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

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 A and B are symmetric matrices of the same order, then ____________.

If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.

If A is any square matrix, then which of the following is skew-symmetric?

If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B 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 diagonal elements of a skew symmetric matrix are ____________.

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