Coordinate Geometry · NDA previous year questions

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2019 25 questions

Q512019 · 17 Nov 2019
What is the length of the chord of a unit circle which subtends an angle $θ$ at the centre?
1. A. $sin (\frac{θ}{2})$
2. B. $cos (\frac{θ}{2})$
3. C. $2 sin (\frac{θ}{2})$
4. D. $2 cos (\frac{θ}{2})$
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Answer: C
Q522019 · 17 Nov 2019
What is $tan {2 tan^{- 1} (\frac{1}{3})}$ equal to?
1. A. $\frac{2}{3}$
2. B. $\frac{3}{4}$
3. C. $\frac{3}{8}$
4. D. $\frac{1}{9}$
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Answer: B
Q532019 · 17 Nov 2019
A ladder $9 m$ long reaches a point $9 m$ below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is $6 0^{\circ}$ . What is the height of the flagstaff?
1. A. $9 m$
2. B. $10.5 m$
3. C. $13.5 m$
4. D. $15 m$
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Answer: C
Q572019 · 17 Nov 2019
The equation $a x + b y + c = 0$ represents a straight line
1. A.for all real numbers $a$ , $b$ and $c$
2. B.only when $a \neq = 0$
3. C.only when $b \neq = 0$
4. D.only when at least one of $a$ and $b$ is non-zero
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Answer: D
Q582019 · 17 Nov 2019
What is the angle between the lines $x cos α + y sin α = a$ and $x sin β - y cos β = a$ ?
1. A. $β - α$
2. B. $π + β - α$
3. C. $\frac{π + 2 β + 2 α}{2}$
4. D. $\frac{π - 2 β + 2 α}{2}$
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Answer: D
Q592019 · 17 Nov 2019
If the angle between the lines joining the end points of minor axis of the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ with one of its foci is $\frac{π}{2}$ , then what is the eccentricity of the ellipse?
1. A. $\frac{1}{2}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D. $\frac{1}{2 2}$
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Answer: B
Q612019 · 17 Nov 2019
A point on the line $\frac{x - 1}{1} = \frac{y - 3}{2} = \frac{z + 2}{7}$ has coordinates
1. A. $(3, 5, 4)$
2. B. $(2, 5, 5)$
3. C. $(- 1, - 1, 5)$
4. D. $(2, - 1, 0)$
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Answer: B
Q622019 · 17 Nov 2019
If the points $(x, y, - 3)$ , $(2, 0, - 1)$ and $(4, 2, 3)$ lie on a straight line, then what are the values of $x$ and $y$ respectively?
1. A.1, -1
2. B.-1, 1
3. C.0, 2
4. D.3, 4
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Answer: A
Q632019 · 17 Nov 2019
A straight line passes through the point $(1, 1, 1)$ makes an angle $6 0^{\circ}$ with the positive direction of $z$ -axis, and the cosine of the angles made by it with the positive directions of the $y$ -axis and the $x$ -axis are in the ratio $3 : 1$ . What is the acute angle between the two possible positions of the line?
1. A. $9 0^{\circ}$
2. B. $6 0^{\circ}$
3. C. $4 5^{\circ}$
4. D. $3 0^{\circ}$
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Answer: B
Q792019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : A curve $y = m e^{m x}$ where $m > 0$ intersects $y$ -axis at a point $P$ . What is the slope of the curve at the point of intersection $P$ ?
1. A. $m$
2. B. $m^{2}$
3. C. $2 m$
4. D. $2 m^{2}$
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Answer: B
Q802019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : A curve $y = m e^{m x}$ where $m > 0$ intersects $y$ -axis at a point $P$ . How much angle does the tangent at $P$ make with $y$ -axis?
1. A. $tan^{- 1} m^{2}$
2. B. $cot^{- 1} (1 + m^{2})$
3. C. $sin^{- 1} (\frac{1}{1 + m ^{4}})$
4. D. $sec^{- 1} 1 + m^{4}$
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Answer: C
Q542019 · 21 Apr 2019
The points $(1, 3)$ and $(5, 1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2 x + c$ . What is the value of c?
