Quadratic Equations · NDA previous year questions

172 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2019 18 questions

Q172019 · 17 Nov 2019
If $p$ and $q$ are the roots of the equation $x^{2} - 30 x + 221 = 0$ , what is the value of $p^{3} + q^{3}$ ?
1. A.7010
2. B.7110
3. C.7210
4. D.7240
Show answer
Answer: B
Q182019 · 17 Nov 2019
Consider the following statements in respect of the quadratic equation $4 (x - p) (x - q) - r^{2} = 0$ , where $p, q$ and $r$ are real numbers: 1. The roots are real 2. The roots are equal if $p = q$ and $r = 0$ 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
Show answer
Answer: C
Q192019 · 17 Nov 2019
How many real roots does the equation $x^{2} + 3∣ x ∣ + 2 = 0$ have?
1. A.Zero
2. B.One
3. C.Two
4. D.Four
Show answer
Answer: A
Q202019 · 17 Nov 2019
What is the solution of $x \leq 4$ , $y \geq 0$ and $x \leq - 4$ , $y \leq 0$ ?
1. A. $x \geq - 4$ , $y \leq 0$
2. B. $x \leq 4$ , $y \geq 0$
3. C. $x \leq - 4$ , $y = 0$
4. D. $x \geq - 4$ , $y = 0$
Show answer
Answer: C
Q212019 · 17 Nov 2019
If $α$ and $β$ are the roots of $x^{2} + x + 1 = 0$ , then what is $\sum_{j = 0}^{3} (α^{j} + β^{j})$ equal to?
1. A.8
2. B.6
3. C.4
4. D.2
Show answer
Answer: D
Q702019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function $f (x) = g (x) + h (x)$ where $g (x) = sin (\frac{x}{4})$ and $h (x) = cos (\frac{4 x}{5})$ What is the period of the function $g (x)$ ? Let $f (x) = x^{2} + 2 x - 5$ and $g (x) = 5 x + 30$ What are the roots of the equation $g [f (x)] = 0$ ?
1. A. $1, - 1$
2. B. $- 1, - 1$
3. C. $1, 1$
4. D. $0, 1$
Show answer
Answer: B
Q92019 · 21 Apr 2019
The common roots of the equations $z^{3} + 2 z^{2} + 2 z + 1 = 0$ and $z^{2017} + z^{2018} + 1 = 0$ are
1. A. $- 1, ω$
2. B. $1, ω^{2}$
3. C. $- 1, ω^{2}$
4. D. $ω, ω^{2}$
Show answer
Answer: D
Q162019 · 21 Apr 2019
What are the roots of the equation $∣ x^{2} - x - 6∣ = x + 2$ ?
1. A. $- 2, 1, 4$
2. B. $0, 2, 4$
3. C. $0, 1, 4$
4. D. $- 2, 2, 4$
Show answer
Answer: D
Q172019 · 21 Apr 2019
The equation $p x^{2} + q x + r = 0$ (where p, q, r, all are positive) has distinct real roots a and b. Which one of the following is correct?
1. A. $a > 0, b > 0$
2. B. $a < 0, b < 0$
3. C. $a > 0, b < 0$
4. D. $a < 0, b > 0$
Show answer
Answer: B
Q182019 · 21 Apr 2019
The number of real roots for the equation $x^{2} + 9∣ x ∣ + 20 = 0$ is
1. A.Zero
2. B.One
3. C.Two
4. D.Three
Show answer
Answer: A
Q192019 · 21 Apr 2019
If $C (20, n + 2) = C (20, n - 2)$ , then what is n equal to?
1. A. $8$
2. B. $10$
3. C. $12$
4. D. $16$
Show answer
Answer: B
Q442019 · 21 Apr 2019
If the roots of the equation $x^{2} + p x + q = 0$ are $tan 1 9^{\circ}$ and $tan 2 6^{\circ}$ , then which one of the following is correct?
1. A. $q - p = 1$
2. B. $p - q = 1$
3. C. $p + q = 2$
4. D. $p + q = 3$
Show answer
Answer: A
Q452019 · 21 Apr 2019
What is $(1 + tan α tan β)^{2} + (tan α - tan β)^{2} - sec^{2} α sec^{2} β$ equal to?
1. A.0
2. B.1
3. C.2
4. D.4
Show answer
Answer: A
Q462019 · 21 Apr 2019
If $sin θ + cos θ = 2 cos θ$ , then what is $(cos θ - sin θ)$ equal to?
1. A. $- 2 cos θ$
2. B. $- 2 sin θ$
3. C. $2 sin θ$
4. D. $2 sin θ$
Show answer
Answer: C
Q472019 · 21 Apr 2019
If $sin θ = - \frac{1}{2}$ and $tan θ = \frac{1}{3}$ , then in which quadrant does $θ$ lie?
1. A.First
2. B.Second
3. C.Third
4. D.Fourth
Show answer
Answer: C
Q482019 · 21 Apr 2019
If $p = cosec θ - cot θ$ and $q = (cosec θ + cot θ)^{- 1}$ , then which one of the following is correct?
1. A. $pq = 1$
2. B. $p = q$
3. C. $p + q = 1$
4. D. $p + q = 0$
Show answer
Answer: B
Q492019 · 21 Apr 2019
What is the value of $sin^{- 1} \frac{4}{5} + sec^{- 1} \frac{5}{4} - \frac{π}{2}$ ?
1. A. $\frac{π}{4}$
2. B. $\frac{π}{2}$
3. C. $π$
4. D.0
Show answer
Answer: D
Q502019 · 21 Apr 2019
If $sin^{- 1} \frac{2 p}{1 + p ^{2}} - cos^{- 1} \frac{1 - q ^{2}}{1 + q ^{2}} = tan^{- 1} \frac{2 x}{1 - x ^{2}}$ , then what is x equal to?
1. A. $\frac{p + q}{1 + pq}$
2. B. $\frac{p - q}{1 + pq}$
3. C. $\frac{pq}{1 + pq}$
4. D. $\frac{p + q}{1 - pq}$
Show answer
Answer: B