Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

If a + b + c ≠ 0 and `|("a", "b","c"),("b", "c", "a"),("c", "a", "b")|` 0, then prove that a = b = c.

Prove tha `|("bc" - "a"^2, "ca" - "b"^2, "ab" - "c"^2),("ca" - "b"^2, "ab" - "c"^2, "bc" - "a"^2),("ab" - "c"^2, "bc" - "a"^2, "ca" - "b"^2)|` is divisible by a + b + c and find the quotient.

If x + y + z = 0, prove that `|(x"a", y"b", z"c"),(y"c", z"a", x"b"),(z"b", x"c", y"a")| = xyz|("a", "b", "c"),("c", "a", "b"),("b", "c", "a")|`

Let f(t) = `|(cos"t","t", 1),(2sin"t", "t", 2"t"),(sin"t", "t", "t")|`, then `lim_("t" - 0) ("f"("t"))/"t"^2` is equal to ______.

If f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`, then ______.

If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A^–1 exists if ______.

If x, y, z are all different from zero and `|(1 + x, 1, 1),(1, 1 + y, 1),(1, 1, 1 + z)|` = 0, then value of x^–1 + y^–1 + z^–1 is ______.

There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.

If A is a matrix of order 3 × 3, then |3A| = ______.

If A is invertible matrix of order 3 × 3, then |A^–1| ______.

If A is a matrix of order 3 × 3, then (A²)^–1 = ______.

`|(0, xyz, x - z),(y - x, 0, y  z),(z - x, z - y, 0)|` = ______.

If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx² + ..., then A = ______.

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`

If f(x) = 2x and g(x) = `x^2/2 + 1`, then which of the following can be a discontinuous function ______.

The function f(x) = `(4 - x^2)/(4x - x^3)` is ______.

The function f(x) = `"e"^|x|` is ______.

Let f(x) = |sin x|. Then ______.

If f.g is continuous at x = a, then f and g are separately continuous at x = a.