The vectors $b$ and $c$ are in the direction of north-east and north-west respectively and $|b|=|c|= 4$. The magnitude and direction of the vector $d = c - b$ are:

If $x-y+1=0$ meets the circle $x^2+y^2+y-1=0$ at $A$ and $B$,then the equation of the circle with $AB$ as diameter is

The catalyst and promoter respectively used in the Haber's process of industrial synthesis of ammonia are

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the triangle $ABC$,then the height of the tower is

Choose the correct option from the following:
$I$. Dehydration and dormancy of mature seed are crucial for seed storage.
$II$. Seed of $Lupinus \; arcticus$ is the oldest one which germinated after $2,000 \; years$.
$III$. Orchid seed is one of the largest seeds in the plant kingdom.
$IV$. Seeds of parasitic plants $Orobanche$ and $Striga$ are tiny seeds.