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

Find the equation of a curve passing through `(1, pi/4)` if the slope of the tangent to the curve at any point P(x, y) is `y/x - cos^2  y/x`.

State the type of the differential equation for the equation. xdy – ydx = `sqrt(x^2 + y^2)  "d"x` and solve it

Which of the following is not a homogeneous function of x and y.

F(x, y) = `(sqrt(x^2 + y^2) + y)/x` is a homogeneous function of degree ______.

F(x, y) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.

F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.

Solve : `x^2 "dy"/"dx"` = x² + xy + y².

Solcve: `x ("d"y)/("d"x) = y(log y – log x + 1)`

If A `= [(1,2),(2,1)]` and f(x) = (1 + x) (1 - x), then f(a) is ____________.

If A `= [(2"x", 0),("x","x")] "and A"^-1 = [(1,0),(-1,2)],` then x equals ____________.

If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.

Find the general solution of the differential equation:

(xy – x²) dy = y² dx

Read the following passage:

Based on the above, answer the following questions:

1. Show that (x² – y²) dx + 2xy dy = 0 is a differential equation of the type `dy/dx = g(y/x)`. (2)
2. Solve the above equation to find its general solution. (2)

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

Find : `int x^2/(x^4+x^2-2) dx`

If `veca=4hati-hatj+hatk` then find a unit vector parallel to the vector `veca+vecb`

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x³ + 5, then find the value of (fog)⁻¹ (x).