Complex Numbers & Quadratic Equations · JEE Main previous year questions

2018 7 questions

1. Q22018 · 16 Apr 2018 · Shift 1

   Let p, q and r be real numbers $(p\ne q,r\ne 0)$, such that the roots of the equation $\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

   1. A.$\frac{p^2+q^2}{2}$
   2. B.$p^2+q^2$
   3. C.$2(p^2+q^2)$
   4. D.$p^2+q^2+r^2$
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   Answer: B

2. Q232018 · 16 Apr 2018 · Shift 1

   If an angle A of a $\Delta \text{ABC}$ satisfies $5\cos \text{A}+3=0$, then the roots of the quadratic equation, $9x^2+27x+20=0$ are :

   1. A.$\sec \text{A},\cot \text{A}$
   2. B.$\sin \text{A},\sec \text{A}$
   3. C.$\sec \text{A},\tan \text{A}$
   4. D.$\tan \text{A},\cos \text{A}$
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   Answer: C

3. Q102018 · 15 Apr 2018 · Shift 1

   If $x^2+y^2+\sin y=4$, then the value of $\frac{d^{2}y}{d{x}^2}$ at the point $(-2,0)$ is :

   1. A.$-34$
   2. B.$-32$
   3. C.4
   4. D.$-2$
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   Answer: A

4. Q222018 · 15 Apr 2018 · Shift 1

   If $\tan \text{A}$ and $\tan \text{B}$ are the roots of the quadratic equation, $3x^2-10x-25=0$, then the value of $3{\sin }^2(\text{A}+\text{B})-10\sin (\text{A}+\text{B}).\cos (\text{A}+\text{B})-25{\cos }^2(\text{A}+\text{B})$ is :

   1. A.$-10$
   2. B.10
   3. C.$-25$
   4. D.25
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   Answer: C

5. Q42018 · 8 Apr 2018 · Shift 1

   If $\alpha ,\beta \in C$ are the distinct roots of the equation $x^2-x+1=0$, then ${\alpha }^{101}+{\beta }^{107}$ is equal to :

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

6. Q122018 · 8 Apr 2018 · Shift 1

   Let $\mathrm{g}(\mathrm{x})=\cos {\mathrm{x}}^2$, $\mathrm{f}(\mathrm{x})=\sqrt{x}$ and $\alpha ,\beta (\alpha <\beta )$ be the roots of the quadratic equation $18x^2-9\pi x+{\pi }^2=0$. Then the area (in sq. units) bounded by the curve $\mathrm{y}=(\mathrm{g}\circ \mathrm{f})(\mathrm{x})$ and the lines $x=\alpha$, $x=\beta$ and $y=0$ is :

   1. A.$\frac{1}{2}\left(\sqrt{2}-1\right)$
   2. B.$\frac{1}{2}\left(\sqrt{3}-1\right)$
   3. C.$\frac{1}{2}\left(\sqrt{3}+1\right)$
   4. D.$\frac{1}{2}\left(\sqrt{3}-\sqrt{2}\right)$
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   Answer: B

7. Q212018 · 8 Apr 2018 · Shift 1

   If the curves $y^2=6x$, $9x^2+b{y}^2=16$ intersect each other at right angles, then the value of b is :

   1. A.$\frac{9}{2}$
   2. B.$6$
   3. C.$\frac{7}{2}$
   4. D.$4$
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   Answer: A