Mathematics Tes...

The solution of differential equation \(x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}+y=\log x\) will be:

The area bounded by the line y = x, x-axis and ordinates x = -1 and x = 2 is:

Find two positive numbers x and y such that x + y = 60 and xy³ is maximum?

The value of determinant \(\left|\begin{array}{ccc}b+c & a+b & a \\ c+a & b+c & b \\ a+b & c+a & c\end{array}\right|\) is equal to:

If a median of 2, 3, x, 2x - 4, 5, 8 is 7 then the mode of given data is:

(Assume that data present are in ascending order)

Direction: There are four boxes A₁, A₂, A₃, A₄. Box A_i has i cards and on each card a number is printed, the number are from 1 to i. A selection of box A_i is \(\frac{i}{10}\) and then a card is drawn. Let E_i represents the event that a card with number i' is drawn.

P(E₁) is equal to:

The sum of the series 0.6 + 0.66 + 0.666 + … to n terms is:

Find the equation of the hyperbola whose foci are \((0, \pm \sqrt{10})\) and passing through the point \((2,3)\).

Let \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 5 & 2 & 0 \\ -1 & 6 & 1\end{array}\right]\), then the adjoint of \(A\) is:

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1 + x)ⁿ are in A. P., then the value of n is:

If C (n, r) : C (n, r + 1) = 1 : 2 and C (n, r + 1) : C (n, r + 2) = 2 : 3. Find the value of r.

Solve for \(x: \frac{x}{2 x+1} \geq \frac{1}{4}\).

Acute angle between the line \(\frac{\mathrm{x}-5}{2}=\frac{\mathrm{y}+1}{-1}=\frac{\mathrm{z}+4}{1}\) and the plane \(3 \mathrm{x}-4 \mathrm{y}-\mathrm{z}+5=0\) is:

The maximum value of the object function Z = 5x + 10y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x - 2y ≥ 0, x ≥ 0, y ≥ 0 is:

If f(x) = 2^|x| and g(x) = [x] where [.] denotes greatest integer function then find the value of f o g \(\left(-\frac{17}{2}\right)\)?