Revision Maths -X(CBSC) 20/23

18/9/22

                 PROBABILITY

1) A fair die is thrown once. Find the probability that the number on it is:

A) an odd number.                   1/2

B) greater than 4.                     1/3

C) at the most 4.                       2/3

D) between 7 and 10                 0 

2) Two fair coins are tossed. Find the probability that

A) head turns up exactly once. 1/2

B) Tail turns up at least once. 3/4

C) Tail does not turn up at all. 1/4

3) A coin is tossed thrice. Find the probability that

A) tail turns up at least twice. 1/2

B) Head does not turn up at all. 1/8 

C) tail comes on the second toss. 1/2.

D) Head turns up at least once. 7/8

4) Two fair dice are tossed. Find the probability that

A) The sum of the score is 9.  1/9

B)  the product of the score is 12.1/9

C) the score on the second die is greater than the score on the first die.                                             5/12

C) the Sum of the scores is a prime number.                       5/12

D) the sum of the score is a multiple of 4.                          1/4

E)  the sum of of the scores is a perfect square.                      7/36

5) One card is drawn from a pack of pack of well shuffled pack of cards. Find the probability that the card drawn is :

A) A Queen.                             1/13

B) not a queen.                     12/13

C) a face card.                        3/13

D) red card .                            1/2

E) bears a number lesson than 4. 3/13

F)  king or black black card.           7/13 

6) In a match between A and B the probability of winning of A is 0.43. What is the probability of winning of B ?                      0.57

7) A bag contains 3 red, 4 white, 5 blue marbles. All the marbles are identical in shape and and size.  One marble is drawn at random from the bag. find the probability that the marble drawn is.      

A) Red.                                      1/4

B) red or white.                      7/12

8) An unbiased coin is is tossed. Find the probability that 

A) A head turns up.               1/2

B) A tail turns up.                   1/2

C) both head and tail turn turn tail turn turn up    0

D) neither head nor tail turns up. 0

9) A Uniform die is thrown. find the the probability of the event A, B and E where 

A: score is an even number.    1/2

B: score is a number number less than 5 but less than 2.                        1/2

E: score is a number that is a multiple of 3 or 5.                    1/2.

10) A perfect cubic die is thrown. find the probability that 

A) A prime number comes up. 1/2.

B) A perfect square comes up. 1/3

11) Two coins are tossed simultaneously. Find the probability of getting exactly one head.                                           1/2

12) Three coins are tossed simultaneously. Find the probability of getting at least one head.                                     7/8.

13) Three unbiased coins are tossed. find the probability of of getting at least two heads up. 1/2

14) A coin is tossed 3 times. Write the sample space. find the probabilities of

E: getting two or more more heads. 1/2

F: the second is a not a head. 1/2

15) Two unbiased dice are thrown in the air. find the probability that the sum of the scores is a multiple of 3 multiple of 3 a multiple of 3 multiple of the scores is a multiple of 3 multiple of 3 a multiple of 3 multiple of is a multiple of 3 multiple of 3.        1/3

16) two dice are are thrown. What is the probability that the sum of the points obtained is greater than 4 ?                                    5/6

17) Two unbiased dice are thrown. Find the probability that the sum of the numbers on their faces is at most 5 5 5.             5/18

18) two fair dice dice are thrown, find the probability of getting the same score on the first die as on the the second.                             1/6

19) two unbiased dice are thrown in the air. Find the probability that the sum of the scores is greater than 9 or an even number.       5/9

20) if two fair dice are thrown,  find the probability that the sum of the points the points points on their uppermost face is a perfect square or a multiple of 3 3.                         5/12

21) a box contains 5 red, 11 white and 7 black balls. one ball is drawn at random, find the probability that ball drawn is a white white ball.                          11/23

22) a bag contains 6 contains 6 red, 5 blue, 3 white and 4 Black Black balls. A ball is drawn at random. find the probability that the ball is red or black .                                     5/9

23) in a bag there are six six black, 4 white and 3 yellow balls. A ball is taken at random. find the probability of of getting a yellow or a white ball.                         7/13

24) A box contains 7 red, 5 white and 8 green balls identical in all respects except colour. one ball is drawn at random. find the probability that that it is not white.                                3/4

25) a card is drawn from a pack of well shuffled 52 playing cards.  find the probability that the card drawn is.     

