Quadratic Equations · NDA previous year questions

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2011 20 questions

Q132011 · 21 Aug 2011
The equation $x^{2} - 4 x + 29 = 0$ has one root $2 + 5 i$ . What is the other root? $(i = - 1)$
1. A.2
2. B.5
3. C. $2 + 5 i$
4. D. $2 - 5 i$
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Answer: D
Q142011 · 21 Aug 2011
What are the square roots of $- 2 i$ ? $(i = - 1)$
1. A. $\pm (1 + i)$
2. B. $\pm (1 - i)$
3. C. $\pm i$
4. D. $\pm 1$
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Answer: B
Q152011 · 21 Aug 2011
What is the area between the curve $y = cos 3 x, 0 \leq x \leq \frac{π}{6}$ and the co-ordinate axes?
1. A.1 square unit
2. B. $\frac{1}{2}$ square unit
3. C. $\frac{1}{3}$ square unit
4. D. $\frac{1}{4}$ square unit
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Answer: C
Q272011 · 21 Aug 2011
1. A. $α$
2. B. $β$
3. C. $γ$
4. D. $α, β$ and $γ$
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Answer: A
Q352011 · 21 Aug 2011
Let $α, β$ be the roots of the equation $(x - a) (x - b) = c, c \neq = 0$ . Then the roots of the equation $(x - α) (x - β) + c = 0$ are
1. A. $a, c$
2. B. $b, c$
3. C. $a, b$
4. D. $a + b, a + c$
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Answer: C
Q362011 · 21 Aug 2011
If the equations $x^{2} - p x + q = 0$ and $x^{2} - a x + b = 0$ have a common root and the roots of the second equation are equal, then which one of the following is correct?
1. A. $a q = 2 (b + p)$
2. B. $a q = b + p$
3. C. $a p = 2 (b + q)$
4. D. $a p = b + q$
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Answer: C
Q532011 · 21 Aug 2011
Let $α$ and $β$ be the roots of the equation $x^{2} + x + 1 = 0$ . The equation whose roots are $α^{19}$ and $β^{7}$ is
1. A. $x^{2} - x - 1 = 0$
2. B. $x^{2} - x + 1 = 0$
3. C. $x^{2} + x - 1 = 0$
4. D. $x^{2} + x + 1 = 0$
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Answer: D
Q1002011 · 21 Aug 2011
If one of the roots of the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ is 1, what is the second root?
1. A. $- \frac{b ( c - a )}{a ( b - c )}$
2. B. $\frac{b ( c - a )}{a ( b - c )}$
3. C. $\frac{c ( a - b )}{a ( b - c )}$
4. D. $- \frac{c ( a - b )}{a ( b - c )}$
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Answer: C
Q1012011 · 21 Aug 2011
What are the roots of the equation $2 (y + 2)^{2} - 5 (y + 2) = 12$ ?
1. A. $- 7/2, 2$
2. B. $- 3/2, 4$
3. C. $- 5/3, 3$
4. D. $3/2, 4$
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Answer: A
Q1022011 · 21 Aug 2011
What is the value of $lo g_{2} (lo g_{3} 81)$ ?
1. A.2
2. B.3
3. C.4
4. D.9
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Answer: A
Q1032011 · 21 Aug 2011
If the roots of the equation $3 x^{2} - 5 x + q = 0$ are equal, then what is the value of q?
1. A.2
2. B. $5/12$
3. C. $12/25$
4. D. $25/12$
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Answer: D
Q12011 · 17 Apr 2011
If 3 is the root of the equation $x^{2} - 8 x + k = 0$ , then what is the value of $k$ ?
1. A. $- 15$
2. B.9
3. C.15
4. D.24
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Answer: C
Q132011 · 17 Apr 2011
If sum of squares of the roots of the equation $x^{2} + k x - b = 0$ is $2 b$ , what is $k$ equal to?
1. A.1
2. B. $b$
3. C. $- b$
4. D.0
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Answer: D
Q142011 · 17 Apr 2011
If one root of the equation $a x^{2} + b x + c = 0, a \neq = 0$ is reciprocal of the other root, then which one of the following is correct?
1. A. $a = c$
2. B. $b = c$
3. C. $a = - c$
4. D. $b = 0$
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Answer: A
Q352011 · 17 Apr 2011
If 5 and 7 are the roots of the equation $x 75 4 x 8 57 x = 0$ then what is the third root?
1. A. $- 12$
2. B.9
3. C.13
4. D.14
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Answer: A
Q472011 · 17 Apr 2011
What is the sum of the roots of the equation $(2 - 3) x^{2} - (7 - 43) x + (2 + 3) = 0$ ?
1. A. $2 - 3$
2. B. $2 + 3$
3. C. $7 - 43$
4. D.4
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Answer: A
Q492011 · 17 Apr 2011
One of the roots of the quadratic equation $a x^{2} + b x + c = 0, a \neq = 0$ is positive and the other root is negative. The condition for this to happen is
1. A. $a > 0, b > 0, c > 0$
2. B. $a > 0, b < 0, c > 0$
3. C. $a < 0, b > 0, c < 0$
4. D. $a < 0, c > 0$
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Answer: D
Q582011 · 17 Apr 2011
What is the condition that one root of the equation $a x^{2} + b x + c = 0, a \neq = 0$ should be double the other?
1. A. $2 a^{2} = 9 b c$
2. B. $2 b^{2} = 9 a c$
3. C. $2 c^{2} = 9 ab$
4. D.None of the above
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Answer: B
Q622011 · 17 Apr 2011
If $α$ and $β$ are the roots of the equation $4 x^{2} + 3 x + 7 = 0$ , then what is the value of $(α^{- 2} + β^{- 2})$ ?
1. A. $47/49$
2. B. $49/47$
3. C. $- 47/49$
4. D. $- 49/47$
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Answer: C
Q632011 · 17 Apr 2011
What is the equation of the line passing through $(2, - 3)$ and parallel to $y$ -axis?
1. A. $y = - 3$
2. B. $y = 2$
3. C. $x = 2$
4. D. $x = - 3$
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Answer: C