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Abstract Algebra By S.K Mapa solution

IIT JAM Mathematics 2022 Short Note on Differential Equation.

Differential Equation
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Rigid body motion/ex-viii/R.M. Khan page 58

 Invariants under Orthogonal Transformation   Orthogonal Transformation We consider here three types of transformation of axes or transformation of coor dinates, namely  translation  rotation  translation and rotation .  These are called orthogonal transformation when both the systems of axes are rectangular.  The combination of translation and rotation is called a rigid body motion.  Invariants Some expressions remain unchanged under an orthogonal transformation. These known as invariants of orthogonal transformation. ----------------------------------------------------------------------------------------------------------------                     Exercises-viii The origin is shifted to the point (3.-3) without changing the directions of axes. If the coordinates of P, Q, R are (5,5), (-2, 4) and (7.-7) respectively in the new system, find the coordinates of these points in the old system.  2...

Analytical geometry of two dimensions by R.M. Khan

 Analytical geometry of two dimensions by R.M. Khan 1.👉 Transformation of axes The coordinates of a point depend on the position of axes. Thus the coordinates of a point and consequently the equation of a locus will be changed with the alteration of origin without the alteration of direction axes, or by altering the direction of axes and keeping the origin fixed, or by altering the origin and also the direction of axes. Either of these processes is known as transformation of ares or transformation of Coordinates.   2.👉 Change of origin without change of direction of axes Let (x, y) be the coordinates of P w.r.t rectangular axes OX and OY and (x',y') be the coordinates of it w.r.t. a new set of axes O'X' and O'Y' which are parallel to the original axes OX and OY respectively.  Let (Îą,β) be the coordinates of the new origin O' w.r.t. axes OX and OY PN is perpendicular to OX and it meets O'X' at N'. O'T is perpendicular to OX. ON = x,.   NP = ...

Group Theory (by Abstract Algebra) Exercise 14 solution pdf

 Group Theory (by Abstract Algebra)  Exercise 14 solution pdf    Exercise 14         👉Normal Subgroup         👉 Quotient group Normal subgroup:     We absorve that when G=(Z,+) and H=(3Z,+) and, H=(3Z,+), each left coset of H  is also a right coset of H ; when G=S3 and H={po,p1,p2), each left coset of H is also a right coset of H . But when G=S3 and H={po,p3}, H is a left coset as well as a right coset  and other left cosets are not right cosets .       Thus we see that for some subgroup the left cosets and and the right cosets  and right cosets differ.     Defination.Normal subgroup:        A subgroup H of a group G is said to be a normal subgroup of G if Ha=aH holds for all a in G. The standard notation for "H is a normal subgroup of G ,is H∆G. Note 1.  The condition aH = Ha does not demand that for every h â‚ŦH,    ah=ha. Note 2. When H is a...

