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how many four-digit numbers can be formed that haVe the digit 5 used exactly once in them? given ans is 3033 which i am not getting

plz elaborate the series topic

If n items are to arranged in a line of which r items must never be together, we can arrange them in (n-r)!r! n−r+1Crn−r+1Cr ways, provided n-r is greater than r. Can someone explain the formulae
here?

How do i solve Syllogism questions?

A sales executive gets 20% bonus of the total sales value and 10% commision besides the bonus on the net profit after charging such commision. If the total sales value be rs. 10 lakh per annum and the total profit of the company be rs. 1.32 lakh per annum, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company?

What is the CAT Exam fee?

2 circles touch each other externally and a single direct common tangent is drawn from a point O to the two circles as shown in the figure. The length of OA is 20 cm and the length of OB is 30 cm. Length of OR = 16 cm. The image is https://cracku.in/media/radpress/entry_images/Screenshot_2015-04-09_13.16.15.png . Can't we solve this question by OB^2=OS*(OS+2SY). here OS will be 25. hence, 900 = 25 ( 25+2x). so the answer will be 5.5. hence the diameter is 11. now obviously i am wrong. i just cant find out where. can u please help me out? By the way, i am assuming chord OY to be extended till the end of the circle Y.

I am unable to take the missed free Mocks and also unable to view the solutions of the ones i have taken..I was able to view them earlier..What is the issue?Looking forward to a solution soon

If 3 coins are tossed are together,find
the probability that at least one of the coins show head.
please explain it clearly

RAM took aloan a loan of RS 15000 from laxman it was agree that to pay 8℅simple interest per annum for three years and 10℅compound interest annually on fourth year onwards so how much amount he want to pay at the end if fifth year