Trigonometry · NDA previous year questions

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2009 32 questions

Q272009 · 30 Aug 2009
What is the modulus of $\frac{1 + 2 i}{1 - ( 1 - i ) ^{2}}$ equal to?
1. A.5
2. B.4
3. C.3
4. D.1
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Answer: D
Q282009 · 30 Aug 2009
What is the value of $(- - 1)^{4 n + 3} + (i^{41} + i^{- 257})^{9}$ , where $n \in N$ ?
1. A.0
2. B.1
3. C. $i$
4. D. $- i$
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Answer: C
Q292009 · 30 Aug 2009
If $x = (1101)_{2}$ and $y = (110)_{2}$ , then what is the value of $x^{2} - y^{2}$ ?
1. A. $(1000101)_{2}$
2. B. $(10000101)_{2}$
3. C. $(10001101)_{2}$
4. D. $(10010101)_{2}$
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Answer: B
Q352009 · 30 Aug 2009
The equation $x - 2 (x - 1)^{- 1} = 1 - 2 (x - 1)^{- 1}$ has
1. A.no roots
2. B.one root
3. C.two equal roots
4. D.infinite roots
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Answer: A
Q492009 · 30 Aug 2009
1. A. $a sec x + b tan x + c$
2. B. $a tan x + b sec x + c$
3. C. $a cot x + b cosec x + c$
4. D. $a cosec x + b cot x + c$
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Answer: D
Q502009 · 30 Aug 2009
If $x = ln t$ and $y = t^{2} - 1$ , then what is $\frac{d ^{2} y}{d x ^{2}}$ at $t = 1$ equal to ?
1. A.2
2. B.3
3. C. $- 4$
4. D.4
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Answer: D
Q772009 · 30 Aug 2009
If $cot θ = 2 cos θ$ , where $(π /2) < θ < π$ , then what is the value of $θ$ ?
1. A. $5 π /6$
2. B. $2 π /3$
3. C. $3 π /4$
4. D. $11 π /12$
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Answer: A
Q782009 · 30 Aug 2009
If $cot θ = 5/12$ and $θ$ lies in the third quadrant, then what is $(2 sin θ + 3 cos θ)$ equal to ?
1. A. $- 4$
2. B. $- p^{2}$ for some odd prime $p$
3. C. $(- q / p)$ where $p$ is an odd prime and $q$ a positive integer with $(q / p)$ not an integer.
4. D. $- p$ for some odd prime $p$ .
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Answer: D
Q792009 · 30 Aug 2009
What is the value of $cos (π /9) + cos (π /3) + cos (5 π /9) + cos (7 π /9)$ ?
1. A.1
2. B. $- 1$
3. C. $- 1/2$
4. D. $1/2$
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Answer: D
Q802009 · 30 Aug 2009
If in a triangle $A B C$ , $cos B = \frac{s i n A}{2 s i n C}$ , then the triangle is :
1. A.Isosceles triangle
2. B.Equilateral triangle
3. C.Right angled triangle
4. D.Scalene triangle
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Answer: A
Q812009 · 30 Aug 2009
During a certain plan period a state out of a total budget of Rs. 1400 crores had spent 28% of the total amount on Agriculture, 35% on Industry, 12% on Energy and 8% on Social Welfare, 105 crores on Education and the balance amount on Transport. What is the amount spent on Transport in crores of rupees ?
1. A.123
2. B.145
3. C.165
4. D.133
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Answer: D
Q1022009 · 30 Aug 2009
Looking from the top of a $20 m$ high building, the angle of elevation of the top of a tower is $6 0^{\circ}$ and the angle of depression of its bottom is $3 0^{\circ}$ . What is the height of the tower ?
1. A. $50 m$
2. B. $60 m$
3. C. $70 m$
4. D. $80 m$
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Answer: D
Q1032009 · 30 Aug 2009
What is the value of $3 cosec 2 0^{\circ} - sec 2 0^{\circ}$ ?