Real Analysis by sk mapa ex-11

Real Analysis by sk mapa ex-11 āĻ¤ā§‹āĻŽāĻ°āĻž āĻ†āĻŽāĻžāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻ•āĻ°āĻž pdf āĻ¯āĻžāĻ°āĻž āĻ¯āĻžāĻ°āĻž āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°āĻ›ā§‹ āĻ¤āĻžāĻĻā§‡āĻ° āĻ•āĻžāĻ›ā§‡  āĻ†āĻŽāĻžāĻ° āĻāĻ•āĻŸāĻž  request ,āĻ¤ā§‹āĻŽāĻ°āĻž āĻĻā§ŸāĻž āĻ•āĻ°ā§‡ āĻœāĻžāĻ¨āĻžāĻŦā§‡ āĻ†āĻŽāĻžāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻ—ā§āĻ˛ā§‹ helpful āĻ•āĻŋāĻ¨āĻž ,āĻĒāĻ°ā§‡āĻ° āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻĻā§‡āĻŦ āĻ•āĻŋāĻ¨āĻž , āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡āĻ° āĻ‰āĻĒāĻ°  āĻ†āĻŽāĻžāĻ° āĻ­āĻŋāĻĄāĻŋāĻ“ upload āĻ•āĻ°āĻžāĻ° āĻ‡āĻšā§āĻ›āĻž āĻĄāĻŋāĻĒā§‡āĻ¨ā§āĻŸ āĻ•āĻ°ā§‡ āĨ¤ āĻ†āĻŽāĻŋ āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡āĻ° āĻ‰āĻĒāĻ° āĻ¨āĻŋāĻ°ā§āĻ­āĻ° āĻ•āĻ°ā§‡āĻ‡ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ†āĻĒāĻ˛ā§‹āĻĄ āĻ•āĻ°āĻŋāĨ¤ āĻ¤ā§‹āĻŽāĻ°āĻž āĻ¯āĻĻāĻŋ āĻ•āĻŋāĻ›ā§ āĻ•āĻŽā§‡āĻ¨ā§āĻŸ  āĻ¨āĻž āĻ•āĻ°ā§‹ āĻ¤āĻžāĻšāĻ˛ā§‡ āĻĒāĻ°āĻŦāĻ°ā§āĻ¤ā§€ āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ°ā§‡āĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻĻā§‡āĻ“ā§ŸāĻžāĻ° āĻĒā§āĻ°āĻ¤āĻŋ āĻ†āĻŽāĻžāĻ° āĻ•ā§‹āĻ¨ā§‹ āĻ†āĻ—ā§āĻ°āĻš āĻĨāĻžāĻ•āĻ›ā§‡ āĻ¨āĻžāĨ¤āĨ¤ āĻāĻŸāĻž āĻ¸āĻ¤ā§āĻ¯āĻŋ āĻ†āĻŽāĻŋ āĻ¯āĻ–āĻ¨ youtube line āĻ āĻāĻ¸ā§‡āĻ›āĻŋāĻ˛āĻžāĻŽ āĻ¨āĻž āĻ¤āĻ–āĻ¨ āĻ†āĻŽāĻŋāĻ“ āĻ­āĻžāĻŦāĻ¤āĻžāĻŽ āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡āĻ° āĻ‰āĻĒāĻ° āĻĄāĻŋāĻĒā§‡āĻ¨ā§āĻĄ āĻ•āĻ°āĻ›ā§‡ āĻ¤āĻžāĻāĻ° āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ†āĻĒāĻ˛ā§‹āĻĄ āĻ•āĻ°āĻžāĻ° āĻ‡āĻšā§āĻ›āĻž āĻāĻŸāĻž āĻ•ā§‡āĻŽāĻ¨ āĻ•āĻĨāĻžāĨ¤āĨ¤       āĻ•āĻŋāĻ¨ā§āĻ¤ā§ āĻāĻ–āĻ¨ āĻ†āĻŽāĻŋ āĻĒā§āĻ°āĻžāĻ•āĻŸāĻŋāĻ•ā§āĻ¯āĻžāĻ˛ āĻ‰āĻĒāĻ˛āĻŦā§āĻ§āĻŋ āĻ•āĻ°āĻ›āĻŋāĨ¤ āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° āĻĒāĻœāĻŋāĻŸāĻŋāĻ­ āĻ•āĻŽā§‡āĻ¨ā§āĻŸ āĻ†āĻŽāĻžāĻ•ā§‡ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ¤ā§ˆāĻ°āĻŋ āĻ•āĻ°āĻ¤ā§‡ āĻ†āĻ—ā§āĻ°āĻšā§€ āĻ•āĻ°ā§‡ āĻ¤ā§‹āĻ˛ā§‡āĨ¤          āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ°  āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡āĻ° āĻŽāĻžāĻ§ā§āĻ¯āĻŽā§‡āĻ‡ āĻ†āĻŽāĻŋ āĻœāĻžāĻ¨āĻ¤ā§‡ āĻĒāĻžāĻ°āĻŦā§‹ āĻ†āĻŽāĻžāĻ° āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻ•āĻ¤āĻœāĻ¨āĻ•ā§‡ āĻšā§‡āĻ˛ā§āĻĒ āĻ•āĻ°āĻ›ā§‡ āĨ¤ āĻ¤āĻžāĻ°āĻœāĻ¨ā§āĻ¯ āĻĻā§ŸāĻž āĻ•āĻ°ā§‡ āĻ¤ā§‹āĻŽāĻ°āĻž āĻ¸āĻŦāĻžāĻ‡ āĻ•āĻŋāĻ›ā§ āĻ¨āĻž ,āĻ•āĻŋāĻ›ā§ āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡ āĻ•āĻ°ā§‹ āĻ†āĻŽāĻ°āĻž āĻ­āĻŋāĻĄāĻŋāĻ“ āĻāĻ° āĻ•āĻŽā§‡āĻ¨ā§āĻŸ āĻŦāĻ•ā§āĻ¸ā§‡āĨ¤āĨ¤ Pdf Download click here Download pdf and follow the condition. Condition:1       pdf āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°āĻžāĻ°...

