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How Do You Write A Log As A Sum Or A Difference

The sum of the logs is the log of a product. loga x + loga y = loga xy The difference of the logs is the log of a quotient loga x - loga y =... View Article

How Do You Find The Foci Of An Ellipse Not Centered At The Origin

Let (h, k) be the center of an ellipse. h and k define the position of the ellipse, where "h" units to the left or right and "k" units up or down... View Article

In A Nonleap Year The Probability Of Having 53 Fridays Or Saturdays Is

1) 3/7 2) 4/7 3) 2/7 4) 1/7 Solution: Option (3) 2/7 In a non-leap year, there are 365 days. It has 52 weeks and 1 extra day. The... View Article

If Ps 03 Pt 04 S And T Are Independent Events Then Pst

1) 0.2 2) 0.3 3) 0. 4 4) 0.12 Solution: Option (2) 0.3 Given that, P(S) = 0.3 P(T) = 0.4 P(S/T) = P(SnT)/P(T) P(SnT) = P(S).P(T)... View Article

There Are 10 Pairs Of Shoes In A Cupboard From Which 4 Shoes Are Packed At Random The Probability That There Is At Least One Pair Is

1) 99/323 2) 224/323 3) 100/323 4) None of these Solution: Option (1) 99/323 Total number of shoes = 10 pairs = 20 shoes The total... View Article

The Chance Of Getting A Doublet With 2 Dice Is

1) 2/3 2) 1/6 3) 5/6 4) 5/36 Solution: Option (2) ? If two dice are thrown, the total number of sample space = 36 The event of... View Article

A Problem In Mathematics Is Given To Three Students A B C And Their Respective Probability Of Solving The Problem Is 12 13 And 14 Probability

1) 3/4 2) 1/2 3) 2/3 4) 1/3 Solution: Option (1) 3/4 The probability that A solves the problem, P(A) = ½ The probability that B solves the... View Article

Two Cards Are Drawn Without Replacement From A Well Shuffled Pack Find The Probability That One Of Them Is An Ace Of Heart

1) 1/25 2) 1/26 3) 1/52 4) None of these Solution: Option (2) 1/26 Total number of cards in a pack = 52 Number of ace of hearts in... View Article

Find The Probability That The Two Digit Number Formed By Digits 1 2 3 4 5 Is Divisible By 4 While Repetition Of Digit Is Allowed

1) 1/30 2) 1/20 3) 1/40 4) None of these Solution: Option (4) None of these Total cases = 25 The event that the two digit numbers... View Article

The Probability That A Leap Year Will Have 53 Fridays Or 53 Saturday Is

1) 2/7 2) 3/7 3) 4/7 4) 1/7 Solution: Option (2) 3/7 In leap year, there are 366 days. A leap year contains 52 weeks and 2 days The... View Article

If A Coin Be Tossed N Times Then Probability That The Head Comes Odd Times Is

1) 1/2 2) 1/2n 3) 1/(2n-1) 4) None of these Solution: Option (1) 1/2 If a coin is tossed “n” number of times, the total sample space = 2n.... View Article

If Any Four Numbers Are Selected And They Are Multiplied Then The Probability That Last Digit In The Product Will Be 1 3 5 Or 7 Is

1) 4/625 2) 18/625 3) 16/625 4) None of these Solution: Option (3) 16/625 Total number of sample space = {0, 1, 2, 3, 4, 5, 6, 7, 8,... View Article

If Two Dice Are Thrown Simultaneously Then Probability That 1 Comes On First Dice Is

1) 1/36 2) 5/36 3) 1/6 4) None of these Solution: Option (3) 1/6 Total number of sample space, if two dice are thrown = 36 The... View Article

In A College 25 Of The Boys And 10 Of The Girls Offer Mathematics The Girls Constitute 60 Of The Total Number Of Students If A Student Is Selected

1) 1/6 2) 3/8 3) 5/8 4) 5/6 Solution: Option (2) ? Assume that there are 100 students in a college. Total number of girls = 60% =... View Article

A Pair Of A Dice Thrown If 5 Appears On At Least One Of The Dice Then Probability That The Sum Is 10 Or Greater Is

1) 11/36 2) 2/9 3) 3/11 4) 1/12 Solution: Option (3) 3/11 If two dice are thrown, the total number of cases = 36. Favourable cases:... View Article

From A Pack Of 52 Cards Two Cards Are Drawn In Succession One By One Without Replacement The Probability That Both Are Aces Is

1) 2/13 2) 1/51 3) 1/221 4) 2/21 Solution: Option (4) 1/221 Total number of cards in a pack = 52 Total number of aces in a pack = 4... View Article

The Probability Of Choosing At Random A Number That Is Divisible By 6 Or 8 From Among 1 To 90 Is Equal To

1) 1/6 2) 1/30 3) 11/80 4) 23/90 Solution: Option (4) 23/90 Total number of cases = {1, 2, 3, …, 90} Favourable cases: Total... View Article

Suppose That A Die With Faces Marked 1 To 6 Is Loaded In Such A Manner That For K 1 2 3 6 The Probability Of The Face Marked K Turning

1) 1/2 2) 4/7 3) 2/5 4) 1/21 Solution: Option (1) 1/2 Total cases = {1, 2, 3, 4, 5, 6} = 6 Favourable cases = {2, 4, 6}= 3 The... View Article

A Probability That In A Year Of The 22nd Century Chosen At Random There Will Be 53 Sundays Is

1) 3/28 2) 2/28 3) 7/28 4) 5/28 Solution: Option (4) 5/28 The probability that leap year occurs in 100 year = 25/100 = ¼ Hence, the... View Article

A Coin Is Tossed 4 Times The Probability That At Least One Head Turns Up Is

1) 1/16 2) 2/16 3) 14/16 4) 15/16 Solution: Option (4) 15/16 If four coins are tossed, the total cases = 24 = 16 In a toss, the... View Article