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

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 ____________.

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

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