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

Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.

Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.

`"A" = abs ((1/"a", "a"^2, "bc"),(1/"b", "b"^2, "ac"),(1/"c", "c"^2, "ab"))` is equal to ____________.

If A, B, and C be the three square matrices such that A = B + C, then Det A is equal to

`abs ((1 + "a", "b", "c"),("a", 1 + "b", "c"),("a", "b", 1 + "c")) =` ____________

The value of the determinant `abs ((1,0,0),(2, "cos x", "sin x"),(3, "sin x", "cos x"))` is ____________.

If A = `[(1,0,0),(2,"cos x","sin x"),(3,"sin x", "-cos x")],` then det. A is equal to ____________.

The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.

The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.

The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.

The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.

The instantaneous rate of change at t = 1 for the function f (t) = te^-t + 9 is ____________.

The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y⁴ are ______.

The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.

`lim_("x"-> pi) (1 + "cos"^2 "x")/("x" - pi)^2` is equal to ____________.

`lim_("x" -> 0) ("x cos x" - "log" (1 + "x"))/"x"^2` is equal to ____________.

`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to ____________.

`lim_("x" -> 0) (1 - "cos x")/"x sin x"` is equal to ____________.

Let `"f"("x") = ("x" - 1)/("x" + 1),` then f(f(x)) is ____________.