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The number of intergral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0,0),(0,21) and (21,0), is

133

190

233

105

Area of the triangle formed by the line x +y=3 and angle bisectors of the pair of straight lines x2 – y2 + 2y=1 is

2 sq. units

4 sq. units

6 sq. units

8 sq. units

Three lines px + qy + r =0, qx + ry +p =0 and rx + py + q =0 are concurrently if

P + q + r =0

P2 + q2 + r2 = pr + rp + pq

P3 + q3 + r3 = 3pqr

None of these

1, 2 and 3

If (P(1,2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then

a=2, b=4

a=3, b=4

a=2, b=3

a=3, b=5

If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is always rational point(s)?

Circumcentre

incentre

centre

Orthocentre

Let L1 be a straight line passing through the origin and L2 be the straight line x +y =1. If the intercepts made by the circle x2 + y2 –x +3y=0 on L1 and L2 are equal , then which of the following equations can represent L1?

X+ y =0

X –y=0

X +7y=0

X –7y=0

2 and 3

1 and 4

If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then locus of the point S satisfying the relation SQ2+ SR2 =2SP2, is

A straight line parallel to x-axis

A circle passing through the origin

A circle with the centre at the origin

A straight line parallel to y-axis

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Square

Circle

Straight

Two intersecting lines

If x1, x2, x3 as well as y1, y2, y3, are in G.P. with the same common ratio, then the points (x1,y1), (x2,y2) and (x3, y3).

Lie on a straight line

lie on an ellipse

lie on a circle

are vertices of a triangle

The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y =9 an y= mx+1 is also an integer, is

2

0

4

1

133

190

233

105

Area of the triangle formed by the line x +y=3 and angle bisectors of the pair of straight lines x2 – y2 + 2y=1 is

2 sq. units

4 sq. units

6 sq. units

8 sq. units

Three lines px + qy + r =0, qx + ry +p =0 and rx + py + q =0 are concurrently if

P + q + r =0

P2 + q2 + r2 = pr + rp + pq

P3 + q3 + r3 = 3pqr

None of these

1, 2 and 3

If (P(1,2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS, then

a=2, b=4

a=3, b=4

a=2, b=3

a=3, b=5

If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is always rational point(s)?

Circumcentre

incentre

centre

Orthocentre

Let L1 be a straight line passing through the origin and L2 be the straight line x +y =1. If the intercepts made by the circle x2 + y2 –x +3y=0 on L1 and L2 are equal , then which of the following equations can represent L1?

X+ y =0

X –y=0

X +7y=0

X –7y=0

2 and 3

1 and 4

If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then locus of the point S satisfying the relation SQ2+ SR2 =2SP2, is

A straight line parallel to x-axis

A circle passing through the origin

A circle with the centre at the origin

A straight line parallel to y-axis

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Square

Circle

Straight

Two intersecting lines

If x1, x2, x3 as well as y1, y2, y3, are in G.P. with the same common ratio, then the points (x1,y1), (x2,y2) and (x3, y3).

Lie on a straight line

lie on an ellipse

lie on a circle

are vertices of a triangle

The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y =9 an y= mx+1 is also an integer, is

2

0

4

1

This test consist of 10 questions.Students should ideally take 10 minutes to complete the test. This test is useful for those students who are preparing for IIT JEE, AIEEE or any other engineering entrance test. This test cosist of questions from Straight Line which, in general, is focused in AIEEE and IIT JEE. Last year - 6 questions was asked from this chapter in AIEEE. In Straight Line slopes, distance from a point to straight line are key topics and mostly application based questions are asked.

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Aishwarya Sai Chamanoor2x+3y=1 (or) 3x+2y=1 is the equation of required straight line

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