Mathematics

Question: What is \(\int \frac{\ln x}{x}\,dx\) equal to? \(\int \frac{\ln x}{x}\,dx\) किसके बराबर है? Options: \(\frac{(\ln x)^2}{2} + c\) \(\frac{\ln

Question: The function \(f(x) = \frac{x^2}{e^x}\) is monotonically increasing if: फलन \(f(x) = \frac{x^2}{e^x}\) एकदिष्ट वर्धमान है यदि: Options: \(x

Question: If \(x\,dy = y\,dx + y^2\,dy\), \(y > 0\) and \(y(1) = 1\), then what is \(y(-3)\) equal to?

Question: What is \(\int_{-2}^2 x\,dx – \int_{-2}^2 [x]\,dx\) equal to, where \([.]\) is the greatest integer function? \(\int_{-2}^2 x\,dx –

Question: The system of equations \(kx + y + z = 1\), \(x + ky + z = k\), and

Question: The value of the determinant \(\begin{vmatrix} 1-\alpha & \alpha-\alpha^2 & \alpha^2 \\ 1-\beta & \beta-\beta^2 & \beta^2 \\ 1-\gamma

Question: If \(\vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k}\) and \(\vec{b} = 3\hat{i} + 2\hat{j} – \lambda\hat{k}\) are perpendicular, then

Question: The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is

Question: If variable takes values \(0, 1, 2, 3, \dots, n\) with frequencies \(1, C(n, 1), C(n, 2), C(n, 3),

Question: The distance between the parallel planes \(4x – 2y + 4z + 9 = 0\) and \(8x – 4y