In a handloom factory different workers workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon.

The time required for students to do a science experiment and the number of students is shown is the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.

Atom of seven elements A,B ,C, D, E,F and G have a different number of electronic shells but have the same number of electrons in their outermost shells. The element A and C combine with chlorine to form an acid and common salt respectively. The oxide of element A is liquid at room temperature and is a neutral substance while the oxides of the remaining six elements are basic in nature . Based on the above information, anwer the following question given ahead : Will element A to G belong to the same period or same group of the periodic table ?

A firm produced 2 different products A and B. Each product has to undergo three operations before takes the shape. The profit per unit and time required per unit of each product in each operation is tabulated below. To formulate a linear programming problems write (i) the non-negativity constraints (ii) Cutting constraints . (iii) Mixing constraints (iv) Packing constraints (v) Objective function

Below is given the frequency distribution of Daily wages (in rs ) of 130 workers . Find the modal wages of a worker .

Covalent radii (in A) for some elements of different groups and periods are listed below. Plot these values against atomic number. From the plot, explain the variation along a period and a group. 2^nd group elements : Be (0.89), Mg (1.36), Ca (1.74), Sr (1.91) Ba(1.98) 17^th group elements : F (0.72), CI (0.99), Br(1.14). T (1.33) 3^rd Period elements : Na(1.57), Mg(1.36). AI (1.25), Si(1.17). P(1.10), S(1.04). C1(0.99) 4^th period elements : K(2.03), Ca(1.74). Sc(1.44). Ti(1.32), V(1.22), Cr(1.17), Mn(1.17) Fe(1.17). Co(1.16). Ni(1.15). Cu(1.17). Zn(1.25), Ga(1.25). Ge(1.22). As(1.21). Se(1.14). Br(1.14)

The electronegativity for some elements on pauline scale of different groups and periods are listed below. Plot these values against atomic number. From the pattern, explain the variation along a period and a group. 2^nd group elements : Be (1.6), Mg (1.2). Ca (1.0), Sr (1.0) Ba(0.9) 17^(th) group elements : F (4.0), CI (3.0), Br (2.8). I (2.5) 3^rd Period elements : Na(0.9), Mg(1.2), AI (1.5), Si(1.8), P(2.1), S(2.5), CI(3.0) 4^th period elements : K(0.8), Ca(1.0). Sc(1.3), Ti(1.5), V(1.6), Cr(16), Mn(1.5), Fe(1.8). Co(1.9), Ni(1.9). Cu(1.9). Zn(16), Ga(16), Ge(1.8), As(2.0), Se(2.4), Br(2.8)

Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs. a. 21 cm (wavelength emitted by atomic hydrogen in interstellar space). b. 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen , known as Lamb shift). c. 2.7 K [temperature associated with the isotropic radiation filling all space - thought to be a relic of the 'big-bang' origin of the universe]. d. 5890 Å-5896 Å [double lines of sodium] e. 14.4 keV [energy of particular transition in ""^(57)Fe nucleus associated with a famous high resolution spectroscopic method (Moss bauer spectroscopy)].

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by (d P)/(dx)=100-12sqrt(xdot) If the firm employs 25 more workers, then the new level of production of items is (1) 3000 (2) 3500 (3) 4500 (4) 2500