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

A function is said to be continuous for x ∈ R, if ____________.

2x³ - 6x + 5 is an increasing function, if ____________.

If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:

The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.

The function f(x) = tan^-1 (sin x + cos x) is an increasing function in:

The function f(x) = x³ + 6x² + (9 + 2k)x + 1 is strictly increasing for all x, if ____________.

The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.

`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.

The function `"f"("x") = "x"/"logx"` increases on the interval

The length of the longest interval, in which the function `3  "sin x" - 4  "sin"^3"x"` is increasing, is ____________.

Let h(x) = f(x) - [f(x)]² + [f(x)]³ for every real number x. Then ____________.

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 value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.

Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.

`(dy)/(dx) + ycotx = 2/(1 + sinx)`

If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`

Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.

Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.

Find the general solution of the differential equation:

`log((dy)/(dx)) = ax + by`.

Find the general solution of the differential equation:

`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`

If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.

If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.