The number of all possible combinations of 4 letters which are taken from the letters of the word ACCOMMODATION is
If \( x \) and \( y \) are two positive real numbers such that \( x + iy = \frac{13\sqrt{5} + 12i}{(2 - 3i)(3 + 2i)} \), then \( 13y - 26x = \):
Three similar urns \(A,B,C\) contain \(2\) red and \(3\) white balls; \(3\) red and \(2\) white balls; \(1\) red and \(4\) white balls, respectively. If a ball is selected at random from one of the urns is found to be red, then the probability that it is drawn from urn \(C\) is ?
In a triangle \(ABC\), \(\displaystyle \frac{a(rr_1+r_2r_3)}{r_1-r+r_2r_3} =\;?\)
Consider the parabola \(25[(x-2)^2 + (y+5)^2] = (3x+4y-1)^2\), match the characteristic of this parabola given in List-I with its corresponding item in List-II.
The length of the normal drawn at \( t = \frac{\pi}{4} \) on the curve \( x = 2(\cos 2t + t \sin 2t) \), \( y = 4(\sin 2t + t \cos 2t) \) is:
If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is:
Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then:
The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:
If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is:
