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Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical.Ans) 48 terms would be common to both the series...first take common terms in both series..7, 13,.....so,this has a common difference of 4 starting with 7.now last term of the given series are 201 and 301 respectively..So we can end our calculation by checking upto 201.201=7+(n-1)4----->n=48(we have to take integer nearest to it)
Stratified sampling In stratified sampling case the population is divided into groups in such a way that units in each group are as same as possible in a process called strati
3 items x, y and z will have 6 different permutations however only one combination. The given formular is generally used to determine the number of combinations in a described situ
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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Given that 2t 2 y′′ + ty′ - 3 y = 0 Show that this given solution are form a fundamental set of solutions for the differential equation? Solution The two solutions f
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