Which of the following quantities vary inversely as each other? The number of `x` men hired to construct a will and the time `y` takes to finish the job. The length `x` of a journey by bus and price `y` of the ticket Journey `(x\ k m)` undertaken by a car and the patrol `(y\ l i t r e s)` consumed by it.

Which of the following quantities vary directly with each other? (i) Number of articles (x) and their price (y). (ii) Weight of articles (x) and their cost (y). (iii) Distance x and time y, speed remaining the same. (iv) Wages (y) and number of hours (x) of work. (v) Speed (x) and time (y) (distance covered remaining the same) (vi) Area of a land (x) and its cost (y).

Fill in the blanks in each of the following so as to make the statement true: (i) Two quantities are said to vary ______ with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same. (ii) x\ a n d\ y are said to vary directly with each other if for some positive number k , _____ (iii) If u\ =3\ v , then u and v vary ______. with each other.

Check whether the following pair of statements are negation of each other. Give reasons for your answer.(i) x + y = y + x is true for every real numbers x and y.(ii) There exists real numbers x and y for which x + y = y + x

Find real values of x and y for which the complex numbers -3+i x^2y and x^2+y+4i are conjugate of each other.

Find real values of x and y for which the complex numbers -3+i x^2y and x^2+y+4i are conjugate of each other.

x+x+x+ .......(y\ t i m e s)=\

Which of the following statements are true and which are false? In each case give a valid reason for saying so, r : Circle is a particular case of an ellipse s : If x and y are integers such that x > y , then= -x<-y , t : sqrt(11) is a rational number.

Find real values of x and y for which the complex numbers 7 + ix^(2)y and x^(2) + y + 18i are conjugate of each other.

Find real values of x and y for which the complex numbers -5 + ix^(2)y and x^(2) + y + 35 i are conjugate of each other .

A physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as L_(x) , and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V_(x) and of widht D and he is swimming in direction perpendicular to the river flow with velocity V_(y) relation to river, assuming no use of directed lengths, the quantities of interest are then V_(x),V_(y) both dimensioned as (L)/(T) , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : S prop V_(x)^(a)V_(y)^(b)D^(c) Or dimensionally L=((L)/(T))^(a+b)xx(L)^(c) from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then V_(x) will be dimensioned as (L_(x))/(T), V_(y) as (L_(y))/(T), S as L_(x)" and " D as L_(y) . The dimensional equation becomes : L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c) and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. A conveyer belt of width D is moving along x-axis with velocity V. A man moving with velocity U on the belt in the direction perpedicular to the belt's velocity with respect to belt want to cross the belt. The correct expression for the drift (S) suffered by man is given by (k is numerical costant )