Three dice are thrown simultaneously and the sum of the three numbers appearing on the top faces of the dice is found to be 10. The probability that these three numbers are distinct, is

Let the circle \(x^2 + y^2 = 2ax + 2by\) intersect the \(x\)-axis at point \(A(\alpha, 0)\) and \(y\)-axis at point \(B(0, \beta)\), where \(\alpha\beta \neq 0\). If the point \(C(p, q)\) lies on the chord AB, then \(\frac{p+\alpha}{a} + \frac{q+\beta}{b}\) equals

If \(x\) is a real number such that \(\max(\min(x, 2-x), x-4, 2x-8) = \pi - 3\), then the number of possible values of \(x\) is

If \(A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}\), then the determinant of \(A + A^2 + A^3 + \cdots + A^{13}\) is

In a class, 25% of all students read news from the Internet. Moreover, 45% of all students read news from printed newspaper. Further, 20% of all students read news from both the Internet and printed newspaper and they do not play video games. It is also known that 30% of the stud…

Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is

The equation \(2^x - x^2 = 0\) has

Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

Gita starts from point A and walks 1000 m east. She then walks 800 m north, followed by 640 m west and 512 m south, reaching point B. After this, she continues moving in the same cyclic order: east, north, west, south, with each successive movement 20% shorter than the previous o…