It is now possible to breed plants and animals with desired characters through

If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $P(-2, 3, 5)$ in the ratio $1: 3$,then the coordinates of $B$ are:

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

Match the common name given in column $I$ with their taxonomic category order given in column $II$ and choose the correct combination from the options given below.

Column-$I$ (Common name)	Column-$II$ (Taxonomic category-Order)
$A$. Wheat	$I$. Primata
$B$. Mango	$II$. Diptera
$C$. Housefly	$III$. Sapindales
$D$. Man	$IV$. Poales

$A$ body is thrown vertically upwards and reaches its maximum height in $t$ seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

$A$ photon and an electron have equal energy $E$. The ratio $\lambda_{\text{photon}} / \lambda_{\text{electron}}$ is proportional to: