ISC Class 12 Maths: Improvement Paper 2025 Solution | Unit 2 Algebra (Matrices & Determinants) скачать в хорошем качестве

ISC Class 12 Maths: Improvement Paper 2025 Solution | Unit 2 Algebra (Matrices & Determinants)

ISC Class 12 Maths Improvement Paper 2025 Solution Unit 2 Algebra (Matrices & Determinants) Dear Students, Welcome back to our Board Exam Preparation Series for ISC Class 12 Maths! 🎓 In today’s video, we are continuing our preparation journey by solving the Improvement Paper 2025. This session specifically covers Unit 2: Algebra, focusing on deep-dive solutions for Matrices & Determinants. Whether you are revising core concepts or practicing high-yield questions, this step-by-step solution guide is designed to help you score maximum marks in your upcoming 2026 Board Examinations. 📥 Download the Study Material: Get the free PDF of this paper/unit to practice along with me: 👉https://drive.google.com/file/d/1QaQI... PDF Link previous year https://drive.google.com/file/d/1poZb... In this video, we cover: Detailed step-by-step solutions for Improvement Paper 2025 (Unit 2). Key concepts of Matrices and Determinants. Tips and tricks to solve algebra questions accurately for the 2026 board exams. 💡 Support the Channel: If you found this video helpful, please hit the LIKE button! Don't forget to SUBSCRIBE for more board exam strategies, and kindly SHARE this channel with your friends and juniors who could benefit from these math tutorials. Thank you for watching, and all the best for your studies! Dr. Ajay Kumar Gupta #ISCClass12 #MathsSolutions #ImprovementPaper2025 #MatricesAndDeterminants #BoardExam2026 #Class12Maths #ISCMaths #DrAjayKumarGupta Question No – 1 [1 Marks each] [MCQ & Short answer] (i) Find the value of μ if the following system of equations is consistent. 2x+ 3y - 8 = 0, 7x - 5y + 3 = 0, 4x - 6y + μ = 0 (a) 4 (b) 6 (c) 8 (d) 2 (v) Assertion: If A is a skew-symmetric matrix of order 3 × 3, then det(A) = 0. Reason: If A is a square matrix, then det(A) = det(A'). (a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion. (b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (c) Assertion is true and Reason is false. (d) Assertion is false and Reason is true. (vii) Statement 1: Every scalar matrix is a diagonal matrix. Statement 2: Every diagonal matrix is an identity matrix. (a) Statement 1 is true and Statement 2 is false. (b) Statement 2 is true and Statement 1 is false. (c) Both the statements are true. (d) Both the statements are false. (xi) 2|■(x&y&z@p&q&r@a&b&c)|+|■(x&y&z@s&t&u@2a&2b&2c)| Which one of the following is equal to the above sum? (a) |■(3x&3y&3z@2p+s&2q+t&2rt+u@4a&4b&4c)| (b) |■(2x&2y&2z@2p+s&2q+t&2r+u@2a&2b&2c)| (c) |■(x&y&z@p+s&q+t&r+u@2a&2b&2c)| (d) |■(2x&2y&2z@p+s&q+t&r+u@4a&4b&4c)| (xiv) For what value of a, is the matrix A = (■(1&-2&3@1&2&1@a&2&-3)) not invertible? Question 6 [2] In a market survey, three commodities A, B and C were studied. Each commodity had three varieties. To find out the index number of A, B and C fixed weights were assigned to the three varieties of each of the commodities. The table given below shows the result of the survey. Commodity variety Variety Total weight I II III A 1 2 3 P B 2 4 5 Q C 3 5 6 R Answer the following question. (i) Represent the above information in a matrix form. (ii) Find the value of P, Q and R if the weight assigned to A, B and C are 2 kg, 3 kg and 1 kg respectively. Question 7 [4] Using the properties of determinants, prove that |■(1&1&1@a&b&c@a^3&b^3&c^3 )| = (a - b)(b - c)(c - a)(a + b + c) cisceclass videos #cisceclassvideos