Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.

The value of sin (2tan^-1 (0.75)) is equal to ____________.

The value of expression 2 `"sec"^-1  2 + "sin"^-1 (1/2)`

The value of the expression tan `(1/2  "cos"^-1 2/sqrt3)`

`"cot" ("cosec"^-1  5/3 + "tan"^-1  2/3) =` ____________.

`"cos" (2  "tan"^-1 1/7) - "sin" (4  "sin"^-1 1/3) =` ____________.

`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.

If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.

If tan^-1 2x + tan^-1 3x = `pi/4,` then x is ____________.

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

The value of cot^-1 9 + cosec^-1 `(sqrt41/4)` is given by ____________.

If `"A" = [("a","b"),("b","a")]` and `"A"^2 = [(alpha,beta),(beta, alpha)]` then ____________.

If matrix A `= [("a","b","c"),("b","c","a"),("c","a","b")]` where a, b, c are real positive numbers, abc = 1 and A^TA = I, then the value of a³ + b³ + c³ is ____________.

Find the values of x, y, z respectively if the matrix A `= [(0,2"y","z"),("x","y","-z"),("x","-y","z")]` satisfy the equation A^TA = I₃.

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 A `= [(0,1,1),(1,0,1),(1,1,0)] "then"  ("A"^2 - 3"I")/2 =` ____________.

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

Evaluate the determinant `Delta = abs (("log"_3  512, "log"_4  3),("log"_3  8, "log"_4  9))`

`abs(("cos"  15°, "sin"  15°),("sin"  75°, "cos"  75°))`

Find the minor of 6 and cofactor of 4 respectively in the determinant `Delta = abs ((1,2,3),(4,5,6),(7,8,9))`