Quadratic Equations · NDA previous year questions

2024 10 questions

1. Q162024 · 1 Sept 2024

   If $n$ is a root of the equation $x^2+px+m=0$ and $m$ is a root of the equation $x^2+px+n=0$, where $m\ne n$, then what is the value of $p+m+n$?

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

2. Q392024 · 1 Sept 2024

   What is the number of real roots of the equation $(x-1{)}^2+(x-3{)}^2+(x-5{)}^2=0$?

   1. A.None
   2. B.Only one
   3. C.Only two
   4. D.Three
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   Answer: A

3. Q402024 · 1 Sept 2024

   In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?

   1. A.60
   2. B.55
   3. C.40
   4. D.35
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   Answer: A

4. Q482024 · 1 Sept 2024
   Directions

   Direction : Consider the following for the items that follow : The roots of the quadratic equation $a^2(b^2-c^2)x^2+b^2(c^2-a^2)x+c^2(a^2-b^2)=0$ are equal $(a^2\ne b^2\ne c^2)$.

   Which one of the following is a root of the equation?

   1. A.$\frac{b^2(c^2-a^2)}{a^2(c^2-b^2)}$
   2. B.$\frac{b^2(c^2-a^2)}{a^2(b^2-c^2)}$
   3. C.$\frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}$
   4. D.$\frac{b^2(c^2-a^2)}{2a^2(b^2-c^2)}$
   Show answer

   Answer: C

5. Q492024 · 1 Sept 2024

   Direction : Consider the following for the items that follow : $$\text{Let A}=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$$ What is A(adj A) equal to?

   1. A.$\left[\begin{array}{ccc}5& 0& 0\\ 0& 5& 0\\ 0& 0& 5\end{array}\right]$
   2. B.$\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]$
   3. C.$\left[\begin{array}{ccc}1/2& 0& 0\\ 0& 1/2& 0\\ 0& 0& 1/2\end{array}\right]$
   4. D.$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
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   Answer: D

6. Q502024 · 1 Sept 2024
   
   1. A.$\left[\begin{array}{ccc}1& -1& 0\\ -2& 3& -4\\ -2& 3& -3\end{array}\right]$
   2. B.$\left[\begin{array}{ccc}1/2& -1/2& 0\\ -1& 3/2& -2\\ -1& 3/2& -3/2\end{array}\right]$
   3. C.$\left[\begin{array}{ccc}2& -2& 0\\ -4& 6& -8\\ -4& 6& -6\end{array}\right]$
   4. D.$\left[\begin{array}{ccc}1/5& -1/5& 0\\ -2/5& 3/5& -4/5\\ -2/5& 3/5& -3/5\end{array}\right]$
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   Answer: A

7. Q82024 · 21 Apr 2024

   If $\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0+a_{1}x+a_2{x}^2+a_3{x}^3+x^4=0$ where $a_0,a_1,a_2,a_3$ are integers, then which one of the following is correct?

   1. A.$a_2=a_3=0$
   2. B.$a_2=0\text{ and }{a}_3=-5$
   3. C.$a_0=6,a_3=0$
   4. D.$a_1=0\text{ and }{a}_2=5$
   Show answer

   Answer: C

8. Q482024 · 21 Apr 2024

   If $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2-6x+8=0$, then what is the value of $\cos (2\alpha +2\beta )$?

   1. A.$\frac{13}{75}$
   2. B.$\frac{13}{85}$
   3. C.$\frac{17}{85}$
   4. D.$\frac{19}{85}$
   Show answer

   Answer: B

9. Q492024 · 21 Apr 2024

   What is the value of $\tan 65^{\circ }+2\tan 45^{\circ }-2\tan 40^{\circ }-\tan 25^{\circ }$?

   1. A.0
   2. B.1
   3. C.2
   4. D.4
   Show answer

   Answer: C

10. Q502024 · 21 Apr 2024

    Consider the following statements: 1. In a triangle $ABC$, if $\cot A\cdot \cot B\cdot \cot C>0$, then the triangle is an acute-angled triangle. 2. In a triangle $ABC$, if $\tan A\cdot \tan B\cdot \tan C>0$, then the triangle is an obtuse-angled triangle. Which of the statements given above is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
    Show answer

    Answer: A