HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

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If ρ(A) ρ([A|B]), then the system AX = B of linear equations is

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If 0 ≤ θ ≤ π and the system of equations x + (sin θ)y – (cos θ)z = 0, (cos θ) x – y + z = 0, (sin θ) x + y + z = 0 has a non-trivial solution then θ is

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The augmented matrix of a system of linear equations is `[(1, 2, 7, 3),(0, 1, 4, 6),(0, 0, lambda - 7, mu + 7)]`. This system has infinitely many solutions if

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Let A = `[(2, -1, 1),(-1, 2, -1),(1, -1, 2)]` and 4B = `[(3, 1, -1),(1, 3, x),(-1, 1, 3)]`. If B is the inverse of A, then the value of x is

If k is real, discuss the nature of the roots of the polynomial equation 2x² + kx + k = 0, in terms of k

Find a polynomial equation of minimum degree with rational coefficients, having `2 + sqrt(3)"i"` as a root

Find a polynomial equation of minimum degree with rational coefficients, having 2i + 3 as a root

Find a polynomial equation of minimum degree with rational coefficients, having `sqrt(5) - sqrt(3)` as a root

Prove that a straight line and parabola cannot intersect at more than two points

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According to the rational root theorem, which number is not possible rational root of 4x⁷ + 2x⁷ – 10x³ – 5?

Find all values of x such that – 6π ≤ x ≤ 6π and cos x = 0

Find all values of x such that – 5π ≤ x ≤ 5π and cos x = 1

State the reason for  `cos^-1 [cos(- pi/6)] ≠ - pi/6`

Is cos^–1(– x) = π – cos^–1 true? justify your answer

Find the principal value of `cos^-1 (1/2)`

Find the value of `2cos^-1 (1/2) + sin^-1 (1/2)`

Find the value of `cos^-1(1/2) + sin^-1( - 1)`

Find the value of `cos-1 [cos  pi/7 cos  pi/17 - sin  pi/7 sin  pi/17]`

Find the domain of `f(x) = sin^-1 ((|x| - 2)/3) + cos^-1 ((1 - |x|)/4)`

Find the domain of `g(x) = sin^-1x + cos^-1x`