Quadratic Equations · NDA previous year questions

2023 11 questions

1. Q372023 · 3 Sept 2023

   Consider the following for the next items that follow: A quadratic equation is given by $(a+b)x^2-(a+b+c)x+k=0$, where a, b, c are real. If $k=\frac{c}{2}$, $(c\ne 0)$, then the roots of the equation are : If $k=c$, then the roots of the equation are:

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

   Answer: C

2. Q382023 · 3 Sept 2023

   Consider the following for the next items that follow: Let $(1+x{)}^n=1+T_{1}x+T_2{x}^2+T_3{x}^3+\cdots +T_n{x}^n$. What is $T_1+2T_2+3T_3+\cdots +n{T}_n$ equal to ?

   1. A.0
   2. B.1
   3. C.$2^n$
   4. D.$n{2}^{n-1}$
   Show answer

   Answer: D

3. Q392023 · 3 Sept 2023

   What is $1-T_1+2T_2-3T_3+\cdots +(-1{)}^{n}n{T}_n$ equal to ?

   1. A.0
   2. B.$-2^{n-1}$
   3. C.$n{2}^{n-1}$
   4. D.1
   Show answer

   Answer: D

4. Q402023 · 3 Sept 2023

   Consider the following for the next items that follow: Let $(1+x{)}^n=1+T_{1}x+T_2{x}^2+T_3{x}^3+\cdots +T_n{x}^n$. What is $T_1+T_2+T_3+\cdots +T_n$ equal to ?

   1. A.$2^n$
   2. B.$2^n-1$
   3. C.$2^{n-1}$
   4. D.$2^n+1$
   Show answer

   Answer: B

5. Q412023 · 3 Sept 2023

   Consider the following for the next items that follow: Let $f(x)=x^2-1$ and $gof(x)=x-\sqrt{x}+1$. Which one of the following is a possible expression for g(x)?

   1. A.$\sqrt{x+1}-\sqrt[4]{x+1}$
   2. B.$\sqrt{x+1}-\sqrt[4]{x+1}+1$
   3. C.$\sqrt{x+1}+\sqrt[4]{x+1}$
   4. D.$x+1-\sqrt{x+1}+1$
   Show answer

   Answer: B

6. Q422023 · 3 Sept 2023

   Consider the following for the next items that follow: Let $f(x)=x^2-1$ and $gof(x)=x-\sqrt{x}+1$. What is g(15) equal to ?

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

   Answer: C

7. Q102023 · 16 Apr 2023
   
   1. A.$a+b+c$
   2. B.$a-b+c$
   3. C.$a+b-c$
   4. D.$a-b-c$
   Show answer

   Answer: B

8. Q112023 · 16 Apr 2023

   If $2-i\sqrt{3}$ where $i=\sqrt{-1}$ is a root of the equation $x^2+ax+b=0$, then what is the value of $(a+b)$?

   1. A.-11
   2. B.-3
   3. C.0
   4. D.3
   Show answer

   Answer: D

9. Q232023 · 16 Apr 2023
   
   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

10. Q492023 · 16 Apr 2023

    Consider the following for the next two (02) items that follow : A quadratic equation is given by $(3+2\sqrt{2})x^2-(4+2\sqrt{3})x+(8+4\sqrt{3})=0$ What is the HM of the roots of the equation ?

    1. A.2
    2. B.4
    3. C.$2\sqrt{2}$
    4. D.$2\sqrt{3}$
    Show answer

    Answer: B

11. Q502023 · 16 Apr 2023
    
    1. A.√2(√6 - √3 + √2 - 1)
    2. B.√2(√6 + √3 - √2 - 1)
    3. C.(√6 - √3 + √2 - 1)
    4. D.(√6 + √3 + √2 - 1)
    Show answer

    Answer: A