Q JEE MAIN_2026

Let $\alpha, \alpha+2, \alpha \in \mathbf{Z}$, be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots .+(x+\mathrm{n}-1)(x+\mathrm{n}+1)=4 \mathrm{n}$ for some $...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

If the quadratic equation $(\lambda+2) x^2-3 \lambda x+4 \lambda=0, \lambda \neq-2$, has two positive roots, then the number of possible...

JEE Main Mathematics Hard

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Q JEE MAIN 2026

Let $\tan A, \tan B$, where $A, B \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, be the roots of the quadratic equation $x^2-2 x-5=0$. Then...

JEE Main Mathematics Easy

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Q Jee Main 2026

Let $\alpha, \beta$ be the roots of the equation $x^2-3 x+\mathrm{r}=0$, and $\frac{\alpha}{2}, 2 \beta$ be the roots of the...

JEE Main Mathematics Easy

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Q JEE Main 2021

\text { The sum of the roots of the equation } x+1-2 \log _2\left(3+2^x\right)+2 \log _4\left(10-2^{-x}\right)=0 \text {, is: }

JEE Main Mathematics Medium

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Q JEE MAIN_2021_

Let $z_1$ and $z_2$ be two complex numbers such that arg $\left(z_1-z_2\right)=\frac{\pi}{4}$ and $z_1, z_2$ satisfy the equation $|z-3|=$ $\operatorname{Re}(z)$....

JEE Main Mathematics Easy

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Q JEE MAIN_2021_

Let $n$ denote the number of solutions of the equation $z^2+3 \bar{z}=0$, where $z$ is a complex number. Then the...

JEE Main Mathematics Medium

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Q JEE MAIN_2021

The area of the triangle with vertices A (z), B (iz) and C (z + iz) is :

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2} x+2=0$. Then $\alpha^{14}+\beta^{14}$ is equal to

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let ${{z}_{1}},{{z}_{2}}$ and ${{z}_{3}}$ be three complex numbers on the circle $|z|=1$ with $...

JEE Main Physics Easy

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