If the tangent at the point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the $y$-axis,then the length of $PQ$ is

$A$ body of mass $0.01 \ kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown in the graph. The period of the $S.H.M.$ is .... $s$

$A$ thin converging lens of focal length $f=25 \ cm$ forms the image of an object on a screen placed at a distance of $75 \ cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \ cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $cm$)

$A$ plane passing through the points $(0, -1, 0)$ and $(0, 0, 1)$ and making an angle $\frac{\pi}{4}$ with the plane $y - z + 5 = 0$,also passes through the point:

If the curves $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{25}+\frac{y^2}{16}=1$ cut each other orthogonally,then $a^2-b^2$ equals to

Which of the following $statement(s)$ is/are not correct?
$(i)$ Reproduction is the production of progeny possessing features dissimilar to their parents.
$(ii)$ The fungi,the filamentous algae,the protonema of mosses,all multiply by budding.
$(iii)$ Many organisms like mules,sterile worker bees do not reproduce.
$(iv)$ Reproduction is not an all-inclusive defining characteristic of living organisms.