Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x+2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2-x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is

In $YDSE$, the separation between the slits is halved and the distance between the slit and the screen is doubled. The fringe width is

The radioactivity of a given sample of whisky due to tritium (half-life $12.3$ years) was found to be only $3\%$ of that measured in a recently purchased bottle marked "$7$ years old". The sample must have been prepared about:

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

If $a = i + j + k$,$b = i + j$,$c = i$ and $(a \times b) \times c = \lambda a + \mu b$,then $\lambda + \mu = $

The self-inductance of a choke coil is $10 \, mH$. When it is connected to a $10 \, V$ $DC$ source,the power loss is $20 \, W$. When it is connected to a $10 \, V$ $AC$ source,the power loss is $10 \, W$. The frequency of the $AC$ source is ....... $Hz$.