Determinants Basics: JEE Questions & Solutions

Among the statements: I: If 1 cosα cosβ cosα 1 cosγ cosβ cosγ 1 = 0 cosα cosβ cosα 0 cosγ cosβ cosγ 0 then cos²α + cos²β + cos²γ = 3/2, and…

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 |, where x ≠ 0, lim_(x → 0) f(x) = λ + μ a + ν b. Then (λ…

If y(x) = sin x cos x sin x + cos x + 1 27 28 27 1 1 1, x ∈ ℝ, then d²y/dx² + y is equal to

The number of singular matrices of order 2, whose elements are from the set {2, 3, 6, 9} is:

The values of α, for which 1 3/2 α+3/2 1 1/3 α+1/3 2α+3 3α+1 0 = 0, lie in the interval:

Let A = 1 0 0 0 α β 0 β α and |2A|³ = 2²¹, where α, β ∈ ℤ. Then a value of α is:

If f(x) = 2cos⁴ x 2sin⁴ x 2 + sin² 2x 3 + 2cos⁴ x 2sin⁴ x sin² 2x 2cos⁴ x 3 + 2sin⁴ x sin² 2x, then 1/5 f'(0) is equal to:

If f(x) = x³ 2x² + 1 1 + 3x 3x² + 2 2x x³ + 6 x³ - x 4 x² - 2 for all x ∈ ℝ, then 2f(0) + f'(0) is equal to:

For α, β ∈ R and a natural number n, let A_r = r 1 n²/2 + α 2r 2 n² - β 3r - 2 3 n(3n - 1)/2 Then 2A₁₀ - A₈ is:

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:

The set of all values of t ∈ ℝ, for which the matrix e^t e^(-t)(sin t - 2cos t) e^(-t)(-2sin t - cos t) e^t e^(-t)(2sin t + cos t)…

Let A = m n p q, d = |A| ≠ 0, and |A - d(Adj A)| = 0. Then:

Let A be an n × n matrix such that |A| = 2. If the determinant of the matrix Adj(2 · Adj(2A⁻¹)) is 2⁸⁴, then n is equal to:

View question

If: x + 1 x x x x + λ x x x x + λ² = 9/8(103x + 81) then λ, λ/3 are the roots of the equation:

View question