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JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 2 - MCQExams.com
JEE
Maths
Rectangular Cartesian Coordinates
Quiz 2
The incentre of the triangle with vertices ( 1, √3 ), (0,and (2,is
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(1,√3/2)
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(2/3, 1/√3)
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(2/3, √3/2)
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(1, 1/√3)
The orthocentre of the ∆OAB, where O is the origin, A (6,and (3, 3√is
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(9/2, √3/2)
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(3, √3)
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(√3. 3)
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(3, - √3)
The equations of the three sides of a triangle are
x
= 2, y + 1 = 0, and
x
+ 2y = 4. The coordinates of the circumcentre of the triangle is
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(4, 0)
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(2, - 1)
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(0, 4)
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(-1, 2)
The orthocentre of the triangle with vertices (-2, -6), (-2,and (1,is
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(3, 1)
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(1, 1/3)
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(1, 3)
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None of these
The incentre of a triangle with vertices (7, 1), (-1,and (3 + 2√3, 3 + 4√is
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0%
0%
2)
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(7, 1)
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None of these
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A = 4, B = 1, C = 5, D = 3
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A = 4, B = 2, C = 5, D = 3
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A = 4, B = 1, C = 6, D = 3
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A = 2, B = 1, C = 6, D = 3
If the three points ( 3q, 0 ), ( 0, 3p )and (1,are collinear,then which one is correct?
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0%
0%
2)
0%
0%
The area (in sq units) of the triangle formed by the points ( 2, 2 ), ( 5, 5 ) and ( 6, 7 )is
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0%
9/2
0%
5
0%
10
0%
3/2
0%
14
The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0,and (6, 8), then least value of areas of the triangles is
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1
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3/2
0%
2
0%
5/2
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3
The area between the curve y = 1 - |
x
| and the X - axis is equal to
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1 sq unit
0%
1/2 sq unit
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1/3 sq unit
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2 sq units
0%
3 sq units
Area (in sq units) of the triangle formed by the lines y = 2
x
, y = 3
x
and y = 5 is
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25/6
0%
25/12
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5/6
0%
17/12
0%
6
If a ∆ABC has vertices (0, 0), (11,and (91, 0). If the line y = k
x
cuts the triangle into two triangles of equal area, then k is equal to
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30/51
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4/7
0%
7/4
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30/91
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27/37
One side of length 3 a of a triangle of area a
2
sq unit lies on the line
x
= a. Then, one of the line on which the third vertex lies, is
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x = - a2
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x = a2
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x = - a
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x = a/3
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x = - (a/3)
If t
1
, t
2
and t
3
are distinct points such that (t
1
, 2at
1
+ at
1
3
), (t
2
, 2at
2
+ at
2
3
) and (t
3
, 2at
3
+ at
3
3
)
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t1t2t3 = 1
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t1 + t2 + t3 = t1t2t3
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t1 + t2 + t3 = 0
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t1 + t2 + t3 = - 1
If a > 0, b > 0, then the maximum area (in sq units) of the triangle formed by the points O (0, 0), A ( a cos θ, b sin θ) and B( a cos θ, - b sin θ) is
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ab/2, when θ = π/4
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3ab/4, when θ = π/4
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ab/2, when θ = - π/2
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a2b2
If A (0, 0), B (12, 0), C (12, 2), D (6,and E (0,are the vertices of the pentagon ABCDE, then its area (in sq units) is
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58
0%
60
0%
61
0%
62
0%
63
The X-axis, Y-axis and a line passing through the point A ( 6,form a ∆ABC. If ∠A = 30°, then the area (in sq units) of the triangle, is
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6√3
0%
12√3
0%
4√3
0%
8√3
ABC is a triangle with ∠A = 30°, BC = 10cm. The area of the circumcircle of the triangle is
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0%
100π sq cm
0%
5 sq cm
0%
25 sq cm
0%
100π/3 sq cm
The area of an equilateral triangle that can be inscribed in the circle
x
2
+ y
2
- 4
x
- 6y - 12 = 0, is
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25√3/ 4 sq units
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35√3/4 sq units
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55√3/4 sq units
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75√3/4 sq units
The area (in sq units) of the triangle formed by the points with polar coordinates (1,(2, π/and (3, 2π/is
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0%
11√3/4
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5√3/4
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5/4
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11/4
If A (- 5,and B (3,are two vertices of a ∆ABC. Its area is 20 sq cm. The vertex C lies on the line
x
- y = 2. The coordinates of C are
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(- 7, - 5 ) or (3, 5)
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(- 3,- 5 ) or (- 5,7)
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(7,or (3, 5)
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(- 3,-or (7, 5)
If the area of the triangle with vertices (
x
, 0), (1,and (0,is 4 sq units, then the value of
x
is
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- 2
0%
- 4
0%
- 6
0%
8
The area enclosed with the curve |
x
| + |y| = 1 is
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1 sq units
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2 √2 sq units
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√2 sq unints
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2 sq units
The area ( in sq units) of the triangle formed by the lines
x
= 0, y = 0 and 3
x
+ 4y = 12, is
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0%
3
0%
4
0%
6
0%
12
Three points are A ( 6, 3), B (- 3,5), C (4, -and P (
x
, y) is a point, then the ratio of area of ∆PBC and ∆ ABC is
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0%
0%
2)
0%
0%
None of the above
A variable line passes through a fixed point ( a, ) and meets the coordinate axes in A and B. The locus of the point of intersection of lines through A ,B parallel to coordinate
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0%
0%
2)
0%
0%
The equation of the locus of the point of intersection of the straight lines
x
sin θ + (1 - cos θ) y = a sin θ and
x
sin θ - (1 + cos θ) y + a sin θ = 0 is
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y = ± ax
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x = ± ay
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y2 = 4x
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x2 + y2 = a2
A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is
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x2 + y2 = 4
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x2 + y2 = 16
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x2 + y2 = 8
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|x| + |y| = 8
A variable line through the point (1/5, 1/cuts the coordinates axes in the points A and B. If the point P divides AB, internally in the ratio 3 : 1, then the locus of P is
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3y + x = 20xy
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y + 3x = 20xy
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x + y = 20xy
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3x + 3y = 20xy
A variable
x
/a + y/b = 1 is such that a +b = 4. The locus of mind-point of the portion of the line intercepted between the axes is
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x + y = 4
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x + y = 8
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x + y = 1
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x + y = 2
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