The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:
$I$. $f$ is one-one
$II$. $f$ is onto
$III$. $f$ is a decreasing function
Which of these statements are true?

In the following circuit,$PN$-junction diodes $D_1, D_2$ and $D_3$ are ideal. For the following potentials of $A$ and $B$,find the correct increasing order of equivalent resistance between $A$ and $B$:
$(i) V_A = -10\,V, V_B = -5\,V$
$(ii) V_A = -5\,V, V_B = -10\,V$
$(iii) V_A = -4\,V, V_B = -12\,V$

In $YDSE$ with two identical slits, when the upper slit is covered with a transparent sheet of mica, the second-order minima is observed above the center of the screen and the second-order maxima below it. Which of the following cannot be a possible value of the phase difference caused by the mica sheet?

The equation of the image of the circle $x^2 + y^2 + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is

The variance of $50$ observations is $7$. If each observation is multiplied by $6$ and then $5$ is subtracted from it,then the variance of the new data is

Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is: