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

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…

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…

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 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

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

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

A certain number of people contributed to a charity. The first person contributed one rupee. The rule for contribution was that the next person would contribute double the amount already raised. If the total money raised for the charity was 2187 rupees, then the number of people…