Coordinate Geometry · NDA previous year questions

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2012 33 questions

Q362012 · 19 Aug 2012
The line making an angle $(- 12 0^{\circ})$ with x-axis is situated in the:
1. A.first quadrant
2. B.second quadrant
3. C.third quadrant
4. D.fourth quadrant
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Answer: C
Q372012 · 19 Aug 2012
The angle subtended at the centre of a circle of radius 3 cm by an arc of length 1 cm is:
1. A. $\frac{3 0 ^{\circ}}{π}$
2. B. $\frac{6 0 ^{\circ}}{π}$
3. C. $6 0^{\circ}$
4. D.None of the above
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Answer: B
Q382012 · 19 Aug 2012
If $sin A = \frac{2}{5}$ and $cos B = \frac{1}{10}$ where A and B are acute angles, then what is A + B equal to?
1. A. $13 5^{\circ}$
2. B. $9 0^{\circ}$
3. C. $7 5^{\circ}$
4. D. $6 0^{\circ}$
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Answer: A
Q392012 · 19 Aug 2012
The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $α$ and $β$ respectively. The height of the hill is:
1. A. $\frac{h c o t β}{c o t β - c o t α}$
2. B. $\frac{h c o t α}{c o t α - c o t β}$
3. C. $\frac{h t a n α}{t a n α - t a n β}$
4. D.None of the above
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Answer: B
Q412012 · 19 Aug 2012
The locus of a point equidistant from three collinear points is:
1. A.a straight line
2. B.a pair of points
3. C.a point
4. D.the null set
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Answer: D
Q422012 · 19 Aug 2012
The equation to the locus of a point which is always equidistant from the points (1, 0) and (0, –2) is:
1. A. $2 x + 4 y + 3 = 0$
2. B. $4 x + 2 y + 3 = 0$
3. C. $2 x + 4 y - 3 = 0$
4. D. $4 x + 2 y - 3 = 0$
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Answer: A
Q432012 · 19 Aug 2012
The points (5, 1), (1, –1) and (11, 4) are:
1. A.collinear
2. B.vertices of right angled triangle
3. C.vertices of equilateral triangle
4. D.vertices of an isosceles triangle
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Answer: A
Q442012 · 19 Aug 2012
What is the perpendicular distance between the parallel lines $3 x + 4 y = 9$ and $9 x + 12 y + 28 = 0$ ?
1. A.7/3 units
2. B.8/3 units
3. C.10/3 units
4. D.11/3 units
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Answer: D
Q452012 · 19 Aug 2012
Let p, q, r, s be the distances from origin of the points (2, 6), (3, 4), (4, 5) and (–2, 5) respectively. Which one of the following is a whole number?
1. A.p
2. B.q
3. C.r
4. D.s
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Answer: B
Q462012 · 19 Aug 2012
From the point (4, 3) a perpendicular is dropped on the x-axis as well as on the y-axis. If the lengths of perpendiculars are p, q respectively, then which one of the following is correct?
1. A.p = q
2. B.3p = 4q
3. C.4p = 3q
4. D.p + q = 5
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Answer: C
Q472012 · 19 Aug 2012
What is the value of $λ$ if the straight line $(2 x + 3 y + 4) + λ (6 x - y + 12) = 0$ is parallel to y-axis?
1. A.3
2. B. $- 6$
3. C.4
4. D. $- 3$
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Answer: A
Q482012 · 19 Aug 2012
The line y = 0 divides the line joining the points (3, –5) and (–4, 7) in the ratio:
1. A.3 : 4
2. B.4 : 5
3. C.5 : 7
4. D.7 : 9
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Answer: C
Q492012 · 19 Aug 2012
The sum of the focal distances of a point on the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1$ is:
1. A.4 units
2. B.6 units
3. C.8 units
4. D.10 units
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Answer: B
Q502012 · 19 Aug 2012
The eccentricity e of an ellipse satisfies the condition:
1. A. $e < 0$
2. B. $0 < e < 1$
3. C. $e = 1$
4. D. $e > 1$
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Answer: B
Q512012 · 19 Aug 2012
The equation of a straight line which makes an angle $4 5^{\circ}$ with the x-axis with y-intercept 101 units is:
1. A. $10 x + 101 y = 1$
2. B. $101 x + y = 1$
3. C. $x + y - 101 = 0$
4. D. $x - y + 101 = 0$
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Answer: D
Q522012 · 19 Aug 2012
If the points $(2, 4)$ , $(2, 6)$ and $(2 + 3, k)$ are the vertices of an equilateral triangle, then what is the value of k?
1. A.6
2. B.5
3. C. $- 3$
4. D.1
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Answer: B
Q532012 · 19 Aug 2012
If the distance between the points $(7, 1, - 3)$ and $(4, 5, λ)$ is 13 units, then what is one of the values of $λ$ ?
1. A.20
2. B.10
3. C.9
4. D.8
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Answer: C
Q172012 · 15 Apr 2012
What is the perimeter of the triangle with vertices $A (- 4, 2)$ , $B (0, - 1)$ and $C (3, 3)$ ?
1. A. $7 + 32$
2. B. $10 + 52$
3. C. $11 + 62$
4. D. $5 + 2$
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Answer: B
Q182012 · 15 Apr 2012
If the mid point between the points $(a + b, a - b)$ and $(- a, b)$ lies on the line $a x + b y = k$ , what is k equal to?
1. A.a/b
2. B.a + b
3. C.ab
4. D.a - b
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Answer: C
Q192012 · 15 Apr 2012
The acute angle which the perpendicular from origin on the line $7 x - 3 y = 4$ makes with the x-axis is
1. A.zero
2. B.positive but not $π /4$
3. C.negative
4. D. $π /4$
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Answer: B
Q202012 · 15 Apr 2012
Out of 500 first year students, 260 passed in the first semester and 210 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters?
1. A.30
2. B.40
3. C.70
4. D.140
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Answer: D
Q282012 · 15 Apr 2012
If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?
1. A. $2/ 3$
2. B. $1/ 3$
3. C. $3 /2$
4. D. $1/ 2$
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Answer: C
Q312012 · 15 Apr 2012
What is the equation of line passing through $(0, 1)$ and making an angle with the y-axis equal to the inclination of the line $x - y = 4$ with x-axis?
1. A. $y = x + 1$
2. B. $x = y + 1$
3. C. $2 x = y + 2$
4. D.None of the above
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Answer: A
Q322012 · 15 Apr 2012
What is $tan (\frac{π}{12})$ equal to?
1. A. $2 - 3$
2. B. $2 + 3$
3. C. $2 - 3$
4. D. $3 - 2$
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Answer: A
Q332012 · 15 Apr 2012
If $θ = 1 8^{\circ}$ , then what is the value of $4 sin^{2} θ + 2 sin θ$ ?
1. A. $- 1$
2. B.1
3. C.0
4. D.2
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Answer: B