Complex Numbers & Quadratic Equations · JEE Main previous year questions

2006 4 questions

1. Q32006 · 29 Apr 2006 · Shift 1

   If $z^2+z+1=0$, where z is a complex number, then the value of $(z+\frac{1}{z}{)}^2+(z^2+\frac{1}{z^2}{)}^2+(z^3+\frac{1}{z^3}{)}^2+\cdots +(z^6+\frac{1}{z^6}{)}^2$ is :

   1. A.18
   2. B.54
   3. C.6
   4. D.12
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   Answer: D

2. Q42006 · 29 Apr 2006 · Shift 1

   If the roots of the quadratic equation $x^2+px+q=0$ are $\tan 30^{\circ }$ and $\tan 15^{\circ }$, respectively, then the value of $2+q-p$ is

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

3. Q52006 · 29 Apr 2006 · Shift 1

   All the values of $m$ for which both roots of the equation $x^2-2mx+m^2-1=0$ are greater than $-2$ but less than 4, lie in the interval

   1. A.$-2<m<0$
   2. B.$m>3$
   3. C.$-1<m<3$
   4. D.$1<m<4$
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   Answer: C

4. Q382006 · 29 Apr 2006 · Shift 1

   Angle between the tangents to the curve $y=x^2-5x+6$ at the points $(2,0)$ and $(3,0)$ is

   1. A.$\pi$
   2. B.$\frac{\pi }{2}$
   3. C.$\frac{\pi }{6}$
   4. D.$\frac{\pi }{4}$
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   Answer: B