If The Function F X Ax 3 Bx 2 11x 6 Satisfies The Condition Of Rolle S Theorem 1) -1, 6 2) -2, 1 3) 1, -6 4) -1, 1/2 Solution: f (x) = ax3 + bx2 + 11x - 6 The function f(x) satisfies the Rolle's theorem in... View Article
F X E 2x 1 E 2x 1 1) an increasing 2) a decreasing 3) an even 4) None of these Solution: (1) an increasing f (x) = [e2x - 1] / [e2x + 1] f’ (x) =... View Article
A Die Is Tossed Twice Getting A Number Greater Than 4 Is Considered A Success The Variance Of Probability Distribution Of Number Of Successes Is 1) 2/9 2) 4/9 3) 1/3 4) None of these Solution: Option (2) 4/9 p = 2/6 = ⅓ q= ⅔ n= 2 Variance = npq = 2(⅓)(⅔) Variance= 4/9.... View Article
A Die Is Tossed Thrice If Getting A Four Is Considered A Success Then Mean And Variance Of Probability Distribution Of The Number Of Successes 1) ½, 1/12 2) ⅙, 5/12 3) ⅚, 1/2 4) None of these Solution: Option (4) None of these p=⅙, q= ⅚, n= 3 Mean = np = 3(⅙) = 3/6 = ½... View Article
The Probability Of A Bomb Hitting A Bridge Is 12 And Two Direct Hits Are Needed To Destroy It The Least Number Of Bombs Required 1) 8 2) 7 3) 6 4) 9 Solution: Option (2) 7 Assume that “n” be the least number of bombs required, and X be the number of bombs... View Article
If The Mean And Variance Of A Binomial Variate X Are 2 And 1 Respectively Then The Probability That X Takes A Value Greater Than Or Equal To 1 Is 1) 2/3 2) 4/5 3) 7/8 4) 15/16 Solution: Option (4) 15/16 Given that mean = 2, and variance = 1 np = 2, npq = 1 2(q) = 1 q= ½.... View Article
A Dice Is Thrown Ten Times If Getting Even Number Is Considered As A Success Then The Probability Of Four Successes Is 1) 10C4 (½)4 2) 10C4 (½)6 3) 10C4 (½)8 4) 10C6 (½)10 Solution: Option (4) 10C6 (½)10 p = 3/6 = ½ Hence, q= ½, n= 10, x= 4 By... View Article
In Binomial Probability Distribution Mean Is 3 And Standard Deviation Is 3by2 Then The Probability Distribution Is 1) (¾ + ¼)12 2) (¼ + ¾)12 3) (¼ + ¾)9 4) (¾ + ¼)9 Solution: Option (1) (¾ + ¼)12 np = 3, √npq = 3/2 npq = 9/4 3q = 9/4 q = ¾... View Article
If A Dice Is Thrown 5 Times Then The Probability Of Getting 6 Exact Three Times Is 1) 125/388 2) 125/3888 3) 625/23328 4) 250/2332 Solution: Option (2) 125/3888 p= ⅙, q= ⅚, n= 5, x = 3 By using binomial... View Article
A Man Makes Attempts To Hit The Target The Probability Of Hitting The Target Is 35 Then The Probability Of Exactly 2 Times In 5 Attempts Is 1) 144/625 2) 72/3125 3) 216/625 4) None of these Solution: Option (1) 144/625 p= ⅗, q= ⅖, n= 5, x = 2 By using binomial... View Article
If X Denotes The Number Of Sixes In Four Consecutive Throws Of A Dice Then Px Equals 4 Is 1) 1/1296 2) 4/6 3) 1 4) 1295/1296 Solution: Option (1) 1/1296 p= ⅙. q= ⅚. n= 4, x= 4 By using binomial distribution, P(X= 4)= 4C4... View Article
If A Dice Is Thrown 7 Times Then The Probability Of Obtaining 5 Exactly 4 Times Is 1) 7C4 (⅙)4 (⅚)3 2) 7C4 (⅙)3 (⅚)4 3) (⅙)4 (⅚)3 4) (⅙)3 (⅚)4 Solution: Option (1) 7C4 (⅙)4 (⅚)3 p= ⅙, q= ⅚, n= 7, x= 4 By using... View Article
If Three Dice Are Thrown Together Then The Probability Of Getting 5 On At Least One Of Them Is 1) 125/216 2) 215/216 3) 1/216 4) 91/216 Solution: Option (5) 91/216 By using binomial distribution, p=⅙, q= ⅚, n= 3 The... View Article
A Fair Coin Is Tossed N Times If The Probability That Head Occurs 6 Time Is Equal To The Probability That Head Occurs 8 Time Then N Is Equal To 1) 15 2) 14 3) 12 4) 7 Solution: Option (2) 14 By using binomial distribution, The probability that head occurs 6 times is equal to... View Article
In A Box Of 10 Electric Bulbs Two Are Defective Two Bulbs Are Selected At Random One After The Other From The Box The First Bulb After Selection 1) 9/25 2) 16/25 3) 4/5 4) 8/25 Solution: Option (2) 16/25 Total number of bulbs = 10 Out of 10 bulbs, 2 are defective. Hence, q =... View Article
In A Box Containing 100 Eggs 10 Eggs Are Rotten The Probability That Out Of A Sample Of 5 Eggs None Is Rotten If The Sampling Is 1) (1/10)5 2) (1/5)5 3) (9/5)5 4) (9/10)5 Solution: Option (4) (9/10)5 Given that total number of eggs = 100. Out of 100 eggs, 10... View Article
8 Coins Are Tossed Simultaneously The Probability Of Getting At Least 6 Heads Is 1) 57/64 2) 229/259 3) 7/64 4) 37/256 Solution: Option (4) 37/256 By using binomial distribution, the required probability is: =... View Article
A Bag X Contains 2 White And 3 Black Balls And Another Bag Y Contains 4 White And 2 Black Balls The Probability For The Ball Chosen Be White Is 1) 2/15 2) 7/15 3) 8/15 4) 14/15 Solution: Option (3) 8/15 Let E1 be the event that the ball is drawn from bag “X” and E2 be the... View Article
A Bag A Contains 2 White And 3 Red Balls And Bag B Contains 4 White And 5 Red Balls One Ball Is Drawn Is Found To Be Red From Bag B Was 1) 5/14 2) 5/16 3) 5/18 4) 25/52 Solution: Option (4) 25/52 Let E1 be the event that the ball is drawn from bag “A” and E2 be the... View Article
One Die Is Thrown Three Times And The Sum Of The Thrown Numbers Is 15 The Probability For Which Number 4 Appears In First Throw 1) 1/18 2) 1/36 3) 1/9 4) 1/3 Solution: Option (1) 1/18 Let A be the event of getting a sum of 15 of the three thrown numbers and B... View Article