Complex Numbers & Quadratic Equations · JEE Main previous year questions

2017 6 questions

1. Q92017 · 9 Apr 2017 · Shift 1

   If $2x=y^{\frac{1}{5}}+y^{-\frac{1}{5}}$ and $(x^2-1)\frac{d^{2}y}{d{x}^2}+\lambda x\frac{dy}{dx}+ky=0$, then $\lambda +k$ is equal to :

   1. A.$-23$
   2. B.$-24$
   3. C.$26$
   4. D.$-26$
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   Answer: B

2. Q22017 · 8 Apr 2017 · Shift 1

   Let $p(x)$ be a quadratic polynomial such that $p(0)=1$. If $p(x)$ leaves remainder $4$ when divided by $x-1$ and it leaves remainder $6$ when divided by $x+1$; then :

   1. A.$p(2)=11$
   2. B.$p(2)=19$
   3. C.$p(-2)=19$
   4. D.$p(-2)=11$
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   Answer: C

3. Q32017 · 8 Apr 2017 · Shift 1

   Let $z\in \mathbb{C}$, the set of complex numbers. Then the equation, $2|z+3i|-|z-i|=0$ represents :

   1. A.a circle with radius $\frac{8}{3}$.
   2. B.a circle with diameter $\frac{10}{3}$.
   3. C.an ellipse with length of major axis $\frac{16}{3}$.
   4. D.an ellipse with length of minor axis $\frac{16}{9}$.
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   Answer: A

4. Q42017 · 8 Apr 2017 · Shift 1

   The number of real values of $\lambda$ for which the system of linear equations $2x+4y-\lambda z=0$ $4x+\lambda y+2z=0$ $\lambda x+2y+2z=0$ has infinitely many solutions, is :

   1. A.$0$
   2. B.$1$
   3. C.$2$
   4. D.$3$
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   Answer: B

5. Q102017 · 8 Apr 2017 · Shift 1

   If $y={\left[x+\sqrt{x^2-1}\right]}^{15}+{\left[x-\sqrt{x^2-1}\right]}^{15}$, then $(x^2-1)\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}$ is equal to :

   1. A.$125y$
   2. B.$124y^2$
   3. C.$225y^2$
   4. D.$225y$
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   Answer: D

6. Q142017 · 8 Apr 2017 · Shift 1

   The area (in sq. units) of the smaller portion enclosed between the curves, $x^2+y^2=4$ and $y^2=3x$, is :

   1. A.$\frac{1}{2\sqrt{3}}+\frac{\pi }{3}$
   2. B.$\frac{1}{\sqrt{3}}+\frac{2\pi }{3}$
   3. C.$\frac{1}{2\sqrt{3}}+\frac{2\pi }{3}$
   4. D.$\frac{1}{\sqrt{3}}+\frac{4\pi }{3}$
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   Answer: D