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 students who do not read news play video games. The minimum percentage of students who do not play video games is

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

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

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

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…

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

The number of values \(a\) can take such that \(x^4 + ax^3 + (3a-4)x^2 + 2(a-1)x - 4\) can be expressed as a product of two quadratic polynomials, \(x^2 + px + 2\) and \(x^2 + qx - 2\), where \(p\) and \(q\) are real, is

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

The approximate value of the expression \(2\log_3 3n - \log_3 (n^2 + 1)\) for a sufficiently large \(n\) is