Quadratic Equations · NDA previous year questions

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2017 8 questions

Q132017 · 10 Sept 2017
The roots of the equation $(q - r) x^{2} + (r - p) x + (p - q) = 0$ are
1. A. $(r - p) / (q - r), 1/2$
2. B. $(p - q) / (q - r), 1$
3. C. $(q - r) / (p - q), 1$
4. D. $(r - p) / (p - q), 1/2$
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Answer: B
Q142017 · 10 Sept 2017
The sum of all real roots of the equation $∣ x - 3 ∣^{2} + ∣ x - 3∣ - 2 = 0$ is
1. A.2
2. B.3
3. C.4
4. D.6
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Answer: D
Q162017 · 10 Sept 2017
If $α$ and $β$ are the roots of the equation $3 x^{2} + 2 x + 1 = 0$ , then the equation whose roots are $α + β^{- 1}$ and $β + α^{- 1}$ is
1. A. $3 x^{2} + 8 x + 16 = 0$
2. B. $3 x^{2} - 8 x - 16 = 0$
3. C. $3 x^{2} + 8 x - 16 = 0$
4. D. $x^{2} + 8 x + 16 = 0$
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Answer: A
Q172017 · 10 Sept 2017
In $△ P QR$ , $∠ R = \frac{π}{2}$ . If $tan (\frac{P}{2})$ and $tan (\frac{Q}{2})$ are the roots of the equation $a x^{2} + b x + c = 0$ , then which one of the following is correct?
1. A. $a = b + c$
2. B. $b = c + a$
3. C. $c = a + b$
4. D. $b = c$
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Answer: C
Q82017 · 23 Apr 2017
The number of roots of the equation $z^{2} = 2 \overset{z}{ˉ}$ is
1. A.2
2. B.3
3. C.4
4. D.zero
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Answer: C
Q142017 · 23 Apr 2017
If the difference between the roots of the equation $x^{2} + k x + 1 = 0$ is strictly less than $5$ , where $∣ k ∣ \geq 2$ , then $k$ can be any element of the interval
1. A. $(- 3, - 2] \cup [2, 3)$
2. B. $(- 3, 3)$
3. C. $[- 3, - 2] \cup [2, 3]$
4. D.None of the above
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Answer: A
Q162017 · 23 Apr 2017
If $cot α$ and $cot β$ are the roots of the equation $x^{2} + b x + c = 0$ with $b \neq = 0$ , then the value of $cot (α + β)$ is
1. A. $\frac{c - 1}{b}$
2. B. $\frac{1 - c}{b}$
3. C. $\frac{b}{c - 1}$
4. D. $\frac{b}{1 - c}$
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Answer: B
Q1162017 · 23 Apr 2017
If the roots of the equation $x^{2} + p x + q = 0$ are in the same ratio as those of the equation $x^{2} + l x + m = 0$ , then which one of the following is correct?
1. A. $p^{2} m = l^{2} q$
2. B. $m^{2} p = l^{2} q$
3. C. $m^{2} p = q^{2} l$
4. D. $m^{2} p^{2} = l^{2} q$
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Answer: A