Coordinate Geometry · NDA previous year questions

If the projections of a straight line segment on the coordinate axes are 2, 3, 6, then the length of the segment is

1. A.5 units
2. B.7 units
3. C.11 units
4. D.49 units

What is the area of the parabola $x^2=y$ bounded by the line $y=1$ ?

1. A.$\frac{1}{3}$ square unit
2. B.$\frac{2}{3}$ square unit
3. C.$\frac{4}{3}$ square units
4. D.2 square units

Two straight line paths are represented by the equations $2x-y=2$ and $-4x+2y=6$. Then the paths will

1. A.cross each other at one point
2. B.not cross each other
3. C.cross each other at two points
4. D.cross each other at infinitely many points

For what value of k, the equations $3x-y=8$ and $9x-ky=24$ will have infinitely many solutions ?

1. A.6
2. B.5
3. C.3
4. D.1

Which one of the following points lies inside a circle of radius 6 and centre at (3, 5)?

1. A.$(-2,-1)$
2. B.$(0,1)$
3. C.$(-1,-2)$
4. D.$(2,-1)$

What is the equation of a straight line which passes through (3, 4) and the sum of whose x and y intercepts is 14?

1. A.$4x+3y=24$
2. B.$x+y=14$
3. C.$4x-3y=0$
4. D.$3x+4y=25$

The equation of the ellipse whose vertices are at $(\pm 5,0)$ and foci at $(\pm 4,0)$ is

1. A.$\frac{x^2}{25}+\frac{y^2}{9}=1$
2. B.$\frac{x^2}{9}+\frac{y^2}{25}=1$
3. C.$\frac{x^2}{16}+\frac{y^2}{25}=1$
4. D.$\frac{x^2}{25}+\frac{y^2}{16}=1$

The point whose abscissa is equal to its ordinate and which is equidistant from A(-1, 0) and B(0, 5) is

1. A.(1, 1)
2. B.(2, 2)
3. C.(-2, -2)
4. D.(3, 3)

The difference of focal distances of any point on a hyperbola is equal to

1. A.latus rectum
2. B.semi-transverse axis
3. C.transverse axis
4. D.semi-latus rectum

What is the area of the triangle whose vertices are (3, 0), (0, 4) and (3, 4)?

1. A.6 square unit
2. B.7.5 square unit
3. C.9 square unit
4. D.12 square unit

A straight line passes through the points (5, 0) and (0, 3). The length of the perpendicular from the point (4, 4) on the line is

1. A.$\frac{\sqrt{17}}{2}$
2. B.$\sqrt{\frac{17}{2}}$
3. C.$\frac{15}{\sqrt{34}}$
4. D.$\frac{17}{2}$

What is the inclination of the line $\sqrt{3}x-y-1=0$?

1. A.$30^{\circ }$
2. B.$60^{\circ }$
3. C.$135^{\circ }$
4. D.$150^{\circ }$

What is the area of the triangle whose vertices are (0, 0, 0), (1, 2, 3) and (-3, -2, 1)?

1. A.$3\sqrt{5}$ square unit
2. B.$6\sqrt{5}$ square unit
3. C.6 square unit
4. D.12 square unit

What is the area of the parabola $y^2=x$ bounded by its latus rectum ?

1. A.$\frac{1}{12}\text{ square unit}$
2. B.$\frac{1}{6}\text{ square unit}$
3. C.$\frac{1}{3}\text{ square unit}$
4. D.None of the above

The line making an angle $(-120^{\circ })$ with x-axis is situated in the:

1. A.first quadrant
2. B.second quadrant
3. C.third quadrant
4. D.fourth quadrant

The angle subtended at the centre of a circle of radius 3 cm by an arc of length 1 cm is:

1. A.$\frac{30^{\circ }}{\pi }$
2. B.$\frac{60^{\circ }}{\pi }$
3. C.$60^{\circ }$
4. D.None of the above

If $\sin A=\frac{2}{\sqrt{5}}$ and $\cos B=\frac{1}{\sqrt{10}}$ where A and B are acute angles, then what is A + B equal to?

1. A.$135^{\circ }$
2. B.$90^{\circ }$
3. C.$75^{\circ }$
4. D.$60^{\circ }$

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $\alpha$ and $\beta$ respectively. The height of the hill is:

1. A.$\frac{h\cot \beta }{\cot \beta -\cot \alpha }$
2. B.$\frac{h\cot \alpha }{\cot \alpha -\cot \beta }$
3. C.$\frac{h\tan \alpha }{\tan \alpha -\tan \beta }$
4. D.None of the above

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

The equation to the locus of a point which is always equidistant from the points (1, 0) and (0, –2) is:

1. A.$2x+4y+3=0$
2. B.$4x+2y+3=0$
3. C.$2x+4y-3=0$
4. D.$4x+2y-3=0$

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

What is the perpendicular distance between the parallel lines $3x+4y=9$ and $9x+12y+28=0$?

1. A.7/3 units
2. B.8/3 units
3. C.10/3 units
4. D.11/3 units

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

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

What is the value of $\lambda$ if the straight line $(2x+3y+4)+\lambda (6x-y+12)=0$ is parallel to y-axis?

1. A.3
2. B.$-6$
3. C.4
4. D.$-3$