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PASSAGE - 3
Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :
Q. The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is
[Note: The trace of a matrix is the sum of its diagonal entries.]
- a)(p – 1) (p2 – p + 1)
- b)p3 – (p – 1)2
- c)(p – 1)2
- d)(p – 1) (p2 – 2)
Correct answer is option 'C'. Can you explain this answer?
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PASSAGE - 3Let p be an odd prime number and Tp be the following set of...
Trace A = a + a = 2a is not divisible by p ⇒ a is not divisible by p
⇒ a ≠ 0
But |A| is divisible by p
⇒ a2 – bc is divisible by p
It will be so if on dividing a2 by p suppose we get
then on dividing bc by p we should get 
for some
integeral values of m, n and l. i.e. the remainder should be same in each case, so that
⇒ a ≠ 0
But |A| is divisible by p
⇒ a2 – bc is divisible by p
It will be so if on dividing a2 by p suppose we get
then on dividing bc by p we should get for someintegeral values of m, n and l. i.e. the remainder should be same in each case, so that
For this to happen a can take any value from 1 to p–1, also if b takes any value from 1 to p–1 then c should take only that value corresponding to which the remainder is same.
∴ No. of ways = (p – 1) × (p – 1) × 1 = (p – 1)2.
∴ No. of ways = (p – 1) × (p – 1) × 1 = (p – 1)2.
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PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer?
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PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer?.
PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer?.
Solutions for PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice PASSAGE - 3Let p be an odd prime number and Tp be the following set of 2 × 2 matrices :Q.The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is[Note: The trace of a matrix is the sum of its diagonal entries.]a)(p – 1) (p2 – p + 1)b)p3 – (p – 1)2c)(p – 1)2d)(p – 1) (p2 – 2)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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