Complex Numbers & Quadratic Equations · JEE Main previous year questions

2021 30 questions

1. Q42021 · 26 Feb 2021 · Shift 2

   A natural number has prime factorization given by $n=2^x{3}^y{5}^z$, where y and z are such that $y+z=5$ and $y^{-1}+z^{-1}=\frac{5}{6}$, $y>z$. Then the number of odd divisors of n, including 1, is :

   1. A.11
   2. B.6
   3. C.12
   4. D.6x
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   Answer: C

2. Q242021 · 26 Feb 2021 · Shift 2· Numerical answer

   Let z be those complex numbers which satisfy $|z+5|\le 4$ and $z(1+i)+\bar{z}(1-i)\ge -10,i=\sqrt{-1}$. If the maximum value of $|z+1{|}^2$ is $\alpha +\beta \sqrt{2}$, then the value of $(\alpha +\beta )$ is _________.

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   Answer: 48

3. Q282021 · 26 Feb 2021 · Shift 2· Numerical answer

   Let a be an integer such that all the real roots of the polynomial $2x^5+5x^4+10x^3+10x^2+10x+10$ lie in the interval $(a,a+1)$. Then, $|a|$ is equal to _________.

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   Answer: 2

4. Q302021 · 26 Feb 2021 · Shift 2· Numerical answer

   Let L be a common tangent line to the curves $4x^2+9y^2=36$ and $(2x{)}^2+(2y{)}^2=31$. Then the square of the slope of the line L is _________.

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   Answer: 3

5. Q142021 · 25 Feb 2021 · Shift 2

   If the curve $x^2+2y^2=2$ intersects the line $x+y=1$ at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

   1. A.$\frac{\pi }{2}-{\tan }^{-1}\left(\frac{1}{4}\right)$
   2. B.$\frac{\pi }{2}+{\tan }^{-1}\left(\frac{1}{3}\right)$
   3. C.$\frac{\pi }{2}-{\tan }^{-1}\left(\frac{1}{3}\right)$
   4. D.$\frac{\pi }{2}+{\tan }^{-1}\left(\frac{1}{4}\right)$
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   Answer: D