A)  a diamond                   1/4 

B) A red card.                     1/2

C) A king                             1/13

D) an ace or a Queen.             2/13

E) a face card card                          3/13

F) A card bearing a number between and including 2 and 6. 5/13

26) Six tokens bearing numbers 1 to 6 are placed in one box and seven tokens bearing 1 to 7 are placed in another box. If one token is drawn from each box, what is the probability that the sum of of the number is 

A) six                                     5/42

B) 11                                     1/14

27) If P(A)= 0.95, find P(not A).  0.05

28) a bag contains a certain number of a blue blue balls. A ball is drawn, find the probability that the ball drawn is.      

A) black.                                   0

B) blue.                                       1

29) the probability that two boys do not have the same birthday is 0.394. What is the probability that the two boys have the same have the same same birthday ?                          0.606

30) which of the following cannot be the probability of an event

A) 5/7 

B) 0.28

C) √2

D) - 2.4                      √2 and - 2.4

31) From a deck of 52 cards, all the face cards are removed and then remaining cards are shuffled. now one card is drawn from the remaining deck. find the probability that the card is.  

A) a black card.                      1/2

B) 8 of red colour.                 1/20

C) A king of black colour.       0

32) a box contains thousand bulbs out of Prit Prit 25 defective, it is not possible to just look at the bulb and tell whether or not it is defective. one bulb is taken out at random from the box. calculate the probability that the bulb taken out is:

A) a good one.                   39/40

B) a defective one.             1/40

33) a bag contains 50 identical cards which are numbered from 1 to 50. If one card is drawn at random from the bag, find the probability that it bears 

A) a perfect square number.  7/50

B) a number divisible by 4 divisible by 4.   6/25

C) A number divisible by 5.    1/5

D) A number divisible by 4 or 5. 2/5

E) a number divisible by 4 and 5. 1/25.

34) A bag contains 6 red, 8 white and x blue balls which are  identical in shape and size. the probability that a ball drawn at random is  blue or white is 5/7.  find x.                                       7.

35)  Two fair dice are thrown. Find the probability of getting

A)  the same score on the first die as on the second.        1/6 

B) the score of second dice is greater than the score of first. 5/12

36) from a group of 5 men and 3 women A committee of 4 persons persons is to be selected selected be selected selected randomly. find the probability that

A) there is a majority of man. 1/2

B) there is majority of women. 1/14

37) A bag contains 6 white and 9 black balls, if 3 balls are drawn at random, find the probability that all of them are black.         12/65

 38)A coin is tossed once. Find the probability of getting head

39) A dice is thrown once. What is the probability of getting a prime number.

40)a) A die is thrown once. What is the probability of getting a number other than 4 ?

b) A ‘3’

c) A ‘4’

c) An odd number

d) A Number greater than 4

41) Three unbiased coins are tossed simultaneously. Find the probability of getting

a)All heads

b) All tails

c) No head.

d) No tail

e) Atleast one head

f) Atleast one tail

g) All not heads

h) Atmost one tail

I) Two or more tails

j) More than two tails

k) Less than one head

l) Heads and tails

m) Heads are the two extremes

n) Heads will come in the 1st row

o) Heads will exceed the number of tails in a particular throw.

p) Exactly 2 heads

q) Atmost two heads.

r) Atleast two heads

5) Two coins are tossed simultaneously. What is the probability

a)All heads

b) All tails

c) No heads

d) No tails

e) All not heads

f) at least one head

g) Exactly one head

h) At Most one head.

i) Atleast two heads

j) Heads will come in first row.

k) Heads and tails will occur alternately.