10 series Full solution Real Analysis by sk mapa

Series Exercise 10 solution series āĻšā§āĻ¯āĻžāĻĒā§āĻŸāĻžāĻ° āĻāĻ° āĻāĻ•ā§āĻ¸āĻžāĻ°āĻ¸āĻžāĻ‡āĻœ 10 āĻāĻ°full āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻĒā§‡āĻ¤ā§‡ āĻ¨āĻŋāĻšā§‡āĻ° āĻ¨āĻŋā§ŸāĻŽ āĻ—ā§āĻ˛ā§‹ āĻĢāĻ˛ā§‹ āĻ•āĻ°ā§‹āĨ¤āĨ¤ Real analysis āĻāĻ° āĻ†āĻ°ā§‹ āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻĒā§‡āĻ¤ā§‡ āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° molecule of mathematics channel āĻŸāĻŋ subscribe āĻ•āĻ°āĻŦā§‡ āĻāĻŦāĻ‚ āĻŦā§‡āĻ˛ āĻŦā§‹āĻ¤āĻžāĻŽ āĻŸāĻŋ on āĻ•āĻ°ā§‡ āĻĻā§‡āĻŦā§‡āĨ¤āĨ¤ How to download Exercise 10 solution?   āĻ¨āĻŋāĻšā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ link āĻĨā§‡āĻ•ā§‡ āĻāĻ‡ pdf āĻŸāĻŋ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°ā§‡ āĻ¨ā§‡āĻ“ā§ŸāĻžāĻ° āĻĒāĻ°,open āĻ•āĻ°āĻžāĻ° āĻ¸āĻŽā§Ÿ āĻāĻ•āĻŸāĻž āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻ˛āĻžāĻ—āĻŦā§‡āĨ¤ āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻŸāĻŋ āĻĒāĻžāĻ“ā§ŸāĻžāĻ° āĻœāĻ¨ā§āĻ¯ āĻ…āĻŦāĻļā§āĻ¯āĻ‡ āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° āĻšā§āĻ¯āĻžāĻ¨ā§‡āĻ˛ molecule of mathematics āĻ āĻ—āĻŋā§Ÿā§‡ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻĻā§‡āĻ–āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤ āĻ­āĻŋāĻĄāĻŋāĻ“āĻ¤ā§‡ āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻĻā§‡āĻ“ā§ŸāĻž āĻ°ā§Ÿā§‡āĻ›ā§‡āĨ¤āĨ¤ Facebook āĻ ubdate āĻĒā§‡āĻ¤ā§‡ : āĻāĻ•ā§āĻ¸āĻžāĻ°āĻ¸āĻžāĻ‡āĻœ āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻ¸āĻŽā§āĻŦāĻ¨ā§āĻ§ā§€ā§Ÿ ubdate āĻĒā§‡āĻ¤ā§‡ āĻšāĻ˛ā§‡ āĻ¤ā§‹āĻŽāĻžāĻĻā§‡āĻ° sk mapa exercise solution āĻ¨āĻžāĻŽāĻ• facebook page āĻŸāĻŋ āĻĢāĻ˛ā§‹ āĻ•āĻ°ā§‹āĨ¤āĨ¤ Follow : Like on Facebook Download pdf: clik here Download pdf and follow the condition. Condition:1       pdf āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°āĻžāĻ° āĻĒāĻ° āĻ¯āĻ–āĻ¨ pdf āĻŸāĻž āĻ“āĻĒā§‡āĻ¨ āĻ•āĻ°āĻŦā§‡ āĻ¤āĻ–āĻ¨ āĻāĻ•āĻŸāĻž āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻšāĻžāĻ‡āĻŦā§‡āĨ¤āĨ¤ condition:2    āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻŸāĻŋ āĻĒāĻžāĻ“ā§ŸāĻžāĻ° āĻœāĻ¨ā§āĻ¯ āĻ¨āĻŋāĻšā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ˛āĻŋāĻ‚āĻ•ā§‡ āĻ•ā§āĻ˛āĻŋāĻ• āĻ•āĻ°ā§‡ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻŸāĻž āĻĻā§‡āĻ–āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤āĨ¤ condition:3 āĻ­āĻŋāĻĄāĻŋāĻ“āĻŸāĻžāĻ¤ā§‡āĻ‡ āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻĻā§‡āĻ“ā§ŸāĻž āĻ†āĻ›ā§‡āĨ¤āĨ¤

