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

Solve the following systems of linear equations by Gaussian elimination method:

2x – 2y + 3z = 2, x + 2y – z = 3, 3x – y + 2z = 1

Solve the following systems of linear equations by Gaussian elimination method:

2x + 4y + 6z = 22, 3x + 8y + 5z = 27, – x + y + 2z = 2

If ax² + bx + c is divided by x + 3, x – 5, and x – 1, the remainders are 21, 61 and 9 respectively. Find a, b and c. (Use Gaussian elimination method.)

An amount of ₹ 65,000 is invested in three bonds at the rates of 6%, 8% and 9% per annum respectively. The total annual income is ₹ 4,800. The income from the third bond is ₹ 600 more than that from the second bond. Determine the price of each bond. (Use Gaussian elimination method.)

A boy is walking along the path y = ax² + bx + c through the points (– 6, 8), (– 2, – 12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? (Use Gaussian elimination method.)

Choose the correct alternative:

If `("AB")^-1 = [(12, -17),(-19, 27)]` and `"A"^-1 = [(1, -1),(-2, 3)]` then `"B"^-1` =

Choose the correct alternative:

If A = `[(3/5, 4/5),(x, 3/5)]` and A^T = A^–1, then the value of x is

Choose the correct alternative:

If A = `[(1, tan  theta/2),(- tan theta/2, 1)]` and AB = I₂, then B = 

Choose the correct alternative:

If A = `[(costheta, sintheta),(-sintheta, costheta)]` and A(adj A) = `[("k", 0),(0, "k")]`, then k =

Choose the correct alternative:

If A = `[(2, 3),(5, -2)]` be such that λA^–1 = A, then λ is

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If adj A = `[(2, 3),(4, 1)]` and adj B = `[(1, -2),(-3, 1)]` then adj (AB) is

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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