mathematics

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

The value of the surface integral ∬_S z dx dy where S is the external surface of the sphere x² + y² + z² = R² is

The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than

If the value of the double integral $\int_{x=3}^{4}\int_{y=1}^{2}\frac{dydx}{(x+y)^2}$ is $\log_e (a/24)$, then $a$ is ________ (answer in integer).

If $x(t)$ satisfies the differential equation $t\frac{dx}{dt} + (t - x) = 0$ subject to the condition $x(1) = 0$, then the value of $x(2)$ is ________ (rounded off to 2 decimal pla...

The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?

If the Laplace transform of a function f(t) is given by (s+3)/((s+1)(s+2)), then f(0) is

The Fourier cosine series for an even function $f(x)$ is given by $f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx)$. The value of the coefficient $a_2$ for the function $f(x) = \cos^...

Consider a function $u$ which depends on position $x$ and time $t$. The partial differential equation $\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}$ is known a...

If $y$ is the solution of the differential equation $y^3 \frac{dy}{dx} + x^3 = 0$, $y(0)=1$, the value of $y(-1)$ is

$F(s)$ is the Laplace transform of the function $f(t) = 2t^2e^{-t}$. $F(1)$ is ________ (correct to two decimal places).