Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

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 ______.

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.

Which of the following solutions may be used to find the number of children who have been given the polio drops?

Find the shortest distance between the following lines:

`vecr = (hati + hatj - hatk) + s(2hati + hatj + hatk)`

`vecr = (hati + hatj - 2hatk) + t(4hati + 2hatj + 2hatk)`

If y = sin^–1x, then (1 – x²)y₂ is equal to ______.

Solve the differential equation: xdy – ydx = `sqrt(x^2 + y^2)dx`