Complex Numbers and Quadratic Equations is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Complex Numbers and Quadratic Equations with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Complex Numbers and Quadratic Equations questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Complex Numbers and Quadratic Equations with Solutions
1.
If $\alpha, \beta$ are the roots of the quadratic equation $x^2+ax+b=0, (b\ne 0)$; then the quadratic equation whose roots are $\alpha -\frac{1}{\beta}, \beta - \frac{1}{\alpha}$ is- $ax^2+a(b-1)x+(a-1)^2=0$
- $bx^2+a(b-1)x+(b-1)^2=0$
- $x^2+ax+b = 0$
- $abx^2+bx+a = 0$
2.
If $z = \frac{4}{1-i}$, then $\bar{z}$ is (where $\bar{z}$ is complex conjugate of $z$ )- $2 (1 + i)$
- $(1 + i)$
- $\frac{2}{1-i}$
- $\frac{4}{1+i}$
3.
If $\sin\,\theta$ and $\cos \theta $ are the roots of the equation $ax^2 - bx + c = 0$, then $a, b$ and $c$ satisfy the relation- $a^2 + b^2 + 2ac = 0$
- $a^2 - b^2 + 2ac = 0$
- $a^2 + c^2 + 2ab = 0$
- $a^2 - b^2 - 2ac = 0$
4.
If $\omega$ is an imaginary cube root of unity, then the value of $\left(2-\omega\right)\left(2-\omega^{2}\right)+2\left(3-\omega\right)\left(3-\omega^{2}\right)+.....+\left(n-1\right)\left(n-\omega\right)\left(n-\omega^{2}\right)$- $\frac{n^{2}}{4}\left(n+1\right)^{2}-n$
- $\frac{n^{2}}{4}\left(n+1\right)^{2}+n$
- $\frac{n^{2}}{4}\left(n+1\right)^{2}$
- $\frac{n^{2}}{4}\left(n+1\right)-n$
5.
If $\frac{z-1}{z+1}$ is purely imaginary, then- $\left|z\right|=\frac{1}{2}$
- $\left|z\right|=1$
- $\left|z\right|=2$
- $\left|z\right|=3$
6.
The modulus of $\frac{1-i}{3+i}+\frac{4i}{5}$ is- $\sqrt{5}$ unit
- $\frac{\sqrt{11}}{5}$ unit
- $\frac{\sqrt{5}}{5}$ unit
- $\frac{\sqrt{12}}{5}$ unit
7.
Let α,β be the roots of the equation, ax2+bx+c=0.a,b,c are real and sn=αn+βn and \(\begin{vmatrix}3 &1+s_1 &1+s_2\\1+s_1&1+s_2 &1+s_3\\1+s_2&1+s_3 &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}\) then k=
- b2-4ac
- b2+4ac
- b2+2ac
- 4ac-b2
8.
If the ratio of the roots of the equation $px^2 + qx + r = 0$ is $a : b$, then $\frac{ab}{\left(a+b\right)^{2}} = $- $\frac{p^{2}}{qr} $
- $\frac{pr}{q^{2}} $
- $\frac{q^{2}}{pr} $
- $\frac{pq}{r^{2}} $
9.
If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2 + px + q = 0\), then the values of \(\alpha^{3}, \beta^{3}\) and \(\alpha^{4}+\alpha^{2}\beta^{3}+\beta^{4}\) are respectively- $3pq - p^3$ and $p^4 - 3p^2q + 3q^2$
- $-p(3q - p^2)$ and $(p^2 - q)(p^2 + 3q)$
- $pq - 4$ and $p^4 - q^4$
- $3pq - p^3$ and $(p^2 - q) (p^2 - 3q)$
10.
If $\left(\frac{3}{2}+i\frac{\sqrt{3}}{2}\right)^{50} \, =3^{25} \left(x+iy\right),$ where $x$ and $y$ are real, then the ordered pair $(x,y)$ is- $(-3, 0)$
- $(0, 3)$
- $(0, -3)$
- $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$
11.
Given that $x$ is a real number satisfying $\frac{5x^{2}-26x+5}{3x^{2}-10x+3} < 0 ,$ then- $x
- $\frac{1}{5} < x < 3$
- $x > 5$
- $\frac{1}{5} < x < \frac{1}{3}$ or $3 < x < 5$
12.
The quadratic expression $\left(2x+1\right)^{2}-px+q\ne0$ for any real $x$ if- $p^2 - 16p - 8q < 0$
- $p^2 - 8p + 16q < 0$
- $p^2 - 8p - 16q < 0$
- $p^2 - 16p + 8q < 0$
13.
If the equation $x^2 + y^2 -10x + 21 = 0$ has real roots $x = a$ and $y=\beta$ then- $3\le x\le7$
- $3\le y\le7$
- $-2 \le y \le2$
- $-2\le x\le2$
14.
For real $x$, the greatest value of $\frac{x^{2}+2x+4}{2x^{2}+4x+9}$ is- $1$
- $-1$
- $\frac{1}{2}$
- $\frac{1}{4}$
15.
If $\alpha, \beta $ be the roots of $x^{2}-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^{2}-a\alpha}+\frac{1}{\beta^{2}-a\beta}+\frac{2}{a+b}$ is- $\frac{4}{a+b}$
- $\frac{1}{a+b}$
- $0$
- $-1$
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