The Function F X 9 X 2 2 Increases In 1) (-3, 0) ∪ (3, ∞) 2) (-∞, -3) ∪ (3, ∞) 3) (-∞, -3) ∪ (0, 3) 4) (-3, 3) 5) (3, ∞) Solution: (-3, 0) ∪ (3, ∞) f (x) = (9 - x2)2... View Article
A Function F Is Defined F X E X Sin X In 0 Pi Which Of The Following Is Not Correct 1) f is continuous in [0, π] 2) f is differentiable in [0, π] 3) f (0) = f (π) 4) Rolle's theorem is not true in [0, π] Solution: (4)... View Article
If The Mean Value Theorem Is F B B A F C Then For The Function X 2 2x 3 1) 6/5 2) 5/4 3) 4/3 4) 7/6 Solution: (2) 5 / 4 f’ (c) = [f (b) - f (a)] / [b - a] f (x) = x2 - 2x + 3 f’ (x) = 2x - 2 f’ (c) =... View Article
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