42) One card is drawn at random from well shuffled pack of cards. What is the probability of

drawing a

a)A King.

b) A queen

c) An eight

d) A black card

e) The six of the clubs.

f) A spade.

g) A King of red suit

h) A queen of black suit

i) A pack of hearts.

j) A red of face’card.

k) A King or a jack

l) A non-Ace

m) A red card

n) Neither king nor a queen

o) Neither a red card nor a queen.

p) It is either a King or a knave

q) It is neither a King nor a Knave

r) It is neither a heart nor a diamond

s) It is neither an Ace, nor a King, nor a Queen, nor a Knave.

t) A spade or an Ace not of a spade.

43) Two dice are rolled simultaneously. What is the probability of getting

a)8 as the sum of two numbers that turn up

b) A doublet

c) Sum is 7

d) Sum is 11

e) It is either 7 or 11.

f) It is neither 7 nor 11.

g) Sum is odd number more 

     than 3.

h) Sum is a multiple of 4.

i) Sum is a multiple of 3 and 4

j) Sum is multiple of 3 or 4.

k) Sum is atleast 8

l) Sum is Atmost 7

m) The product of the faces is 12.

n) Sum of the faces is more

     than 12

44) There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a

a)A Boy

b) A girl.

45) Seventeen cards numbered 1,2,3...16,17 are put in a box and mix thoroughly. One person draw a card from the box. Find probability that the number on the card is

a)A prime

b) Divisible by 3

c) Divisible by 2 and 3 both

d) Not divisible by 2

e) Divisible by 2 but not by 3

f) Divisible by 3 but not by 2

g) Divisible by either 3 or 2

h) Neither Divisible by 2 nor 3

i) multiple of 4

10) A bag contains 6 Red,8 white balls, 5 green and 3 black balls . One ball is drawn at random from the bag. Find the probability that the ball is:

a) White

b) Red or White

c) Not green

d) Neither white nor black

e) A pink ball

46) From a pack of cards jacks, queens,kings and aces of red colours are removed. From the remaining, a card is drawn random. Find the probability:

a)A black queen

b) A red card

c) A picture card

47) The probability that will rain today is 0.84. what is the probability that will not rain today ?

48) What is the probability that an ordinary year has 53 Sundays

49) Find the probability of getting 53 Friday in a leap year

50) In a lottery there are 10 prizes and 25 blanks . What is the probability of getting a prize ?

51) It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out random from the box. What is the probability that the bulb drawn is

a) Defective

b) not defective.

52) A bag contains 3 green and 8 white balls. If one ball is drawn at random. Find the probability that:

a)It is green

b) It is white

53) There are 17 numbered 1 to 17 in a bag, If a person selects one ball is drawn randomly. Find the probability that the number printed on the ball will be an even number greater than 9.

54) One card is drawn from a pack of cards. Find the probability that

a)Either a spade or a diamond

b) Either a spade or a king.

c) Neither king nor diamond.

d) Either red or queen.

55) One counter is drawn at random from a bag contain 70 counters marked with the first 70 numerical. Find the chance that:

a) multiple of 8 or 9

b) either multiple of 3 or 4

56) What is the probability that in a group of 3 people

a) 3 people having same Birthday

b) 2 people have same birthday

c) All have different birthdays

d) atleast one have same birthday

e) Atleast 2 have same birthday

f) Atmost 2 have same birthday.

57) the face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random.find probability that they belong to different suits?