Real Analysis by sk mapa # series #exercise 9 solution

Index Real Analysis by S.K. Mapa Exercise Solution   āĻ¯āĻžāĻ°āĻž āĻāĻ–āĻ¨ā§‹ sequence āĻ° solution āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°ā§‹āĻ¨āĻŋ āĻ¤āĻžāĻ°āĻž āĻāĻ–āĻ¨āĻ‡ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°ā§‡ āĻ¨āĻžāĻ“āĨ¤āĨ¤āĨ¤ āĻāĻ‡ āĻĒā§‹āĻ¸ā§āĻŸāĻŸāĻŋāĻ¤ā§‡ series āĻāĻ° āĻāĻ•ā§āĻ¸āĻžāĻ°āĻ¸āĻžāĻ‡āĻœ 9 āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻĻā§‡āĻ“ā§ŸāĻž āĻ†āĻ›ā§‡āĨ¤āĨ¤ Real Analysis by sk mapa # series #exercise 9 solution How to download series exercise solution āĻāĻ‡  exercise  āĻāĻ° pdf āĻĒā§‡āĻ¤ā§‡ āĻšāĻ˛ā§‡ āĻ¨ā§€āĻšā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ˛āĻŋāĻ‚āĻ•ā§‡ click āĻ•āĻ°ā§‡ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°āĻžāĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻĻā§‡āĻ–ā§‡ āĻ¨āĻŋāĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤āĨ¤āĨ¤ āĻ¨ā§€āĻšā§‡ āĻĻā§‡āĻ“ā§ŸāĻž pdf āĻ˛āĻŋāĻ‚āĻ•ā§‡ click āĻ•āĻ°āĻ˛ā§‡ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻšā§Ÿā§‡ āĻ¯āĻžāĻŦā§‡ āĻ•āĻŋāĻ¨ā§āĻ¤ā§ āĻ“āĻĒā§‡āĻ¨ āĻ•āĻ°āĻžāĻ° āĻœāĻ¨ā§āĻ¯ āĻāĻ•āĻŸāĻž āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻ˛āĻžāĻ—āĻŦā§‡ āĨ¤āĨ¤āĻĒ  āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻŸāĻž āĻĒāĻžāĻ“ā§ŸāĻžāĻ° āĻœāĻ¨ā§āĻ¯ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ¤āĻž āĻĻā§‡āĻ–āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤āĨ¤ LIKE ON FACEBOOK .     FOLLOW US pdf download click here Download pdf and follow the condition. Condition:1       pdf āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ•āĻ°āĻžāĻ° āĻĒāĻ° āĻ¯āĻ–āĻ¨ pdf āĻŸāĻž āĻ“āĻĒā§‡āĻ¨ āĻ•āĻ°āĻŦā§‡ āĻ¤āĻ–āĻ¨ āĻāĻ•āĻŸāĻž āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻšāĻžāĻ‡āĻŦā§‡āĨ¤āĨ¤ condition:2    āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻŸāĻŋ āĻĒāĻžāĻ“ā§ŸāĻžāĻ° āĻœāĻ¨ā§āĻ¯ āĻ¨āĻŋāĻšā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻ­āĻŋāĻĄāĻŋāĻ“ āĻ˛āĻŋāĻ‚āĻ•ā§‡ āĻ•ā§āĻ˛āĻŋāĻ• āĻ•āĻ°ā§‡ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻŸāĻž āĻĻā§‡āĻ–āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤āĨ¤ condition:3 āĻ­āĻŋāĻĄāĻŋāĻ“āĻŸāĻžāĻ¤ā§‡āĻ‡ āĻĒāĻžāĻ¸āĻ“ā§ŸāĻžāĻ°ā§āĻĄ āĻĻā§‡āĻ“ā§ŸāĻž āĻ†āĻ›ā§‡āĨ¤āĨ¤ watch video on youtube  click here āĻāĻ‡ āĻĒā§āĻ°āĻĨāĻŽ āĻāĻ‡ āĻ°āĻ•...