Properties of Determinants

JEE Main Mathematics · Matrices and Determinants · 11 questions, latest first

• If f: N → Z is defined by f(n)= |n, -1, -5; -2 n^2, 3(2 k+1), 2 k+1; -3 n^3, 3 k(2 k+1), 3 k(k+2)+1|, k ∈ N, and Σ_n=1^k f(n)=98,…20265 April, Shift 2 · Q3
• Among the statements: I: If |1, cos α, cos β; cos α, 1, cos γ; cos β, cos γ, 1| = |0, cos α, cos β; cos α, 0, cos γ; cos β, cos…202623 January, Shift 1 · Q5
• Let M and m respectively be the maximum and the minimum values of f(x)= |1+ sin^2 x, cos^2 x, 4 sin 4 x; sin^2 x, 1+ cos^2 x, 4…202529 January, Shift 1 · Q17
• For some a, b, let f(x)= |a+(sin x)/x, 1, b; a, 1+(sin x)/x, b; a, 1, b+(sin x)/x|, x ≠ 0, lim_x → 0 f(x)=λ+μ a+ν b. Then…202524 January, Shift 2 · Q4
• If α ≠ a, β ≠ b, γ ≠ c and |α, b, c; a, β, c; a, b, γ| =0, then a/(α-a)+b/(β-b)+(γ)/(γ-c) is equal to:20248 April, Shift 2 · Q4
• For α, β ∈ R and a natural number n, let A_r= |r, 1, n^2/2+α; 2 r, 2, n^2-β; 3 r-2, 3, (n(3 n-1))/2|. Then 2 A_10-A_8 is20246 April, Shift 1 · Q5
• Let A= [1, 0, 0; 0, α, β; 0, β, α] and |2 A|^3=2^21 where α, β ∈ Z, Then a value of α is202429 January, Shift 1 · Q5
• The values of α, for which |1, 3/2, α+3/2; 1, 1/3, α+1/3; 2 α+3, 3 α+1, 0| =0, lie in the interval202427 January, Shift 2 · Q4
• Let D_k= |1, 2 k, 2 k-1; n, n^2+n+2, n^2; n, n^2+n, n^2+n+2|. If Σ_k=1^n D_k=96, then n is equal to ____.202312 April, Shift 1 · Q22
• Let f(x)= |1+ sin^2 x, cos^2 x, sin 2 x; sin^2 x, 1+ cos^2 x, sin 2 x; sin^2 x, cos^2 x, 1+ sin 2 x|, x ∈[(π)/6, (π)/3]. If α and…20231 February, Shift 1 · Q64
• The set of all values of t ∈ R, for which the matrix [e^t, e^-t( sin t-2 cos t), e^-t(-2 sin t- cos t); e^t, e^-t(2 sin t+ cos…202329 January, Shift 2 · Q62