {sp }}$ of AgBr is $12 \times 10^{-14}$. If $10^{-7}$...

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