Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

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 → R be given by f(x) = tan x. Then f^-1(1) is ____________.

If f : `(1, infty) → (2, infty)  "is given by f"("x") = "x" + 1/"x"`, then f^-1 equals to ____________.

Let f(x) = x² – x + 1, x ≥ `1/2`, then the solution of the equation f(x) = f^-1(x) is ____________.

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 ______.

If `|vec"a"| = |vec"b"|`, then necessarily it implies `vec"a" = +- vec"b"`.

Find the shortest distance between the lines given by `vec"r" = (8 + 3lambdahat"i" - (9 + 16lambda)hat"j" + (10 + 7lambda)hat"k"` and `vec"r" = 15hat"i" + 29hat"j" + 5hat"k" + mu(3hat"i" + 8hat"j" - 5hat"k")`

`"d"/"dx" {"cosec"^-1 ((1 + "x"^2)/(2"x"))}` is equal to ____________.

If `"y = sin"^-1 ((sqrt"x" - 1)/(sqrt"x" + 1)) + "sec"^-1 ((sqrt"x" + 1)/(sqrt"x" - 1)), "x" > 0, "then"  "dy"/"dx"` is ____________.

If y `= "cos"^2 ((3"x")/2) - "sin"^2 ((3"x")/2), "then"  ("d"^2"y")/("dx"^2)` is ____________.

If e^x + e^y = e^x+y, then `"dy"/"dx"` is:

Given that the fuel cost per hour is k times the square of the speed the train generates in km/h, the value of k is:

If the train has travelled a distance of 500 km, then the total cost of running the train is given by the function:

The most economical speed to run the train is:

The fuel cost for the train to travel 500 km at the most economical speed is:

The total cost of the train to travel 500 km at the most economical speed is:

The derivative of sin x with respect to log x is ____________.

f(x) = 3x² + 6x + 8, x ∈ R

Find the height of a cylinder, which is open at the top, having a given surface area, greatest volume, and radius r.

Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2^nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3^rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

The solution of the differential equation `"dy"/"dx" = "k"(50 - "y")` is given by ______.