Quadratic Equations · NDA previous year questions

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2012 8 questions

Q12012 · 19 Aug 2012
If the roots of a quadratic equation are $m + n$ and $m - n$ , then the quadratic equation will be:
1. A. $x^{2} + 2 m x + m^{2} - mn + n^{2} = 0$
2. B. $x^{2} + 2 m x + (m - n)^{2} = 0$
3. C. $x^{2} - 2 m x + m^{2} - n^{2} = 0$
4. D. $x^{2} + 2 m x + m^{2} - n^{2} = 0$
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Answer: C
Q22012 · 19 Aug 2012
If $α, β$ are the roots of $x^{2} + p x - q = 0$ and $γ, δ$ are the roots of $x^{2} - p x + r = 0$ then what is $(β + γ) (β + δ)$ equal to?
1. A. $p + r$
2. B. $p + q$
3. C. $q + r$
4. D. $p - q$
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Answer: C
Q32012 · 19 Aug 2012
Consider the following statements: 1. The sum of cubes of first 20 natural numbers is 44400. 2. The sum of squares of first 20 natural numbers is 2870. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: B
Q42012 · 19 Aug 2012
Consider the following statements: 1. $(ω^{10} + 1)^{7} + ω = 0$ 2. $(ω^{105} + 1)^{10} = p^{10}$ for some prime number p where $ω \neq = 1$ is a cubic root of unity. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: B
Q82012 · 19 Aug 2012
If the roots of the quadratic equation $3 x^{2} - 5 x + p = 0$ are real and unequal, then which one of the following is correct?
1. A. $p = 25/12$
2. B. $p < 25/12$
3. C. $p > 25/12$
4. D. $p \leq 25/12$
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Answer: B
Q12012 · 15 Apr 2012
What is the sum of the squares of the roots of the equation $x^{2} + 2 x - 143 = 0$ ?
1. A.170
2. B.180
3. C.190
4. D.290
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Answer: D
Q582012 · 15 Apr 2012
If one of the roots of the equation $x^{2} + a x - b = 0$ is 1, then what is $(a - b)$ equal to?
1. A. $- 1$
2. B.1
3. C.2
4. D. $- 2$
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Answer: A
Q592012 · 15 Apr 2012
If $α$ and $β$ are the roots of the equation $x^{2} - q (1 + x) - r = 0$ , then what is $(1 + α) (1 + β)$ equal to?
1. A. $1 - r$
2. B. $q - r$
3. C. $1 + r$
4. D. $q + r$
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Answer: A