Complex Numbers and Quadratic Equations

JEE Main · Mathematics · 10 past questions

These are the board's own papers. 165 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026 2 Apr Shift 1

   Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i$…

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2. Q2 2026 4 Apr Shift 1

   Let $z$ be a complex number such that $|z+2|=|z-2|$ and $\arg\left(\dfrac{z+3}{z-i}\right)=\dfrac{\pi}{4}$.…

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3. Q3 2026 4 Apr Shift 2

   Let $S = \{z \in \mathbb{C} : z^2 + 4z + 16 = 0\}$. Then $\sum_{z \in S} |z + \sqrt{3}\,i|^2$ is equal to…

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4. Q4 2026 4 Apr Shift 2

   If $\alpha = 1$ and $\beta = 1+i\sqrt{2}$, where $i=\sqrt{-1}$, are two roots of the equation…

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5. Q5 2026 4 Apr Shift 2

   If the quadratic equation $(\lambda+2)x^2 - 3\lambda x + 4\lambda = 0$, $\lambda \neq -2$, has two positive…

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6. Q6 2026 5 Apr Shift 2

   Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2 + 4z - (1+12i) = 0$. Then…

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7. Q7 2026 6 Apr Shift 1

   Let the set of all values of $k\in\mathbb{R}$ such that the equation $z(\bar{z}+2+i)+k(2+3i)=0$…

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8. Q8 2026 6 Apr Shift 2

   Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$, $n\in\mathbf{R}$. Let $\alpha$ be the…

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9. Q9 2026 6 Apr Shift 2

   Let $S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}$. Then $\displaystyle\sum_{z\in S} z^8$ is equal to…

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10. Q10 2026 8 Apr Shift 2

    The number of values of z ∈ ℂ, satisfying the equations |z - (4+8i)| = √10 and |z - (3+5i)| + |z - (5+11i)| =…

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