Quadratic Equations · NDA previous year questions

2022 6 questions

1. Q82022 · 4 Sept 2022

   For how many quadratic equations, the sum of roots is equal to the product of roots?

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

2. Q112022 · 4 Sept 2022

   Let p, q($p>q$) be the roots of the quadratic equation $x^2+bx+c=0$ where $c>0$. If $p^2+q^2-11pq=0$, then what is p - q equal to ?

   1. A.$3\sqrt{c}$
   2. B.$3c$
   3. C.$9\sqrt{c}$
   4. D.$9c$
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   Answer: A

3. Q172022 · 10 Apr 2022

   Let $\alpha$ and $\beta$ be the roots of the equation $x^2+px+q=0$. If ${\alpha }^3$ and ${\beta }^3$ are the roots of the equation $x^2+mx+n=0$, then what is the value of $m+n$ ?

   1. A.$p^3+q^3+pq$
   2. B.$p^3+q^3-pq$
   3. C.$p^3+q^3+3pq$
   4. D.$p^3+q^3-3pq$
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   Answer: D

4. Q182022 · 10 Apr 2022

   Let $\alpha$ and $\beta$ be the roots of the equation $x^2-ax-bx+ab-c=0$. What is the quadratic equation whose roots are a and b?

   1. A.$x^2-\alpha x-\beta x+\alpha \beta +c=0$
   2. B.$x^2-\alpha x-\beta x+\alpha \beta -c=0$
   3. C.$x^2+\alpha x+\beta x+\alpha \beta +c=0$
   4. D.$x^2+\alpha x+\beta x+\alpha \beta -c=0$
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   Answer: A

5. Q192022 · 10 Apr 2022

   If the roots of the equation $x^2-ax-bx-cx+bc+ca=0$ are equal, then which one of the following is correct?

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

6. Q202022 · 10 Apr 2022

   Let $\alpha$ and $\beta$ ($\alpha >\beta$) be the roots of the equation $x^2-8x+q=0$. If ${\alpha }^2-{\beta }^2=16$, then what is the value of q?

   1. A.$-15$
   2. B.$-10$
   3. C.10
   4. D.15
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   Answer: D