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

General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.

The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.

The solution of the differential equation ydx + (x + xy)dy = 0 is ______.

General solution of `("d"y)/("d"x) + y` = sinx is ______.

The solution of differential equation coty dx = xdy is ______.

The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.

Number of arbitrary constants in the particular solution of a differential equation of order two is two.

The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.

The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx².

If A is a square matrix, then A – A’ is a ____________.

For any square matrix A, AA^T is a ____________.

If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.

If A `= [(0,-1,2),(1,0,3),(-2,-3,0)],` then A + 2A^T equals

If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.

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

The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.

The matrix A `=[(0,1),(1,0)]` is a ____________.

The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]`  is a ____________.

If `[(1,2),(3,4)],` then A² - 5A is equal to ____________.

Find the angle between the lines whose direction cosines are given by the equations: 3l + m + 5n = 0 and 6mn – 2nl + 5lm = 0.