Complex Numbers & Quadratic Equations · JEE Main previous year questions

2004 8 questions

1. Q42004 · 24 Apr 2004 · Shift 1

   Let z and w be complex numbers such that $\overline{z}+i\overline{w}=0$ and arg zw = $\pi$. Then arg z equals :

   1. A.$\frac{5\pi }{4}$
   2. B.$\frac{\pi }{2}$
   3. C.$\frac{3\pi }{4}$
   4. D.$\frac{\pi }{4}$
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   Answer: C

2. Q52004 · 24 Apr 2004 · Shift 1

   If $z=x-iy$ and $z^{\frac{1}{3}}=p+iq$, then $\frac{\left(\frac{x}{p}+\frac{y}{q}\right)}{(p^2+q^2)}$ is equal to :

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

3. Q72004 · 24 Apr 2004 · Shift 1

   Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

   1. A.$x^2-18x-16=0$
   2. B.$x^2-18x+16=0$
   3. C.$x^2+18x-16=0$
   4. D.$x^2+18x+16=0$
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   Answer: B

4. Q82004 · 24 Apr 2004 · Shift 1

   If $(1-p)$ is a root of quadratic equation $x^2+px+(1-p)=0$ then its roots are

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

5. Q92004 · 24 Apr 2004 · Shift 1

   If one root of the equation $x^2+px+12=0$ is 4, while the equation $x^2+px+q=0$ has equal roots, then the value of ${}^{\prime }{q}^{\prime }$ is

   1. A.4
   2. B.12
   3. C.3
   4. D.$\frac{49}{4}$
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   Answer: D

6. Q382004 · 24 Apr 2004 · Shift 1

   If the straight lines $x=1+s,y=-3-\lambda s,z=1+\lambda s$ and $x=\frac{t}{2},y=1+t,z=2-t$, with parameters $s$ and $t$ respectively, are co-planar, then $\lambda$ equals :

   1. A.$0$
   2. B.$-1$
   3. C.$-\frac{1}{2}$
   4. D.$-2$
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   Answer: D

7. Q552004 · 24 Apr 2004 · Shift 1

   If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product, then $c$ has the value :

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

8. Q562004 · 24 Apr 2004 · Shift 1

   If one of the lines given by $6x^2-xy+4c{y}^2=0$ is $3x+4y=0$, then $c$ equals :

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