Quadratic Equations · NDA previous year questions

2021 14 questions

1. Q62021 · 14 Nov 2021

   The quadratic equation $3x^2-(k^2+5k)x+3k^2-5k=0$ has real roots of equal magnitude and opposite sign. Which one of the following is correct?

   1. A.$0<k<\frac{5}{3}$
   2. B.$0<k<\frac{3}{5}$ only
   3. C.$\frac{3}{5}<k<\frac{5}{3}$
   4. D.No such value of k exists
   Show answer

   Answer: D

2. Q72021 · 14 Nov 2021

   If $a_n=n(n!)$, then what is $a_1+a_2+a_3+\cdots +a_{10}$ equal to?

   1. A.$10!-1$
   2. B.$11!+1$
   3. C.$10!+1$
   4. D.$11!-1$
   Show answer

   Answer: D

3. Q82021 · 14 Nov 2021

   If p and q are the non-zero roots of the equation $x^2+px+q=0$, then how many possible values can q have?

   1. A.Nil
   2. B.One
   3. C.Two
   4. D.Three
   Show answer

   Answer: B

4. Q92021 · 14 Nov 2021
   
   1. A.$\Delta$
   2. B.$7\Delta$
   3. C.$72\Delta$
   4. D.$-72\Delta$
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   Answer: D

5. Q162021 · 14 Nov 2021

   If $\sin \theta$ and $\cos \theta$ are the roots of the equation $a{x}^2+bx+c=0$, then which one of the following is correct?

   1. A.$a^2+b^2-2ac=0$
   2. B.$-a^2+b^2+2ac=0$
   3. C.$a^2-b^2+2ac=0$
   4. D.$a^2+b^2+2ac=0$
   Show answer

   Answer: C

6. Q262021 · 14 Nov 2021

   Consider all the real roots of the equation $x^4-10x^2+9=0$. What is the sum of the absolute values of the roots?

   1. A.4
   2. B.6
   3. C.8
   4. D.10
   Show answer

   Answer: C

7. Q452021 · 14 Nov 2021

   If the roots of the equation $4x^2-(5k+1)x+5k=0$ differ by unity, then which one of the following is a possible value of k?

   1. A.-3
   2. B.-1
   3. C.$-\frac{1}{5}$
   4. D.$-\frac{3}{5}$
   Show answer

   Answer: C

8. Q462021 · 14 Nov 2021

   Consider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?

   1. A.240
   2. B.180
   3. C.120
   4. D.60
   Show answer

   Answer: A

9. Q272021 · 18 Apr 2021

   If $\alpha$ and $\beta$ are the roots of the equation $4x^2+2x-1=0$, then which one of the following is correct?

   1. A.$\beta =-2{\alpha }^2-2\alpha$
   2. B.$\beta =4{\alpha }^3-3\alpha$
   3. C.$\beta ={\alpha }^2-3\alpha$
   4. D.$\beta =-2{\alpha }^2+2\alpha$
   Show answer

   Answer: B

10. Q282021 · 18 Apr 2021

    If one root of $5x^2+26x+k=0$ is reciprocal of the other, then what is the value of $k$?

    1. A.2
    2. B.3
    3. C.5
    4. D.8
    Show answer

    Answer: C

11. Q362021 · 18 Apr 2021

    The equation ${\sin }^{-1}x-{\cos }^{-1}x=\frac{\pi }{6}$ has

    1. A.no solution
    2. B.unique solution
    3. C.two solutions
    4. D.infinite number of solutions
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    Answer: B

12. Q532021 · 18 Apr 2021

    If the roots of the quadratic equation $x^2+2x+k=0$ are real, then

    1. A.$k<0$
    2. B.$k\le 0$
    3. C.$k<1$
    4. D.$k\le 1$
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    Answer: D

13. Q542021 · 18 Apr 2021

    If n = 100!, then what is the value of the following?

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

    Answer: B

14. Q682021 · 18 Apr 2021

    If k is one of the roots of the equation x(x + 1) + 1 = 0, then what is its other root?

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