Three Squares Of A Chess Board The Chosen At Random The Probability That Two Are Of One Color And One Of Another Is 1) 16/21 2) 8/21 3) 32/12 4) None of these Solution: Option (1) 16/21 Total number of cases = 64C3 Two squares of one colour and... View Article
Out Of 21 Tickets Marked With Numbers From 1 To 21 Three Are Drawn At Random The Chance That The Numbers On Then Are In Ap Is 1) 10/133 2) 9/133 3) 9/1330 4) None of these Solution: Option (1) 10/133 Total Ways = 21C3 If the common difference is 1, then... View Article
Three Six Faced Fair Dice Are Thrown Together The Probability That The Sum Of The Numbers Appearing On The Dice Is K 3 Lte K Lte 8 Is 1) [(k-1)(k-2)]/432 2) [k(k-1)]/432 3) k2/432 4) None of these Solution: Option (1) [(k-1)(k-2)]/432 If three dice are, the total... View Article
A And B Toss A Fair Coin Each Simultaneously 50 Times The Probability That Both Of Them Will Not Get Tail At The Same Toss Is 1) (¾)50 2) (2/7)50 3) (⅛)50 4) (⅞)50 Solution: Option (1) (¾)50 For each toss, there will be 4 choices. Choice 1: A gets head, B... View Article
A Man Alternately Tosses A Coin And Throws A Dice Beginning With The Coin The Probability That He Gets A Head In The Coin Before Gets A 5 Or 6 1) 3/4 2) 1/2 3) 1/3 4) None of these Solution: Option (1) ¾ The probability of getting head, p = ½ The probability of getting 5 or... View Article
Two Squares Are Chosen At Random On A Chessboard The Probability That They Have A Side In Common Is 1) 1/9 2) 2/7 3) 1/18 4) None of these Solution: Option (3) 1/18 Out of 64 squares, two squares are selected = 64C2 ways = 32 x 63... View Article
A Box Contains 15 Tickets Numbered 1 2 15 Seven Tickets Are Drawn Probability That The Greatest Number On A Drawn Ticket Is 9 Is 1) (9/10)6 2) (8/15)7 3) (â…—)7 4) None of these Solution: Option (3) (â…—)7 Total outcomes = 157 Favourable outcomes = 97 (Since,... View Article
There Are N Urns Each Containing N 1 Balls E Denotes The Event Of Choosing Even Numbered Urn Pui 1n Then The Value Of Pwe Is 1) (n+2)/(2n+1) 2) (n+2)/(2(n+1)) 3) n/(n+1) 4) 1/(n+1) Solution: Option (2) (n+2)/(2(n+1)) P(E) = P(u2) + P(u4) + …+P(un) = (1/n)+... View Article
A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Conditional Probability That X Gte 6 Given X Gt 3 Equals 1) 125/216 2) 25/216 3) 5/36 4) 25/36 Solution: Option (4) 25/36. P[(X ≥ 6)/X>3] = [P[(X>3)/(X ≥ 6)].P(X ≥ 6) / P(X ≥ 6) =... View Article
A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Required The Probability That X Gte 3 Equals 1) 125/216 2) 25/36 3) 5/36 4) 25/216 Solution: Option (2) 25/36 P(X ≥ 3) = 1- [P(X=1) + P(x= 2)] P(X ≥ 3) = 1-[(⅙) +(⅙)(⅚)] P(X ≥... View Article
A Fair Die Is Tossed Repeatedly Until A Six Is Obtained Let X Denote The Number Of Tosses Required The Probability That X Equals 3 Equals 1) 25/216 2) 25/36 3) 5/36 4) 125/216 Solution: Option (1) 25/216 P(X= 3) = (â…š)(â…š)(â…™) P(X= 3) = 25/216.... View Article
Let U1 And U2 Be Two Urns U1 Contains 3 White And 2 Red Balls U2 Contains Only 1 White Ball The Probability That Head Appeared On The Coin 1) 17/23 2) 11/23 3) 15/23 4) 12/23 Solution: Option (4) 12/23 P(H) = ½, P(T) = ½, Let W be the event of drawing white ball form U2... View Article
Let U1 And U2 Be Two Urns U1 Contains 3 White And 2 Red Balls U2 Contains Only 1 White Ball Probability Of The Drawn Ball From U2 Being White 1) 13/30 2) 23/30 3) 19/30 4) 11/30 Solution: Option (2) 23/30 (i) Head - one white from U1, white from U2 = (½)(⅗)(2/2) = 3/10... View Article
A Box Contains 24 Identical Balls Of Which 12 Are White 12 Are Black The Probability That A White Ball Is Drawn For The 4th Time On The 7th Draw Is 1) 5/64 2) 27/32 3) 5/32 4) 1/2 Solution: Option (3) 5/32 Given that a box contains 24 identical balls, of which 12 are white and 12... View Article
A Dice Is Thrown 2n Plus 1 Times The Probability Of Getting 1 3 Or 4 At Most N Times Is 1) 1/2 2) 1/3 3) 1/4 4) None of these Solution: Option (1) ½ Let p be the probability of getting 1, 3 or 4 = 3/6= ½ q= 1-p=½ By... View Article
If A Straight Line Is Tangent To One Point And Normal To Another Point 1) x - y = √2 2) √2x - y = [(89 √2) / 27] + 1 3) x - y = 89√2 4) None of these Solution: (2) √2x - y = [(89 √2) / 27] + 1... View Article
Which One Of The Following Curves Cuts The Parabola 1) x2 + y2 = a2 2) y = e-x/2a 3) y = ax 4) x2 = 4ay Solution: (4) x2 = 4ay For y2 = 4ax, y-axis is tangent at (0, 0), while for x2... View Article
The Number Of Solutions Of The Equation 1) 0 2) 1 3) 2 4) 3 Solution: (1) 0 f (x) = x3 + 2x2 + 5x + 2 cos x f’ (x) = 3x2 + 4x + 5 - 2 sinx = 3 [(x + (2 / 3))2 + (11 /... View Article
A Cylindrical Gas Contained Is Closed At The Top And Open At The Bottom 1) 2 / 3 2) 1 / 2 3) 4 / 5 4) 1 / 3 Solution: (3) 4 / 5 Let h be the thickness of sides. Then that of the top will be 5h / 4. S... View Article
The Maximum Value Of X 2 X 1 X 2 X 1 For Real Values Of X Is 1) 1 / 2 2) 1 3) 2 4) 3 Solution: (4) 3 y = [x2 - x + 1] / [x2 + x + 1] y = [x2 - x + 1 + x - x] / [x2 + x + 1] y = 1 - [2x /... View Article