Complex Numbers & Quadratic Equations · JEE Main previous year questions

2020 28 questions

1. Q52020 · 7 Jan 2020 · Shift 1

   If $\text{Re}\left(\frac{z-1}{2z+i}\right)=1$, where $z=x+iy$, then the point (x, y) lies on a :

   1. A.straight line whose slope is $\frac{3}{2}$
   2. B.straight line whose slope is $-\frac{2}{3}$
   3. C.circle whose diameter is $\frac{\sqrt{5}}{2}$
   4. D.circle whose centre is at $\left(-\frac{1}{2},-\frac{3}{2}\right)$
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   Answer: C

2. Q252020 · 7 Jan 2020 · Shift 1· Numerical answer

   If the sum of the coefficients of all even powers of x in the product $(1+x+x^2+\cdots +x^{2n})(1-x+x^2-x^3+\cdots +x^{2n})$ is 61, then n is equal to _____.

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   Answer: 30

3. Q232020 · 7 Jan 2020 · Shift 2· Numerical answer

   If the system of linear equations, $$\begin{array}{rl}x+y+z& =6\\ x+2y+3z& =10\\ 3x+2y+\lambda z& =\mu \end{array}$$ has more than two solutions, then $\mu -{\lambda }^2$ is equal to _______.

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   Answer: 13