58) In a throw of two dice, find the probability of getting one prime and one composite number?          ⅓

59) Find the probability that a leap year chosen at random will have 53 Sundays.                                     2/7

60) An integer is chosen at random from the first 100 integers. What is the probability that this number will not be divisible by 5 or 8?         7/10

61) In throwing a fair dice, what is the probability of getting the number' 3'                                      ⅙

62) Find the probability of throwing atleast one ace in a sample throw with two dice.  11/36

63) From a pack of 52 Cards, two are drawn at random. Find the probability that one is a knave and the other a queen.                  8/663

64) If a card is picked up at random from a pack of 52 Cards. Find the probability that it is

A) a spade.                               1/4

B) a king or queen.                    2/23

C) a spade or king or a queen. 19/52

65) Three coins are tossed. What is the probability of getting

A) 2 Tails and 1 Head..               3/8

B) 1 tail and 2 heads.                  3/8

C) neither 3 heads nor tails.         3/4

D) three heads.                             1/8

E) atleast one tail.                         ⅞

66) Two fair dice are thrown. Find the probability of getting

A) a number divisible by 2 or 4.  1/2

B) a number divisible by 2 & 4.   1/4

C) a prime no. less than 8.      13/36

67) What is the probability of throwing a number greater than 2 with a fair dice.                           ⅔

68) Two fair coins are tossed. Find the probability of getting

A) 2 heads.                                1/4

B) 1 head and 1 tail.                   1/2

C) 2 tails.                                     ⅔

69) In rolling two dices, find the probability that

A) atleast one '6'.                   11/16

B) the sum is 5.                      22/36

70) Two fair dice are thrown. What is the probability of

A) throwing a double.                  1/6

B) the sum is greater than 10.   1/12

C) The sum is less than 10.        ⅚

71) From a pack of 52 Cards, three cards are drawn at random. Find the probability of drawing a king, a queen and Jack.              16/5525

72) A bag contains 20 balls marked 1 to 20. One ball is drawn at random. Find the probability that it is marked with a number multiple of 5 or 7.  

73) Two fair dice are thrown. Given that the sum of the dice is less than or equal to 4, find the probability that only one dice shows two.                                  ⅓

74) Out of all the 2digit Integers between 1 to 200, a 2digit number has to be selected at random. What is the probability that the selected number is not divisible by 7 ?    77/90

75) Two dice are thrown. If the total on the faces of the two dices are 6, find the probability that there are two odd numbers on the faces.        ⅗

ARITHMETIC PROGRESSION

1) If the sum of the three numbers in A. P be 18 then what is the middle term? 

2) If 10 be added to each term of an AP then, will the new progression be in AP also. ? Y

3) If 5 be multiplied with each term of an AP then will the new progression an AP also?

4) Find the 8th term of an AP., 13, 10, 17, 24...... 

5) Which term of the AP. 7, 11, 15, 19, ....... is 103? 

6) If the 7th term of an AP be 20 and the 10th term be 29 then find the first and the common difference. 

7) In an AP 1st term be -5, last term be 25 and number of terms be 10. Find the sum of the terms. 

8) What do you mean by natural numbers? Find the sum of first 100 natural numbers. 

9) a²+ 3a + 2, 3a²+ 2a+5, 4a²+ 5a + 4 are in AP, then find a.

10) Find the arithmetic progression of which nth term is 3n -1. 

11) If the pth term of an AP be q and qth term be p, then find the p+ q th term. 

12) The sum of first n terms of an AP is n². Find the common difference. 

13) Find the sum of the first 20 terms of the AP. 20, 17, 14... 

14) The 5th term and the 11th term of an AP are 41 and 20 respectively. Find the 1st term. What will be the sum of first 11 terms of this AP. 

15) The sum of p th term of an AP is 3p²+ 5p; show that it is an AP.

16) Insert five A. M between 2 and 20.

17) The n th term of an AP is p. Show that the sum of first (2n -1) terms is (2n -1)p.

18) The sum of how many terms of the series 27 + 24+21+...... will be equal to 132 ? 

19) If the sum of n th term of an AP is n² + 3n, then eight term is equal to the sum of first eleven terms.

20) Find the sum upto n terms of the following series. 1+ 5 + 12+ 22+ 35+ ....... {n²(n+1)/2}

21) Find the following sum:

1²+ 3² + 5²+ ...... upto n terms.

