Coordinate Geometry · NDA previous year questions

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

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

The eccentricity e of an ellipse satisfies the condition:

1. A.$e<0$
2. B.$0<e<1$
3. C.$e=1$
4. D.$e>1$

The equation of a straight line which makes an angle $45^{\circ }$ with the x-axis with y-intercept 101 units is:

1. A.$10x+101y=1$
2. B.$101x+y=1$
3. C.$x+y-101=0$
4. D.$x-y+101=0$

If the points $(2,4)$, $(2,6)$ and $(2+\sqrt{3},k)$ 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

If the distance between the points $(7,1,-3)$ and $(4,5,\lambda )$ is 13 units, then what is one of the values of $\lambda$?

1. A.20
2. B.10
3. C.9
4. D.8

What is the perimeter of the triangle with vertices $A(-4,2)$, $B(0,-1)$ and $C(3,3)$?

1. A.$7+3\sqrt{2}$
2. B.$10+5\sqrt{2}$
3. C.$11+6\sqrt{2}$
4. D.$5+\sqrt{2}$

If the mid point between the points $(a+b,a-b)$ and $(-a,b)$ lies on the line $ax+by=k$, what is k equal to?

1. A.a/b
2. B.a + b
3. C.ab
4. D.a - b

The acute angle which the perpendicular from origin on the line $7x-3y=4$ makes with the x-axis is

1. A.zero
2. B.positive but not $\pi /4$
3. C.negative
4. D.$\pi /4$

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

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

1. A.$2/\sqrt{3}$
2. B.$1/\sqrt{3}$
3. C.$\sqrt{3}/2$
4. D.$1/\sqrt{2}$

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.$2x=y+2$
4. D.None of the above

What is $\tan \left(\frac{\pi }{12}\right)$ equal to?

1. A.$2-\sqrt{3}$
2. B.$2+\sqrt{3}$
3. C.$\sqrt{2}-\sqrt{3}$
4. D.$\sqrt{3}-\sqrt{2}$

If $\theta =18^{\circ }$, then what is the value of $4{\sin }^2\theta +2\sin \theta$?

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

Two poles are 10 m and 20 m high. The line joining their tips makes an angle of $15^{\circ }$ with the horizontal. What is the distance between the poles?

1. A.$10(\sqrt{3}-1)\mathrm{m}$
2. B.$5(4+2\sqrt{3})\mathrm{m}$
3. C.$20(\sqrt{3}+1)\mathrm{m}$
4. D.$10(\sqrt{3}+1)\mathrm{m}$

How many tangents are parallel to x-axis for the curve $y=x^2-4x+3$ ?

1. A.1
2. B.2
3. C.3
4. D.No tangent is parallel to x-axis

Let O be the origin and P, Q, R be the points such that $\overrightarrow{PO}+\overrightarrow{OQ}=\overrightarrow{QO}+\overrightarrow{OR}$. Then which one of the following is correct ?

1. A.P, Q, R are the vertices of an equilateral triangle
2. B.P, Q, R are the vertices of an isosceles triangle
3. C.P, Q, R are collinear
4. D.None of the above

What is the value of $2{\log }_{8}2-\frac{1}{3}{\log }_{3}9$ ?

1. A.0
2. B.1
3. C.2
4. D.1/3

What is the eccentricity of the conic $4x^2+9y^2=144$?

1. A.$\frac{\sqrt{5}}{3}$
2. B.$\frac{\sqrt{5}}{4}$
3. C.$\frac{3}{\sqrt{5}}$
4. D.2/3

What is the perpendicular distance of the point (x, y) from x-axis?

1. A.x
2. B.y
3. C.|x|
4. D.|y|

If ABCD is a cyclic quadrilateral then what is $\sin A+\sin B-\sin C-\sin D$ equal to?

1. A.0
2. B.1
3. C.2
4. D.$2(\sin A+\sin B)$

What is the value of $\sin 420^{\circ }.\cos 390^{\circ }+\cos (-300^{\circ }).\sin (-330^{\circ })$?

1. A.0
2. B.1
3. C.2
4. D.-1

What is the area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of the latus rectum?

1. A.9 square units
2. B.12 square units
3. C.14 square units
4. D.18 square units

What is the focal distance of any point $P(x_1,y_1)$ on the parabola $y^2=4ax$ ?

1. A.$x_1+y_1$
2. B.$x_1{y}_1$
3. C.$a{x}_1$
4. D.$a+x_1$

If $(p,q)$ is the point on the x-axis equidistant from the points $(1,2)$ and $(2,3)$, then which one of the following is correct ?

1. A.$p=0,q=4$
2. B.$p=4,q=0$
3. C.$p=3/2,q=0$
4. D.$p=1,q=0$