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

If f : R → R, g : R → R and h : R → R is such that f(x) = x², g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = `sqrtpi/2` will be ____________.

Let f : N → R : f(x) = `((2"x"−1))/2` and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) `(3/2)` is ____________.

If f : R → R, g : R → R and h : R → R are such that f(x) = x², g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be ____________.

If f(x) = `(3"x" + 2)/(5"x" - 3)` then (fof)(x) is ____________.

`("d"y)/("d"x) + y/(xlogx) = 1/x` is an equation of the type ______.

Integrating factor of the differential equation of the form `("d"x)/("d"y) + "P"_1x = "Q"_1` is given by `"e"^(int P_1dy)`.

Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.

Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.

Let f : R → R be the functions defined by f(x) = x³ + 5. Then f^-1(x) is ____________.

Correct substitution for the solution of the differential equation of the type `("d"x)/("d"y) = "g"(x, y)` where g(x, y) is a homogeneous function of the degree zero is x = vy.

Let f : R – `{3/5}`→ R be defined by f(x) = `(3"x" + 2)/(5"x" - 3)` Then ____________.

If f(x) = (ax² – b)³, then the function g such that f{g(x)} = g{f(x)} is given by ____________.

Which one of the following functions is not invertible?

The inverse of the function `"y" = (10^"x" - 10^-"x")/(10^"x" + 10^-"x")` is ____________.

If f : R → R defind by f(x) = `(2"x" - 7)/4` is an invertible function, then find f^-1.

Consider the function f in `"A = R" - {2/3}` defiend as `"f"("x") = (4"x" + 3)/(6"x" - 4)` Find f^-1.

If f is an invertible function defined as f(x) `= (3"x" - 4)/5,` then f^-1(x) is ____________.

If f : R → R defined by f(x) `= (3"x" + 5)/2` is an invertible function, then find f^-1.

If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + vec"b" + vec"a" = vec0` and `|vec"a"|` = 2, `|vec"b"|` = 3, `|vec"c"|` = 5, then value of `vec"a"*vec"b" + vec"b"*vec"c" + vec"c"*vec"a"` is ______.

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