22) The middle term of an AP having 11 terms is 12. Find the sum of the 11 terms of that progression.

23) The sum of the three numbers in AP is 21 and their product is 231. Find the numbers.

24) There are n arithmetic means between 4 and 31. If the second mean: last mean= 5: 14 then find the value of n. 

25) If the sum of the first P terms of an AP be equal to the sum of the first Q terms then show that the sum of the first P+ Q terms is zero.

26) The first term of an AP is a, the second term is b and the last term is c. Show that the sum is {(a+ c)(b+ c - 2a)}/{2(b - a)}.

27) The interior angles of a polygon are in AP. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

28) The sides of a right angled triangle are in AP. If the smallest side is 5cm then find the largest side. 

29) A man divided ₹24000 among his four sons in such a way that the amounts of four sons are in AP. The product of the amounts of 1st and 3rd sons is to the product of amounts of 2nd and 4th sons as 7: 15. Calculate the amounts received by each son. 3000, 5000, 7000, 9000

30) Two posts are offered to a man. In the one, the starting salary is ₹1200 and increases annually by ₹80; in the other, the salary starts at 850 and increases annually by ₹120. The man decides to accept the post that will give him better total income in the first 16 years. Which post will be accept ? 1st offer

31) A polygon has 25 sides, the lengths of which starting from the smallest side are in AP. If the perimeter of the polygon is 2100 cm, and the length of the largest side is 20 times that of the smallest, find the length of the smallest side and the common difference of the AP. 

**32) If the sum of p-terms of an AP be q and the sum of q terms be p then show that the sum of its (p+ q) terms is -(p+ q).

Continue.....

Revision

 20/9/22

Banking

1) On recurring deposit Shyam received ₹36 as interst for 8 months on ₹150 (deposited monthly). Find the rate. 

2) Miss x deposited ₹350 per month for 20 months under Recurring deposit scheme. Find the total amount payable by the bank on maturity of the account if the rate of interest is 11% p.a.        7673.75

3) Ram has a cumulative time deposit account of ₹140 per month at 6% p.a. If she gets ₹7157 at the time of maturity, find the total time for which the account was held.   20 months.

4) seema opened a Recurring deposit Account with a bank and deposited ₹75 per month for 4 years. If the interest reckoned at the rate of 10% p.a., find the amount she got at the end of the maturity period.

5) Arsh has a cumulative time deposit account in a bank. She deposits ₹800 per month and gets ₹15198 as maturity value. If the rate of interest be 7% p a., Find the total time for which the account was held. 

6) Recurring deposit calculation are based on

A) simple interest only

B) compound interest only

C) both A and B

D) neither A nor B

7)If Rupam deposits ₹225 per month for 5 years at 9% p a. Then maturity value is..

A) 17660 B)17000 C) 17066.88 D) n

8) Amit deposited ₹150 per month in a bank for 8 months under the Recurring Deposit Scheme. what will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of the year.    1236

18/9/22

              

 PROBABILITY

1) A fair die is thrown once. Find the probability that the number on it is:

A) an odd number. 1/2

B) greater than 4. 1/3

C) at the most 4. 2/3

D) between 7 and 10 0 

2) Two fair coins are tossed. Find the probability that

A) head turns up exactly once. 1/2

B) Tail turns up at least once. 3/4

C) Tail does not turn up at all. 1/4

3) A coin is tossed thrice. Find the probability that

A) tail turns up at least twice. 1/2

B) Head does not turn up at all. 1/8 

C) tail comes on the second toss. 1/2.

