31. If 5√5 x 5^3 + 5^-3/2 = 5 ^(a + 2), then the value of a is:
Answer:
Explanation:5^1x5^1/2x5^3+5^-3/2 = 5^(a+2)
5^3/2x5^3+5^-3/2
5^9/2+5^-3/2
5^6/2
5^3 = 5^(a+2)
now, 3 = a+2
a=1
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32. A and B can do a piece of work in 12 days, B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each take to complete the job?
Answer:
Explanation:(A+B)'s one day work is 1/12
(B+C)'s one day work is 1/15
(C+A)'s one day work is 1/20
Thus,2(A+B+C)'s one day work is 1/12+1/15+1/20=1/5
so,(A+B+C) can complete the work in 10 days.
(A+B+C)'s one day work=1/10
A 's one day work=1/10-1/15=1/30
B's one day work=1/10-1/20=1/20
C's one day work=1/10-1/12=1/60
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MindTree HCL Technologies Broadcom Ltd
33. There are two sections in a question paper each contain five questions. A student has to answer 6 questions. Maximum no. of questions that can be answered from any section is 4. How many ways he can attempt the paper?
Answer:
Explanation:If the max number from each section is 4 and a total of 6 questions must be answered then the possible ways to answer are:
4 from A and 2 from B
or 2 from A and 4 from B
or 3 from both A and B
Number of ways of choosing 4 from part A AND 2 from part B = 5C4 * 5C2 = 50 ... (AND means multiply)
Number of ways of choosing 2 from part A AND 4 from part B = 5C2 * 5C4 = 50
Number of ways of choosing 3 from part A AND 3 from part B = 5C3 * 5C3 = 100
So total number of ways to answer the paper = 50 + 50 + 100 = 200
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MindTree HCL Technologies Broadcom Ltd
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