Quadratic Equations · NDA previous year questions

172 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2010 9 questions

Q112010 · 22 Aug 2010
If the roots of the equation $(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0$ are equal, then which one of the following is correct?
1. A. $2 b = a + c$
2. B. $b^{2} = a c$
3. C. $b + c = 2 a$
4. D. $b = a c$
Show answer
Answer: B
Q182010 · 22 Aug 2010
If $α$ and $β$ are the roots of the equation $x^{2} - 2 x + 4 = 0$ , then what is the value of $α^{3} + β^{3}$ ?
1. A.16
2. B.-16
3. C.8
4. D.-8
Show answer
Answer: B
Q192010 · 22 Aug 2010
What is the value of $(- 1 + i 3)^{48}$ ?
1. A.1
2. B.2
3. C. $2^{24}$
4. D. $2^{48}$
Show answer
Answer: D
Q232010 · 22 Aug 2010
Which of the following are the two roots of the equation $(x^{2} + 2)^{2} + 8 x^{2} = 6 x (x^{2} + 2)$ ?
1. A. $1 \pm i$
2. B. $2 \pm i$
3. C. $1 \pm 2$
4. D. $2 \pm i 2$
Show answer
Answer: A
Q252010 · 22 Aug 2010
If $α$ and $β$ are the roots of the equation $x^{2} + x + 1 = 0$ , then which of the following are the roots of the equation $x^{2} - x + 1 = 0$ ?
1. A. $α^{7}$ and $β^{13}$
2. B. $α^{13}$ and $β^{7}$
3. C. $α^{20}$ and $β^{20}$
4. D.None of the above
Show answer
Answer: D
Q142010 · 18 Apr 2010
If the product of the roots of the equation $x^{2} - 5 x + k = 15$ is $- 3$ , then what is the value of k?
1. A.12
2. B.15
3. C.16
4. D.18
Show answer
Answer: A
Q292010 · 18 Apr 2010
If p and q are the roots of the equation $x^{2} - p x + q = 0$ , then what are the values of p and q respectively?
1. A.1, 0
2. B.0, 1
3. C. $- 2, 0$
4. D. $- 2, 1$
Show answer
Answer: A, C
Q1052010 · 18 Apr 2010
If $α, β$ are the roots of the quadratic equation $x^{2} - x + 1 = 0$ , then which one of the following is correct?
1. A. $(α^{4} - β^{4})$ is real
2. B. $2 (α^{5} + β^{5}) = (α β)^{5}$
3. C. $(α^{6} - β^{6}) = 0$
4. D. $(α^{8} + β^{8}) = (α β)^{8}$
Show answer
Answer: C
Q1062010 · 18 Apr 2010
What is the value of $3 cosec 2 0^{\circ} - sec 2 0^{\circ}$ ?
1. A.1/4
2. B.4
3. C.2
4. D.1
Show answer
Answer: B