$\int_{0}^{1000} e^{x - [x]} \, dx$ is equal to:

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$,then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$

$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s.$

The oxoanion which contains all equivalent $M-O$ bonds is:
$(I)$ $CrO_4^{2-}$
$(II)$ $MnO_4^{-}$
$(III)$ $Cr_2O_7^{2-}$

If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2-3x+4}{x^2+3x+4}$ will be

Match the following columns.

Column-$I$	Column-$II$
$A.$ $500$ million years ago	$1.$ Invertebrates
$B.$ $350$ million years ago	$2.$ Jawless fishes
$C.$ $320$ million years ago	$3.$ Sea weeds and few plants