CAMT104 Mathematics I
Mathematics I: most repeated questions
Questions that have come up in more than one paper, matched by what they ask rather than exact wording. Most repeated first.
- 7×Asked in 2024, 2023, 2022, 2021, 2020, 2019, Model questionProve that vmatrix 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \\ vmatrix = xyz ( 1x + 1y + 1z )Answer coming5
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- Prove that vmatrix 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \\ vmatrix = xyz ( 1x + 1y + 1z )TU Board 2024
- a) Prove that vmatrix 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab vmatrix = (a b)(b c)(c a) . b) By using the vector method, prove that (A B) = A B + A B .TU Board 2023
- Prove that: vmatrix a & b & c \\ a^2 & b^2 & c^2 vmatrix = (a b)(b c)(c a)TU Board 2022
- Prove by vector method: (A B) = A B + A B .TU Board 2021
- Prove by vector method: (A + B) = A B A B .TU Board 2020
- Prove that: vmatrix x & x^2 \\ 1 & y \\ z & z^2 vmatrix = (x y)(y z)(z x)TU Board 2019
- Prove that bmatrix 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z bmatrix = xy ( 1x + 1y + 1z + 1 )Model question
- 5×Asked in 2024, 2023, 2021, 2019, Model questionFind the domain and range of the function f(x) = 6 x x^2 .Answer coming5
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- Find the domain and range of the function f(x) = 6 x x^2 .TU Board 2024
- Find the domain and range of the function f(x) = 6 x x^2 .TU Board 2023
- Define a function, its domain, and range. Find the domain and range of f(x) = 2 x x^2 .TU Board 2021
- Find the domain and range of the function f(x) = 2x + 13 x .TU Board 2019
- Find the domain and range of the function f(x) = 9 x^2 .Model question
- 4×Asked in 2023, 2022, 2021, 2020Find the inverse matrix of the matrix pmatrix 1 & 4 & 1 \\ 3 & 3 & 2 \\ 0 & 4 & 1 pmatrix .Answer coming5
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- Find the inverse matrix of the matrix pmatrix 1 & 4 & 1 \\ 3 & 3 & 2 \\ 0 & 4 & 1 pmatrix .TU Board 2023
- Define matrix. If A = pmatrix 2 & 0 \\ 1 & 3 pmatrix and B = pmatrix 2 & 1 \\ 3 & 2 pmatrix , show that: (AB)^T = B^T A^T .TU Board 2022
- If A = pmatrix 4 & 0 \\ 0 & 5 pmatrix , find a matrix X such that AX = pmatrix 1 & 2 \\ 2 & 4 pmatrix .TU Board 2021
- Define singular and non singular matrix. Find the inverse of the matrix A : A = bmatrix 1 & 2 & 1 \\ 2 & 1 & 1 \\ 3 & 5 & 8 bmatrixTU Board 2020
- 3×Asked in 2024, 2021, Model questionFind the equation of the ellipse whose latus rectum is 5 and the eccentricity is 1 2 .Answer coming5
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- 3×Asked in 2024, 2020, Model questionHow many numbers of three different digits less than 500 can be formed from the integers 1, 2, 3, 4, 5, and 6?Answer coming5
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- How many numbers of three different digits less than 500 can be formed from the integers 1, 2, 3, 4, 5, and 6?TU Board 2024
- How many numbers of at least three different digits can be formed using the digits 1, 2, 3, 4, 5, 6?TU Board 2020
- How many numbers of three different digits less than 500 can be formed from the integers 1, 2, 3, 4, 5, and 6?Model question
- 3×Asked in 2022, 2020If x ty = 5 6i5 + 6i , prove that x^2 + y^2 = 1 .Answer coming5
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- 3×Asked in 2024, 2023, Model questionSolve the inequality 3 + 2x x^2 0 .Answer coming5
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- Solve the inequality 3 + 2x x^2 0 .TU Board 2024
- Solve the inequality 6 + 5x x^2 0 .TU Board 2023
- Solve the inequality 3 + 2x x^2 0 .Model question
- 2×Asked in 2024, Model questiona.Find the equation of a hyperbola in standard form having focus ( 2, 0) and Directrix x = 12 . b.In an examination paper on mathematics, 20 questions are set. In how many different ways you can choose 18 questions to answer?Answer coming10
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- a.Find the equation of a hyperbola in standard form having focus ( 2, 0) and Directrix x = 12 . b.In an examination paper on mathematics, 20 questions are set. In how many different ways you can…TU Board 2024
- a. Find the equation of a hyperbola in standard form having focus ( 2, 0) and Diretrix x = 12 . b. In an examination paper on mathematics, 20 questions are set. In how many different ways you can…Model question
- 2×Asked in 2023, 2022Prove that the function f : R R defined by f(x) = 3x 1 is bijective.Answer coming5
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- 2×Asked in 2024, Model questionIf a = 3 i + j and a b = (1, 2, 2) , find the angle between a and b .Answer coming5
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