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CAT Previous Year Questions - Coordinate Geometry (July 8) - CAT MCQ


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10 Questions MCQ Test Daily Test for CAT Preparation - CAT Previous Year Questions - Coordinate Geometry (July 8)

CAT Previous Year Questions - Coordinate Geometry (July 8) for CAT 2024 is part of Daily Test for CAT Preparation preparation. The CAT Previous Year Questions - Coordinate Geometry (July 8) questions and answers have been prepared according to the CAT exam syllabus.The CAT Previous Year Questions - Coordinate Geometry (July 8) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Previous Year Questions - Coordinate Geometry (July 8) below.
Solutions of CAT Previous Year Questions - Coordinate Geometry (July 8) questions in English are available as part of our Daily Test for CAT Preparation for CAT & CAT Previous Year Questions - Coordinate Geometry (July 8) solutions in Hindi for Daily Test for CAT Preparation course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt CAT Previous Year Questions - Coordinate Geometry (July 8) | 10 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study Daily Test for CAT Preparation for CAT Exam | Download free PDF with solutions
*Answer can only contain numeric values
CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 1
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The area of the quadrilateral bounded by the Y -axis, the line x = 5, and the lines |x − y| − |x − 5| = 2, is

[2023]


Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 1




So, every point on the line y = 2x − 7 where x ≤ 5 satisfies the given condition.
We are to find the area enclosed by the y-axis, x = 5 and the lines of |x−y|−|x−5|=2 .
Because the area we are interested is bounded by x = 0 (y-axis) and x = 5, 0 ≤ x ≤ 5.
So, we’ll only be concerned about Case III and Case IV.
A rough sketch of the bounded region looks like…

The line y = 2x – 7 touches x = 0 and x = 5 at (0, -7) and (5, 3) respectively.

*Answer can only contain numeric values
CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 2
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The area of the region satisfying the inequalities | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is


Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 2

The graph of | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is as follows:

Area of ABCD = Area of EFCD - Area of EAD - Area of BFC
= 
= 
= 4 - 1 = 3 Square units.

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CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 3
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The area, in sq. units, enclosed by the lines x = 2, y =| x - 2 | + 4 , the X -axis and the Y -axis is equal to

[2020]

Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 3

The line y =| x - 2 | + 4 intersects the y -axis at (0,6) and intersects x = 2 at (2, 4)
The other vertices are (0,0) and (2,0)
The figure formed is a trapezium of parallel sides 6 and 4 and the distance between the parallel sides is 2.
Required answer = 1/2 x 2 x (6 + 4) = 10

CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 4
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The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is

[2020]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 4


Area of the triangle = 1/2 x 4 x 9 = 18
The circumradius of the triangle 
Area of the circle
= 
= 

CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 5
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The points (2,1) and (-3,-4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9 y + c = 0 , then c is

[2020]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 5

The given line also passes through the point of intersection of the diagonals of the parallelogram, which is the mid-point of (2,1) and (-3,-4) The mid-point of the given two points is (-1/2, -3/2).
Substituting the point in the given equation 

⇒ c = 14

CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 6
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Let C be the circle x2 + y2 + 4x - 6y - 3 = 0 and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to 60°. Then, the point at which L touches the line x = 6 is

[2023]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 6


This is the equation of a circle with radius 4 units and centered at (-2, 3)
From a point L we drop two tangents on the circle such that the angle between the tangents is 60o.


Therefore the locus of the point L, is a circle centered at (-2, 3) and has a radius of (4 + x = 8) units.

The equation of this locus is thus, (x + 2)2 + (y - 3)2 = 82

When X = 6, we have, (8)2 + (y - 3)2 = 82, that is y = 3

The circle, (x + 2)2 + (y - 3)2 = 82, touches the line x = 6 at (6, 3).

CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 7
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A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

[2023]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 7


∠DAC=∠DBC
(Angles subtended by the chord DC on the same side.)
∠ADB=∠ACB
(Angles subtended by the chord AB on the same side.)
∠AED=∠BEC
(Vertically Opposite angles.)
Therefore, △AED∼△BEC

(Angles subtended by the chord AD on the same side.)
∠BAC=∠BDC
(Angles subtended by the chord BC on the same side.)
∠AEB=∠DEC
(Vertically Opposite angles.)
Therefore, △AEB∼△DEC

Therefore, AE : EC = 8 : 5

*Answer can only contain numeric values
CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 8
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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is

[2023]

Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 8

The construction of the triangle according to the question is as follows:


CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 9
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In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

[2023]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 9

Let BP = x, PQ = y and QC = z.


CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 10
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A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is

[2023]
Detailed Solution for CAT Previous Year Questions - Coordinate Geometry (July 8) - Question 10

Since the angle subtended by the diameter on the circle is a right-angle, such a triangle inscribed in a circle with the diameter as one of its sides will be right angled.

“…and the other two sides have their lengths in the ratio a: b.”
Let the two sides be ax and bx.

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