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

`"cos"^-1 1/2 + 2  "sin"^-1 1/2` is equal to ____________.

`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`

`"sin"^-1 (1/sqrt2)`

`"tan"^-1 (sqrt3)`

`"cos"^-1 (1/2)`

`"sin"^-1 ((-1)/2)`

If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.

If `"sin"^-1 (1 - "x") - 2  "sin"^-1 ("x") = pi/2,` then x is equal to ____________.

If `3  "sin"^-1 ((2"x")/(1 + "x"^2)) - 4  "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.

Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50

If A is a square matrix such that A² = A, then (I + A)² - 3A is ____________.

If a matrix A is both symmetric and skew symmetric then matrix A is ____________.

If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.

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 ____________.