Complex Numbers & Quadratic Equations · JEE Main previous year questions

2002 8 questions

1. Q32002 · 27 Apr 2002 · Shift 1

   z and w are two nonzero complex numbers such that $|z|=|w|$ and Arg z + Arg w = $\pi$ then z equals

   1. A.$\overline{\omega }$
   2. B.$-\overline{\omega }$
   3. C.$\omega$
   4. D.$-\omega$
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   Answer: B

2. Q42002 · 27 Apr 2002 · Shift 1

   If $|z-4|<|z-2|$, its solution is given by :

   1. A.$\mathrm{Re}(z)>0$
   2. B.$\mathrm{Re}(z)<0$
   3. C.$\mathrm{Re}(z)>3$
   4. D.$\mathrm{Re}(z)>2$
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   Answer: C

3. Q52002 · 27 Apr 2002 · Shift 1

   The locus of the centre of a circle which touches the circle $|z-z_1|=a$ and $|z-z_2|=b$ externally ($z,z_1$ & $z_2$ are complex numbers) will be :

   1. A.an ellipse
   2. B.a hyperbola
   3. C.a circle
   4. D.none of these
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   Answer: B

4. Q72002 · 27 Apr 2002 · Shift 1

   Difference between the corresponding roots of $x^2+ax+b=0$ and $x^2+bx+a=0$ is same and $a\ne b$, then

   1. A.$a+b+4=0$
   2. B.$a+b-4=0$
   3. C.$a-b-4=0$
   4. D.$a-b+4=0$
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   Answer: A

5. Q82002 · 27 Apr 2002 · Shift 1

   Product of real roots of equation $t^2{x}^2+|x|+9=0$

   1. A.is always positive
   2. B.is always negative
   3. C.does not exist
   4. D.none of these
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   Answer: C

6. Q92002 · 27 Apr 2002 · Shift 1

   If $p$ and $q$ are the roots of the equation $x^2+px+q=0$, then

   1. A.$p=1,q=-2$
   2. B.$p=0,q=1$
   3. C.$p=-2,q=0$
   4. D.$p=-2,q=1$
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   Answer: A

7. Q262002 · 27 Apr 2002 · Shift 1

   If $a>0$ and discriminant of $a{x}^2+2bx+c$ is $-ve$, then $\left|\begin{array}{ccc}a& b& ax+b\\ b& c& bx+c\\ ax+b& bx+c& 0\end{array}\right|$ is equal to

   1. A.$+ve$
   2. B.$(ac-b^2)(a{x}^2+2bx+c)$
   3. C.$-ve$
   4. D.$0$
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   Answer: C

8. Q652002 · 27 Apr 2002 · Shift 1

   If $2a+3b+6c=0,(a,b,c\in R)$ then the quadratic equation $a{x}^2+bx+c=0$ has

   1. A.at least one root in $[0,1]$
   2. B.at least one root in $[2,3]$
   3. C.at least one root in $[4,5]$
   4. D.none of these
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   Answer: A