MATHS(XSTD)- 1/10 : MATHS(XSTD)- 1/10 BY
MANJULA B
manjulab64@gmail.com
INTRODUCTION : INTRODUCTION THIS SESSION RUNS FOR 60 MINUTES
PLEASE ENSURE YOUR AUDIO SETTINGS CORRECTLYE
THIS IS AN AUDIO CLASS ONLY
CLASSES WILL BE RESCHEDULED IF ENCOUNTERED WITH TECHNICAL PROBLEMS LIKE AUDIO DISBURNANCE, POWER CUTS ,INTERNET ISSUES.
LAST TWENTY MINUTES DEVOTED FOR STUDENTS FOR ATTENDING TO TEST BEFORE END OF CLASS.
TOPICS ARE SELECTED AND RESTRICTED TO SYLLABUS PRESCRIBED
ABOUT SEQUENCES : ABOUT SEQUENCES IN THIS FIRST CLASS , WE WILL LEARN ABOUT SEQUENCE
A SEQUENCE IS AN ORDERED ARRANGEMENT OF NUMBERS ACCORDING TO A GIVEN RULE
SEQUENCES HAVING FINITE NUMBER OF TERMS ARE CALLED FINITE SEQUENCES
A SEQUENCE HAVING INFINTE NUMBER OF NUMBERS IS AN INFINITE SEQUENCE
WE DISCUSS ARTITHEMATIC PROGRESSION WHICH IS A SEQUENCE IN WHICH DIFFERENCE BETWEEN THE TERM AND THE PRECEDING TERM IS CONSTANT. WE WILL SEE THIS IN EXAMPLES
PLEASE PLEASE MEMORISE : PLEASE PLEASE MEMORISE SUM OF FIRST ‘n’ NATURAL NUMBERS
Tn = a + (n - 1)d
SUM OF FIRST ‘n’ TERMS OF AN AP
Sn = n(n+1)/2 or denoted by ? N
SUM WHERE FIRST TERM ‘a’ COMMON DIFFERENCE IS D
Sn = ?/2[2a + (n-1) d]
SUM WHERE FIRST TERM IS a AND LAST TERRN IS l
Sn = ?/2 = n/2(a+l)
nthTERM OF AN AP, WHERE a IS FIRST TERRM AND D IS COMMON DIFFERENCE
QUESTIONS ON SEQUENCES : QUESTIONS ON SEQUENCES 1)What are sequences
a)1 2 3 4 5 b)7 5 4 3 2 1 c)3 7 11 15
d) 1 -1 -3 -5 e) ½ 1/3 ¼ 1/5
Ans:
2)Find the next three terms
3/1 4/3 5/4 ----- ------ -------
3)Test whether 25 is an term of an Arithematic Progression 6 9 12 Y/N
4)Sum of 3+7+11+…………upto 35terms
Ans:
QUESTIONS ON SEQUENCES-CONTD : QUESTIONS ON SEQUENCES-CONTD 5) Sum of first 25 odd natural numbers
Ans:
6) Find sum of natural numbeers from 1 to 50
Ans:
7) Sum of all natural numbers below 50
which are divisible by 7
Ans:
QUESTIONS ON SEQUENCES-CONTD : QUESTIONS ON SEQUENCES-CONTD 8) Fifth term of an AP is 15 and the fifteenth term is 5. Find the 20th term
Ans:
9)Sum of three numbers in AP is 36 and their product is 1680. Find the Numbers
Ans:
10) The angles of a quadrilaternal are in AP. If the smallest angle is 15 degrees, find the angles of the quadrilaternal.
Ans:
OTHER TYPES OF PROGRESSION : OTHER TYPES OF PROGRESSION A Geometric Progression is sequence in which ration of term and its preceding term is a constant, called common ratio “r”
Nth term of the GP Tn = ar n-1
Sum of first n terms of GP
Sn=a(r?n -1)/r-1 if r>1; Sn=a(1-r?n)/1-r if r<1
A sequence in which the reciprocals of terms form an AP is known as Harmonic Progression(HP)
Tn=1/a+(n-1)d
ARTHMETIC, GEOMETRIC AND HARMONIC MEANS : ARTHMETIC, GEOMETRIC AND HARMONIC MEANS If a and b are any two number, then
AM=(a+b)/2 (A); GM = vab(G); HM= 2ab/a+b(H)
So, If a,A,b are in AP, then A = a+b/2
If a, G ,b are in GP, the G = vab
If a, H, b are in HP, then H = 2ab/a+b
ALSO, IF A, G AND H ARE AM, GM AND HM RESPECTIVELY between any two numbers a and b, theN A G H form a descending GP
QUESTIONS on GP &HP : QUESTIONS on GP &HP 1) If 2,4,8,16…is a GP, then a= _____&r=____
2) The AM,GM and HM between 2 and 32 are A =____, G = _____ and H______
3) Which term of GP 1, 2 4 … will be 256? ___term
4) The common ration of a GP in which S2 = 6 and a=2 is _________
5) In a GP of six terms the first and last terms are 5 and 160, find the remaining terms__ ___ ____ ___
QUESTIONS ON GP&HP(CONTD) : QUESTIONS ON GP&HP(CONTD) 6)In a HP, T4 =1/12 and T10= 1/42, then T12th of an HP is _______
7)The GM between 4 & 37 is _____
8) The HM between 2 and 6 is _____
9)The three numbers in GP, whose sum is 26 and product is 216 are ___ ____ ____
10)If A G H are in AM, GM and HM of pair of numbers, verify that A G H are in GP & A>G>H
PERMUTATION & COMBINATION : PERMUTATION & COMBINATION Fundamental Principle of counting says that if one event occurs in “m” different ways and another even occurs independently in “n” different ways, then the two events together occur in m x n ways
Permutation is an orderly arrangement of objects
n P r represents permutation of n things taking r at a time
n C r represents combination of n things taking r at a time
FORMULAE TO MEMORISE : FORMULAE TO MEMORISE n P r = n(n-1)(n-2)……………( n-r+1), where both n and r are positive integers n is greater than or equal to r
Factorial n is represented by n! or I n is a continuous product of first n natural numbers
n C r = n P r /r!
QUESTIONS ON P&C : QUESTIONS ON P&C 1)The value of 5 P 3 is _______
2) The total number of three digit numbers that can be formed from the digits 1,2,3,4,5 is ___
3) The number of permutations of the letters of the word “LUCKY” without repetition of any letter____
4) The number of combinations of 4 letters that are possible from the word “PROBLEM” ARE _____
5) If Ten friends shake hands mutually, then the total number of handshakes will be _______
QUESTIONS ON P&C-CONTD : QUESTIONS ON P&C-CONTD 6)Find the permutations of 5 persons sitting in the chairs in a row _____
7) There are 3 white and 5 red roses in a garden. In how many ways can a flowers of which two are red be plucked. _____
8)In how many ways can a committee of 2 persons be chose out of a group of 5 persons____
9)The number of diagonals that cana be drawn in a pentagon is ______
10) Mr. Sewag is one among 15 cricketers. In how many ways a cricket team of ELEVEN can be formed.
KIND ATTENTION PLEASE : KIND ATTENTION PLEASE This class is uploaded in the contents folder
Learners are requested to browse through the presentation, which is self explanatory
In case of non-conduct of class due to power failure, internet problems, the matter is available in the wiziq site.
Depending upon the learners’ requests, the class may be rescheduled/repeated
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