alleryStart learning →tan(45°) equals:
- ∞
- 0
- 1
- √3
Show answer and solution
Correct answer: C. 1
We have tan(45°) = sin(45°)/cos(45°).
That is tan(45°) = (1/√2)/(1/√2).
So tan(45°) = 1.
JEECUP (UP Polytechnic) Matrices and Determinants — practice questions
Explore 95 free Matrices and Determinants questions in JEECUP (UP Polytechnic) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Matrices and Determinants with Quill →Matrices and Determinants questions and exercises with answers
Showing questions 1–30 of 95.
tan(45°) equals:Read the answer and worked solution →A matrix is:Read the answer and worked solution →Identity matrix I has:Read the answer and worked solution →For matrix multiplication AB to be defined:Read the answer and worked solution →Determinant of 2×2 matrix [[a, b], [c, d]]:Read the answer and worked solution →Determinant of triangular (upper or lower) matrix:Read the answer and worked solution →A matrix is invertible iff:Read the answer and worked solution →For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =Read the answer and worked solution →Transpose of [[1,2,3],[4,5,6]] is:Read the answer and worked solution →For matrices A, B (square, same size): (AB)^T =Read the answer and worked solution →A matrix is symmetric if:Read the answer and worked solution →A matrix is skew-symmetric if:Read the answer and worked solution →Determinant of identity matrix I_n:Read the answer and worked solution →Determinant: if two rows are equal, det =Read the answer and worked solution →For matrix A with |A| = 5 and A is 3×3, |2A| =Read the answer and worked solution →For matrix A and its adjugate adj(A): A × adj(A) =Read the answer and worked solution →For non-singular A and scalar k: |k A^(-1)| = (A is n × n)Read the answer and worked solution →Solve: x + y + z = 6, 2x + y - z = 1, x - y + z = 2. Determinant of coefficient matrix:Read the answer and worked solution →If A is orthogonal (A A^T = I), then |A| =Read the answer and worked solution →For A = [[3, 1], [2, 4]], characteristic polynomial:Read the answer and worked solution →Eigenvalues of A = [[3,1],[2,4]]:Read the answer and worked solution →For matrix A, rank(A) + nullity(A) =Read the answer and worked solution →For A symmetric n×n matrix, all eigenvalues are:Read the answer and worked solution →Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]:Read the answer and worked solution →System of equations Ax = b has unique solution iff:Read the answer and worked solution →For 3×3 matrix with rows R₁, R₂, R₃ = R₁ + 2R₂. Determinant =Read the answer and worked solution →If A is 3×3 with |A| = -2, then |adj(A)| =Read the answer and worked solution →Product of eigenvalues of square matrix A =Read the answer and worked solution →SAT · Mathematics · Trig Ratios (SOHCAHTOA)Read the answer and worked solution →SAT · Mathematics · Trig Identities — T/FRead the answer and worked solution →
Worked practice questions
A matrix is:
- A vector
- A rectangular array of numbers arranged in rows and columns
- A single number
- A point
Show answer and solution
Correct answer: B. A rectangular array of numbers arranged in rows and columns
**Matrix:** rectangular array of numbers in m rows × n columns.
**Notation:** A_(ij) = element in row i, column j. Size denoted m × n.
Identity matrix I has:
- 1s on diagonal, 0s elsewhere; AI = A for any A
- All 1s except diagonal
- All zeros
- All 1s
Show answer and solution
Correct answer: A. 1s on diagonal, 0s elsewhere; AI = A for any A
Identity matrix I_n: square n × n with 1's on diagonal, 0's off-diagonal.
**For any compatible A:** AI = A = IA.
Multiplicative identity for matrices.
How to practise
- Choose a Matrices and Determinants question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.