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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) is
  • a)
    {(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}
  • b)
    {(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}
  • c)
     {(x, x) (y, x) (z, x)}
  • d)
    {(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)&cu...
, Q, R) forms a triangle.

To determine if the triangle is a right triangle, we need to check if the sum of the squares of two of its sides equals the square of the third side.

Let's first find the distances between the points:

d(PQ) = sqrt((a-1)^2 + (x-2)^2 + (y-x)^2)
d(PR) = sqrt((x-1)^2 + (y-2)^2 + (z-x)^2)
d(QR) = sqrt((x-a)^2 + (y-x)^2 + (z-y)^2)

Now we check if any of the following conditions hold:

- d(PQ)^2 + d(PR)^2 = d(QR)^2
- d(PQ)^2 + d(QR)^2 = d(PR)^2
- d(PR)^2 + d(QR)^2 = d(PQ)^2

Simplifying each expression, we get:

- (a-1)^2 + (x-2)^2 + (y-x)^2 + (x-1)^2 + (y-2)^2 + (z-x)^2 = (x-a)^2 + (y-x)^2 + (z-y)^2
- (a-1)^2 + (x-2)^2 + (y-x)^2 + (x-a)^2 + (y-x)^2 + (z-y)^2 = (x-1)^2 + (y-2)^2 + (z-x)^2
- (x-1)^2 + (y-2)^2 + (z-x)^2 + (x-a)^2 + (y-x)^2 + (z-y)^2 = (a-1)^2 + (x-2)^2 + (y-x)^2

Expanding and simplifying each expression, we get:

- a^2 + 2x^2 - 2ax + 2y^2 - 4y + 3 = 0
- a^2 + 2x^2 - 2ax + 2y^2 - 4y - z^2 + 4z + 5 = 0
- a^2 + 2x^2 - 2ax + 2y^2 - 4y + z^2 - 4z + 5 = 0

We can solve for y in terms of a and x from the first equation:

y = (a-x)/2 +/- sqrt(x^2 - a^2 + 4ax - 4x^2 + 8y - 12)/2

Substituting this into the second and third equations, we get:

- a^2 + 2x^2 - 2ax + (a-x)^2 + (x^2 - a^2 + 4ax - 4x^2 + 8y - 12)/2 - z^2 + 4z + 5 = 0
- a^2 + 2x^2 - 2ax + (a-x)^2 + (x^2 - a^2 + 4ax - 4x^2 + 8y - 12)/2 + z^2 - 4z + 5 = 0

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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)&cu...
It's so obvious ans...(d)
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer?
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (P×Q)∪(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
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