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 Meanings Into Words (Upper-Intermediate) STUDENT'S BOOK HSEB Class: XII SCIENCE | MANAGEMENT | EDUCATION | ARTS 5.1 HOW LONG? Rules : 1. Activities : if the action is not complete and the actor could not show his achievement, that is activity.             Question: How long did + sub + v1 +obj + for?              Prepositions:   Period of time = for                                      Point of time = until 2. Achievement : If the action is complete and the actor could show his/her achievement what he/she had done, that is achievement.             Question: How long did it take + sub (objective form) + to + v1 + obj?       [he = him, she = her, they = them, I = you]             Prepositions:    Period of time = in   ...

Conic Section (Notes) Definition : The locus of a point which moves in a plane in such a way that the ratio of its distance from a fixed point to its distance from a fixed line is constant is called a conic section. The fixed point is called focus , the fixed line is called directrix and the constant ratio is called the eccentricity (e). Any line through focus and perpendicular to directrix is called the axis of conic section. Note: (1) When the eccentricity is equal to unity i.e. e = 1 then the conic section is called parabola.           (2) When the eccentricity is less than unity i.e. e < 1 then the conic section is called ellipse.          (3) When the eccentricity is greater than unity i.e. e > 1 then the conic section is called hyperbola. Parabola :- The locus of a point in a plain which moves in such a way that it is always equidistant from a fixed point (focus) and from a fixed line (directrix) is called a par...

Plane:- A surface such that the straight line joining any two point on it lies wholly on the surface is called a plane. Equation of Plane:- The equation of plane is the general equation of first degree in x, y, z : Ax + By + Cz + D = 0 when A, B, C, D re constant and A, B, C are not all zero. Equation of plane in intercept from:- Let the equation of plane be, Ax + By + Cz + D = 0         ........(i) which meets x-axis at point (a,0,0); then, A.a + B.0 + C.0 + D = 0 or, Aa = -D or, A = -D a 1 2 Similarly, plane (i) meets y-axis and z-axis at the point (0,b,0) and (0,0,c); than, we get; B = -D b and C = -D c

A boy puts his hand into a bag which contains 10 differently coloured marbles and brings out 3. How many different results are possible? Solution :  3 marbles can be choosen from 10 marbles in,                 C(10, 3) = 10 ! 7 ! .3 ! = 10 ∗ 9 ∗ 8 3 ∗ 2 ∗ 1 = 120 ways.   Find the number of ways in which a student can select 5 courses out of 8 courses. If 3 courses are compulsory, in how many ways can the selections be made? Solution : The student can be select 5 courses out of 8 courses in,                 C(8, 5) = 8 ...