Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

F(x, y) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.

F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.

Solve : `x^2 "dy"/"dx"` = x² + xy + y².

Solcve: `x ("d"y)/("d"x) = y(log y – log x + 1)`

If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph ____________.

`2  "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.

If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.

`"cos" ["tan"^-1 {"sin" ("cot"^-1  "x")}]` is equal to ____________.

If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.

`"A" = [(1,-1),(2,-1)], "B" = [("x", 1),("y", -1)]` and (A + B)² = A² + B², then x + y = ____________.

Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).

If ` abs((1 + "a"^2 "x", (1 + "b"^2)"x", (1 + "c"^2)"x"),((1 + "a"^2) "x", 1 + "b"^2 "x", (1 + "c"^2) "x"), ((1 + "a"^2) "x", (1 + "b"^2) "x", 1 + "c"^2 "x"))`, then f(x) is apolynomial of degree ____________.

`abs (("a"^2, 2"ab", "b"^2),("b"^2, "a"^2, 2"ab"),(2"ab", "b"^2, "a"^2))` is equal to ____________.

If `alpha, beta, gamma` are in A.P., then `abs (("x" - 3, "x" - 4, "x" - alpha),("x" - 2, "x" - 3, "x" - beta),("x" - 1, "x" - 2, "x" - gamma)) =` ____________.

`abs ((1, "a"^2 + "bc", "a"^3),(1, "b"^2 + "ca", "b"^3),(1, "c"^2 + "ab", "c"^3))`

Solve the following system of equations x − y + z = 4, x − 2y + 2z = 9 and 2x + y + 3z = 1.

If the system of equations x + ky - z = 0, 3x - ky - z = 0 & x - 3y + z = 0 has non-zero solution, then k is equal to ____________.

If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx - 12y - 14 = 0 has non-trivial solution, then the value of k is ____________.

`abs ((("b" + "c"^2), "a"^2, "bc"),(("c" + "a"^2), "b"^2, "ca"),(("a" + "b"^2), "c"^2, "ab")) =` ____________.

Find the angle between the lines whose direction cosines are given by the equations: 3l + m + 5n = 0 and 6mn – 2nl + 5lm = 0.