Quadratic Equations · NDA previous year questions

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2016 10 questions

Q202016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : Let $α$ and $β$ be the roots of the equation $x^{2} - (1 - 2 a^{2}) x + (1 - 2 a^{2}) = 0$ . Under what condition does the above equation have real roots ?
1. A. $a^{2} < \frac{1}{2}$
2. B. $a^{2} > \frac{1}{2}$
3. C. $a^{2} \leq \frac{1}{2}$
4. D. $a^{2} \geq \frac{1}{2}$
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Answer: D
Q212016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : Let $α$ and $β$ be the roots of the equation $x^{2} - (1 - 2 a^{2}) x + (1 - 2 a^{2}) = 0$ . Under what condition is $\frac{1}{α ^{2}} + \frac{1}{β ^{2}} < 1$ ?
1. A. $a^{2} < \frac{1}{2}$
2. B. $a^{2} > \frac{1}{2}$
3. C. $a^{2} > 1$
4. D. $a^{2} \in (\frac{1}{3}, \frac{1}{2})$ only
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Answer: A
Q222016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : $2 x^{2} + 3 x - α = 0$ has roots $- 2$ and $β$ while the equation $x^{2} - 3 m x + 2 m^{2} = 0$ has both roots positive, where $α > 0$ and $β > 0$ . What is the value of $α$ ?
1. A. $\frac{1}{2}$
2. B.1
3. C.2
4. D.4
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Answer: C
Q1182016 · 18 Sept 2016
If both the roots of the equation $x^{2} - 2 k x + k^{2} - 4 = 0$ lie between $- 3$ and 5, then which one of the following is correct ?
1. A. $- 2 < k < 2$
2. B. $- 5 < k < 3$
3. C. $- 3 < k < 5$
4. D. $- 1 < k < 3$
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Answer: D
Q102016 · 17 Apr 2016
For the next two (2) items that follow : Let $α$ and $β$ ( $α < β$ ) be the roots of the equation $x^{2} + b x + c = 0$ , where $b > 0$ and $c < 0$ . Consider the following : 1. $β < - α$ 2. $β < ∣ α ∣$ Which of the above 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: C
Q112016 · 17 Apr 2016
For the next two (2) items that follow : Let $α$ and $β$ ( $α < β$ ) be the roots of the equation $x^{2} + b x + c = 0$ , where $b > 0$ and $c < 0$ . Consider the following : 1. $α + β + α β > 0$ 2. $α^{2} β + β^{2} α > 0$ Which of the above 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
Q122016 · 17 Apr 2016
If $x^{2} - p x + 4 > 0$ for all real values of $x$ , then which one of the following is correct?
1. A. $∣ p ∣ < 4$
2. B. $∣ p ∣ \leq 4$
3. C. $∣ p ∣ > 4$
4. D. $∣ p ∣ \geq 4$
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Answer: A
Q132016 · 17 Apr 2016
If one root of the equation $(l - m) x^{2} + l x + 1 = 0$ is double the other and $l$ is real, then what is the greatest value of $m$ ?
1. A. $- \frac{9}{8}$
2. B. $\frac{9}{8}$
3. C. $- \frac{8}{9}$
4. D. $\frac{8}{9}$
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Answer: B
Q252016 · 17 Apr 2016
For the next two (2) items that follow : Given that $tan α$ and $tan β$ are the roots of the equation $x^{2} + b x + c = 0$ with $b \neq = 0$ . What is $tan (α + β)$ equal to?
1. A. $b (c - 1)$
2. B. $c (b - 1)$
3. C. $c (b - 1)^{- 1}$
4. D. $b (c - 1)^{- 1}$
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Answer: D
Q262016 · 17 Apr 2016
For the next two (2) items that follow : Given that $tan α$ and $tan β$ are the roots of the equation $x^{2} + b x + c = 0$ with $b \neq = 0$ . What is $sin (α + β) sec α sec β$ equal to?
1. A. $b$
2. B. $- b$
3. C. $c$
4. D. $- c$
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Answer: B