D) Head turns up at least once. 7/8

4) Two fair dice are tossed. Find the probability that

A) The sum of the score is 9. 1/9

B) the product of the score is 12.1/9

C) the score on the second die is greater than the score on the first die. 5/12

C) the Sum of the scores is a prime number. 5/12

D) the sum of the score is a multiple of 4. 1/4

E) the sum of of the scores is a perfect square. 7/36

5) One card is drawn from a pack of pack of well shuffled pack of cards. Find the probability that the card drawn is :

A) A Queen. 1/13

B) not a queen. 12/13

C) a face card. 3/13

D) red card . 1/2

E) bears a number lesson than 4. 3/13

F) king or black black card. 7/13 

6) In a match between A and B the probability of winning of A is 0.43. What is the probability of winning of B ? 0.57

7) A bag contains 3 red, 4 white, 5 blue marbles. All the marbles are identical in shape and and size. One marble is drawn at random from the bag. find the probability that the marble drawn is.      

A) Red. 1/4

B) red or white. 7/12

8) An unbiased coin is is tossed. Find the probability that 

A) A head turns up. 1/2

B) A tail turns up. 1/2

C) both head and tail turn turn tail turn turn up 0

D) neither head nor tail turns up. 0

9) A Uniform die is thrown. find the the probability of the event A, B and E where 

A: score is an even number. 1/2

B: score is a number number less than 5 but less than 2. 1/2

E: score is a number that is a multiple of 3 or 5. 1/2.

10) A perfect cubic die is thrown. find the probability that 

A) A prime number comes up. 1/2.

B) A perfect square comes up. 1/3

11) Two coins are tossed simultaneously. Find the probability of getting exactly one head. 1/2

12) Three coins are tossed simultaneously. Find the probability of getting at least one head. 7/8.

13) Three unbiased coins are tossed. find the probability of of getting at least two heads up. 1/2

14) A coin is tossed 3 times. Write the sample space. find the probabilities of

E: getting two or more more heads. 1/2

F: the second is a not a head. 1/2

15) Two unbiased dice are thrown in the air. find the probability that the sum of the scores is a multiple of 3 multiple of 3 a multiple of 3 multiple of the scores is a multiple of 3 multiple of 3 a multiple of 3 multiple of is a multiple of 3 multiple of 3. 1/3

16) two dice are are thrown. What is the probability that the sum of the points obtained is greater than 4 ? 5/6

17) Two unbiased dice are thrown. Find the probability that the sum of the numbers on their faces is at most 5 5 5. 5/18

18) two fair dice dice are thrown, find the probability of getting the same score on the first die as on the the second. 1/6

19) two unbiased dice are thrown in the air. Find the probability that the sum of the scores is greater than 9 or an even number. 5/9

20) if two fair dice are thrown, find the probability that the sum of the points the points points on their uppermost face is a perfect square or a multiple of 3 3. 5/12

21) a box contains 5 red, 11 white and 7 black balls. one ball is drawn at random, find the probability that ball drawn is a white white ball. 11/23

22) a bag contains 6 contains 6 red, 5 blue, 3 white and 4 Black Black balls. A ball is drawn at random. find the probability that the ball is red or black . 5/9

23) in a bag there are six six black, 4 white and 3 yellow balls. A ball is taken at random. find the probability of of getting a yellow or a white ball. 7/13

24) A box contains 7 red, 5 white and 8 green balls identical in all respects except colour. one ball is drawn at random. find the probability that that it is not white. 3/4

25) a card is drawn from a pack of well shuffled 52 playing cards. find the probability that the card drawn is.     

A) a diamond 1/4 

B) A red card. 1/2

C) A king 1/13

D) an ace or a Queen. 2/13

E) a face card card 3/13

F) A card bearing a number between and including 2 and 6. 5/13

26) Six tokens bearing numbers 1 to 6 are placed in one box and seven tokens bearing 1 to 7 are placed in another box. If one token is drawn from each box, what is the probability that the sum of of the number is 

A) six 5/42

B) 11 1/14

27) If P(A)= 0.95, find P(not A). 0.05

28) a bag contains a certain number of a blue blue balls. A ball is drawn, find the probability that the ball drawn is.      

