Complex Numbers & Quadratic Equations · JEE Main previous year questions

2012 5 questions

1. Q22012 · 12 May 2012 · Shift 1

   If the sum of the square of the roots of the equation $x^2-(\sin \alpha -2)x-(1+\sin \alpha )=0$ is least, then $\alpha$ is equal to

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

2. Q32012 · 12 May 2012 · Shift 1

   The area of the triangle whose vertices are complex numbers $z,iz,z+iz$ in the Argand diagram is

   1. A.$2|z{|}^2$
   2. B.$\frac{1}{2}|z{|}^2$
   3. C.$4|z{|}^2$
   4. D.$|z{|}^2$
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   Answer: B

3. Q12012 · 7 May 2012 · Shift 1

   The value of $K$ for which the equation $(K-2)x^2+8x+K+4=0$ has both roots real, distinct and negative is

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

4. Q22012 · 7 May 2012 · Shift 1

   Let $Z_1$ and $Z_2$ be any two complex number. Statement 1: $|Z_1-Z_2|\ge |Z_1|-|Z_2|$ Statement 2: $|Z_1+Z_2|\le |Z_1|+|Z_2|$

   1. A.Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
   2. B.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
   3. C.Statement 1 is true, Statement 2 is false.
   4. D.Statement 1 is false, Statement 2 is true.
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   Answer: B

5. Q122012 · 7 May 2012 · Shift 1

   If the system of equations $x+y+z=6$ $x+2y+3z=10$ $x+2y+\lambda z=0$ has a unique solution, then $\lambda$ is not equal to

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