1. A.2
2. B. $- 2$
3. C.4
4. D. $- 4$
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Answer: D
Q552019 · 21 Apr 2019
If the lines $3 y + 4 x = 1$ , $y = x + 5$ and $5 y + b x = 3$ are concurrent, then what is the value of b?
1. A.1
2. B.3
3. C.6
4. D. $\frac{1}{2}$
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Answer: C
Q562019 · 21 Apr 2019
What is the equation of the straight line which is perpendicular to $y = x$ and passes through $(3, 2)$ ?
1. A. $x - y = 5$
2. B. $x + y = 5$
3. C. $x + y = 1$
4. D. $x - y = 1$
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Answer: B
Q572019 · 21 Apr 2019
The straight lines $x + y - 4 = 0$ , $3 x + y - 4 = 0$ and $x + 3 y - 4 = 0$ form a triangle, which is
1. A.isosceles
2. B.right-angled
3. C.equilateral
4. D.scalene
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Answer: A
Q582019 · 21 Apr 2019
A circle is drawn on the chord of a circle $x^{2} + y^{2} = a^{2}$ as diameter. The chord lies on the line $x + y = a$ . What is the equation of the circle?
1. A. $x^{2} + y^{2} - a x - a y + a^{2} = 0$
2. B. $x^{2} + y^{2} - a x - a y = 0$
3. C. $x^{2} + y^{2} + a x + a y = 0$
4. D. $x^{2} + y^{2} + a x + a y - 2 a^{2} = 0$
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Answer: B
Q592019 · 21 Apr 2019
The circle $x^{2} + y^{2} + 4 x - 7 y + 12 = 0$ , cuts an intercept on y-axis equal to
1. A.1
2. B.3
3. C.4
4. D.7
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Answer: A
Q602019 · 21 Apr 2019
In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord ?
1. A. $\frac{484}{21}$ cm
2. B. $\frac{242}{21}$ cm
3. C. $\frac{121}{21}$ cm
4. D. $\frac{44}{7}$ cm
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Answer: A
Q612019 · 21 Apr 2019
The sum of the focal distances of a point on an ellipse is constant and equal to the
1. A.length of minor axis
2. B.length of major axis
3. C.length of latus rectum
4. D.sum of the lengths of semi-major and semi-minor axes
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Answer: B
Q622019 · 21 Apr 2019
The equation $2 x^{2} - 3 y^{2} - 6 = 0$ represents
1. A.a circle
2. B.a parabola
3. C.an ellipse
4. D.a hyperbola
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Answer: D
Q632019 · 21 Apr 2019
The two parabolas $y^{2} = 4 a x$ and $x^{2} = 4 a y$ intersect
1. A.at two points on the line $y = x$
2. B.only at the origin
3. C.at three points one of which lies on $y + x = 0$
4. D.only at $(4 a, 4 a)$
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Answer: A
Q642019 · 21 Apr 2019
The centroid of the triangle with vertices $A (2, - 3, 3)$ , $B (5, - 3, - 4)$ and $C (2, - 3, - 2)$ is the point
1. A. $(- 3, 3, - 1)$
2. B. $(3, - 3, - 1)$
3. C. $(3, 1, - 3)$
4. D. $(- 3, - 1, - 3)$
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Answer: B
Q712019 · 21 Apr 2019
For $r > 0$ , $f (r)$ is the ratio of perimeter to area of a circle of radius r. Then $f (1) + f (2)$ is equal to
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: C
Q722019 · 21 Apr 2019
If $f (x) = 3^{1 + x}$ , then $f (x) f (y) f (z)$ is equal to
1. A. $f (x + y + z)$
2. B. $f (x + y + z + 1)$
3. C. $f (x + y + z + 2)$
4. D. $f (x + y + z + 3)$
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Answer: C
Q872019 · 21 Apr 2019
What is the area of one of the loops between the curve $y = c sin x$ and x-axis ?
1. A. $c$
2. B. $2 c$
3. C. $3 c$
4. D. $4 c$
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Answer: B