1. A.4
2. B.3
3. C.2
4. D.1
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Answer: A
Q1042009 · 30 Aug 2009
Match List-I with List-II and select the correct answer using the code given below the lists : | List-I | List-II | | --- | --- | | A. $tan 1 5^{\circ}$ | 1. $- 2 - 3$ | | B. $tan 7 5^{\circ}$ | 2. $2 + 3$ | | C. $tan 10 5^{\circ}$ | 3. $- 2 + 3$ | | | 4. $2 - 3$ | Code : | | A | B | C | | --- | --- | --- | --- | | (a) | 4 | 1 | 2 | | (b) | 4 | 2 | 1 | | (c) | 3 | 2 | 1 | | (d) | 2 | 1 | 4 |
1. A.4 1 2
2. B.4 2 1
3. C.3 2 1
4. D.2 1 4
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Answer: B
Q1052009 · 30 Aug 2009
In a triangle $A B C$ , $a + b = 3 (1 + 3) cm$ and $a - b = 3 (1 - 3) cm$ . If angle $A$ is $3 0^{\circ}$ , then what is the angle $B$ ?
1. A. $12 0^{\circ}$
2. B. $9 0^{\circ}$
3. C. $7 5^{\circ}$
4. D. $6 0^{\circ}$
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Answer: A, D
Q1062009 · 30 Aug 2009
If $N_{a} = {a x ∣ x \in N}$ , then what is $N_{12} \cap N_{8}$ equal to ?
1. A. $N_{12}$
2. B. $N_{20}$
3. C. $N_{24}$
4. D. $N_{48}$
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Answer: C
Q552009 · 19 Apr 2009
One radian is approximately equal to which one of the following?
1. A. $9 0^{\circ}$
2. B. $18 0^{\circ}$
3. C. $5 7^{\circ}$
4. D. $4 7^{\circ}$
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Answer: C
Q562009 · 19 Apr 2009
If $cot (x + y) = 1/ 3$ and $cot (x - y) = 3$ , then what are the smallest positive values of $x$ and $y$ respectively?
1. A. $4 5^{\circ}, 3 0^{\circ}$
2. B. $3 0^{\circ}, 4 5^{\circ}$
3. C. $1 5^{\circ}, 6 0^{\circ}$
4. D. $4 5^{\circ}, 1 5^{\circ}$
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Answer: D
Q572009 · 19 Apr 2009
If $sin A = 1/ 5, cos B = 3/ 10$ ; $A, B$ being positive acute angles, then what is $(A + B)$ equal to?
1. A. $π /6$
2. B. $π /4$
3. C. $π /3$
4. D. $π /2$
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Answer: B
Q582009 · 19 Apr 2009
If $sin^{- 1} (\frac{2 a}{1 + a ^{2}}) - cos^{- 1} (\frac{1 - b ^{2}}{1 + b ^{2}}) = tan^{- 1} (\frac{2 x}{1 - x ^{2}})$ , then what is the value of $x$ ?
1. A. $a / b$
2. B. $ab$
3. C. $b / a$
4. D. $\frac{a - b}{1 + ab}$
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Answer: D
Q592009 · 19 Apr 2009
$x = sin θ cos θ$ and $y = sin θ + cos θ$ are satisfied by which one of the following equations?
1. A. $y^{2} - 2 x = 1$
2. B. $y^{2} + 2 x = 1$
3. C. $y^{2} - 2 x = - 1$
4. D. $y^{2} + 2 x = - 1$
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Answer: A
Q602009 · 19 Apr 2009
A man observes the elevation of a balloon to be $3 0^{\circ}$ . He then walks $1 km$ towards the balloon and finds that the elevation is $6 0^{\circ}$ . What is the height of the balloon?
1. A. $1/2 km$
2. B. $3 /2 km$
3. C. $1/3 km$
4. D. $1 km$
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Answer: B
Q612009 · 19 Apr 2009
If $sin^{4} x - cos^{4} x = p$ , then which one of the following is correct?
1. A. $p = 1$
2. B. $p = 0$
3. C. $∣ p ∣ > 1$
4. D. $∣ p ∣ \leq 1$
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Answer: D
Q622009 · 19 Apr 2009
If $cos θ < sin θ$ and $θ$ lies in the first quadrant, then which one of the following is correct?
1. A. $0 < θ < π /4 only$
2. B. $π /4 < θ < π /2$
3. C. $0 < θ < π /3$
4. D. $π /3 < θ < π /2$
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Answer: B
Q632009 · 19 Apr 2009
The angle of elevation from a point on the bank of a river of the top of a temple on the other bank is $4 5^{\circ}$ . Retreating $50 m$ , the observer finds the new angle of elevation as $3 0^{\circ}$ . What is the width of the river?
1. A. $50 m$
2. B. $503 m$
3. C. $50/ (3 - 1) m$
4. D. $100 m$
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Answer: C