

7logp+((3)^(1/2))/2logq-(1/2)log2r =logp^(7)+logq^((3^(1/2))/2)-log2r^(1/2) =log((p^(7)*q^((3^(1/2))/2))/(2r^(1/2))
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No of students who passed in atleast one subject: AUB=65+70-50=85 If total students are 100 .no of students who failed in both subjects = total students-students who passed in atleast one subjective. 100-85=15
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Total fruits are 12. Chances to select banana or apple is: 4+3=7 Probability =7/12
So option (b) is correct.
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LCM (20,30, 40) = 120 and HCF of (20, 30, 40) = 10 Hence Difference of LCM and HCF = 120 – 10 = 110
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Apply Allegation Rule :
Average Age of girl 12.3 Average Age of Boys 12.5
Average age of class 12.42
We get ratio between boys and girls - 1 : 1
Total no. of students is 50 i.e 25:25