Quadratic Equations · NDA previous year questions

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2013 16 questions

Q12013 · 11 Aug 2013
What is the positive square root of $7 + 43$ ?
1. A. $3 - 1$
2. B. $3 + 1$
3. C. $3 - 2$
4. D. $3 + 2$
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Answer: D
Q22013 · 11 Aug 2013
If $A = {1, 2}, B = {2, 3}$ and $C = {3, 4}$ , then what is the cardinality of $(A \times B) \cap (A \times C)$ ?
1. A.8
2. B.6
3. C.2
4. D.1
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Answer: C
Q32013 · 11 Aug 2013
If $α, β$ are the roots of the equation $x^{2} + x + 2 = 0$ , then what is $\frac{α ^{10} + β ^{10}}{α ^{- 10} + β ^{- 10}}$ equal to?
1. A.4096
2. B.2048
3. C.1024
4. D.512
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Answer: C
Q42013 · 11 Aug 2013
If $a$ and $b$ are rational and $b$ is not perfect square, then the quadratic equation with rational coefficients whose one root is $3 a + b$ is
1. A. $x^{2} - 6 a x + 9 a^{2} - b = 0$
2. B. $3 a x^{2} + x - b = 0$
3. C. $x^{2} + 3 a x + b = 0$
4. D. $b x^{2} + x - 3 a = 0$
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Answer: A
Q132013 · 11 Aug 2013
How many real roots does the quadratic equation have?
1. A.One
2. B.Two
3. C.Four
4. D.No real root
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Answer: D
Q352013 · 11 Aug 2013
If $α, β$ are the roots of the equation $a x^{2} + b x + b = 0$ , then what is the value of $\frac{α}{β} + \frac{β}{α} + \frac{b}{a}$ ?
1. A. $- 1$
2. B.0
3. C.1
4. D.2
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Answer: Dropped in the final answer key (full marks to everyone)
Q432013 · 11 Aug 2013
What is the difference in the roots of the equation $x^{2} - 10 x + 9 = 0$ ?
1. A.2
2. B.3
3. C.5
4. D.8
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Answer: D
Q442013 · 11 Aug 2013
If $8 x - 9 y = 20$ and $7 x - 10 y = 9$ , then what is $2 x - y$ equal to?
1. A.10
2. B.11
3. C.12
4. D.13
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Answer: A
Q452013 · 11 Aug 2013
The quadratic equation $x^{2} + b x + 4 = 0$ will have real roots if
1. A. $b \leq - 4$ only
2. B. $b \geq 4$ only
3. C. $- 4 < b < 4$
4. D. $b \leq - 4, b \geq 4$
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Answer: D
Q132013 · 14 Apr 2013
If the sum of the roots of a quadratic equation is 3 and the product is 2, then the equation is
1. A. $2 x^{2} - x + 3 = 0$
2. B. $x^{2} - 3 x + 2 = 0$
3. C. $x^{2} + 3 x + 2 = 0$
4. D. $x^{2} + 3 x - 2 = 0$
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Answer: B
Q142013 · 14 Apr 2013
If $α$ and $β$ are the roots of the equation $x^{2} + b x + c = 0$ , then what is the value of $α^{- 1} + β^{- 1}$ ?
1. A. $- b / c$
2. B. $b / c$
3. C. $c / b$
4. D. $- c / b$
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Answer: A
Q152013 · 14 Apr 2013
The area of a rectangle whose length is five more than twice its width is 75 square unit. The length is
1. A.5 unit
2. B.10 unit
3. C.15 unit
4. D.20 unit
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Answer: C
Q162013 · 14 Apr 2013
What is $- i$ where $i = - 1$ equal to ?
1. A. $\pm \frac{1 - i}{2}$
2. B. $\pm \frac{1 + i}{2}$
3. C. $\pm \frac{1 - i}{2}$
4. D. $\pm \frac{1 + i}{2}$
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Answer: A
Q232013 · 14 Apr 2013
If the roots of a quadratic equation $a x^{2} + b x + c = 0$ are $α$ and $β$ , then the quadratic equation having roots $α^{2}$ and $β^{2}$ is
1. A. $x^{2} - (b^{2} - 2 a c) x + c = 0$
2. B. $a^{2} x^{2} - (b^{2} - 2 a c) x + c = 0$
3. C. $a x^{2} - (b^{2} - 2 a c) x + c^{2} = 0$
4. D. $a^{2} x^{2} - (b^{2} - 2 a c) x + c^{2} = 0$
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Answer: D
Q242013 · 14 Apr 2013
If the roots of the equation $3 a x^{2} + 2 b x + c = 0$ are in the ratio $2 : 3$ , then which one of the following is correct ?
1. A. $8 a c = 25 b$
2. B. $8 a c = 9 b^{2}$
3. C. $8 b^{2} = 9 a c$
4. D. $8 b^{2} = 25 a c$
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Answer: D
Q312013 · 14 Apr 2013
The roots of the equation $t - 1 11 1 t - 1 1 11 t - 1 = 0$ are
1. A.1, 2
2. B. $- 1$ , 2
3. C.1, $- 2$
4. D. $- 1$ , $- 2$
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Answer: B