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

Evaluate the following:

`int_0^pi x log sin x "d"x`

`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.

`int tan^-1 sqrt(x)  "d"x` is equal to ______.

Find the general solution of the differential equation `"dy"/"dx" = y/x`.

A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.

Let A = `[(1, "a" ("b + c"), "bc"),(1, "b" ("c + a"), "ca"),(1, "c" ("a + b"), "ab")],` then Det. A is ____________.

If A and B are square matrices of order 3, then ____________.

`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.

`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.

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.

The points (1, 2, 3), (–2, 3, 4) and (7, 0, 1) are collinear.

If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.

Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).

If `"y" = "e"^(1/2log (1 +  "tan"^2"x")), "then"  "dy"/"dx"` is equal to ____________.

If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.

Given that A is a square matrix of order 3 and |A| = −4, then |adj A| is equal to:

Given that A = [a_ij] is a square matrix of order 3 × 3 and |A| = −7, then the value of `sum_("i" = 1)^3 "a"_("i"2)"A"_("i"2)`, where A_ij denotes the cofactor of element a_ij is:

If matrices A and B are inverse of each other then ____________.