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For a linear plot of log (x/m) versus log p in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are constants)

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The integral $∫_{0}1+4sin_{2}(2x )−4sin(2x )dx $equal

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

The integral $∫(x_{4}−1)_{41}dx $ equal:

The integral $∫_{2}gx_{2}+g(36−12x+x_{2})dxgx_{2} $ is equal to:

Match List-I (Electromagnetic wave type) with List-II (Its association/application) and select the correct option from the choice given below the lists :

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately :

In the following sequence of reactions : Toluene $→KMnO_{4}A→SOCl_{2}BBaSO_{4}→ H_{2}/Pd C,$ The product C is :