A) black. 0

B) blue. 1

29) the probability that two boys do not have the same birthday is 0.394. What is the probability that the two boys have the same have the same same birthday ? 0.606

30) which of the following cannot be the probability of an event

A) 5/7 

B) 0.28

C) √2

D) - 2.4 √2 and - 2.4

31) From a deck of 52 cards, all the face cards are removed and then remaining cards are shuffled. now one card is drawn from the remaining deck. find the probability that the card is.  

A) a black card. 1/2

B) 8 of red colour. 1/20

C) A king of black colour. 0

32) a box contains thousand bulbs out of Prit Prit 25 defective, it is not possible to just look at the bulb and tell whether or not it is defective. one bulb is taken out at random from the box. calculate the probability that the bulb taken out is:

A) a good one. 39/40

B) a defective one. 1/40

33) a bag contains 50 identical cards which are numbered from 1 to 50. If one card is drawn at random from the bag, find the probability that it bears 

A) a perfect square number. 7/50

B) a number divisible by 4 divisible by 4. 6/25

C) A number divisible by 5. 1/5

D) A number divisible by 4 or 5. 2/5

E) a number divisible by 4 and 5. 1/25.

34) A bag contains 6 red, 8 white and x blue balls which are identical in shape and size. the probability that a ball drawn at random is blue or white is 5/7. find x. 7.

35) Two fair dice are thrown. Find the probability of getting

A) the same score on the first die as on the second. 1/6 

B) the score of second dice is greater than the score of first. 5/12

36) from a group of 5 men and 3 women A committee of 4 persons persons is to be selected selected be selected selected randomly. find the probability that

A) there is a majority of man. 1/2

B) there is majority of women. 1/14

37) A bag contains 6 white and 9 black balls, if 3 balls are drawn at random, find the probability that all of them are black. 12/65

 38)A coin is tossed once. Find the probability of getting head

39) A dice is thrown once. What is the probability of getting a prime number.

40)a) A die is thrown once. What is the probability of getting a number other than 4 ?

b) A ‘3’

c) A ‘4’

c) An odd number

d) A Number greater than 4

41) Three unbiased coins are tossed simultaneously. Find the probability of getting

a)All heads

b) All tails

c) No head.

d) No tail

e) Atleast one head

f) Atleast one tail

g) All not heads

h) Atmost one tail

I) Two or more tails

j) More than two tails

k) Less than one head

l) Heads and tails

m) Heads are the two extremes

n) Heads will come in the 1st row

o) Heads will exceed the number of tails in a particular throw.

p) Exactly 2 heads

q) Atmost two heads.

r) Atleast two heads

5) Two coins are tossed simultaneously. What is the probability

a)All heads

b) All tails

c) No heads

d) No tails

e) All not heads

f) at least one head

g) Exactly one head

h) At Most one head.

i) Atleast two heads

j) Heads will come in first row.

k) Heads and tails will occur alternately.

42) One card is drawn at random from well shuffled pack of cards. What is the probability of

drawing a

a)A King.

b) A queen

c) An eight

d) A black card

e) The six of the clubs.

f) A spade.

g) A King of red suit

h) A queen of black suit

i) A pack of hearts.

j) A red of face’card.

k) A King or a jack

l) A non-Ace

m) A red card

n) Neither king nor a queen

o) Neither a red card nor a queen.

p) It is either a King or a knave

q) It is neither a King nor a Knave

r) It is neither a heart nor a diamond

s) It is neither an Ace, nor a King, nor a Queen, nor a Knave.

t) A spade or an Ace not of a spade.

43) Two dice are rolled simultaneously. What is the probability of getting

a)8 as the sum of two numbers that turn up

b) A doublet

c) Sum is 7

d) Sum is 11

e) It is either 7 or 11.

f) It is neither 7 nor 11.

g) Sum is odd number more 

     than 3.

h) Sum is a multiple of 4.

i) Sum is a multiple of 3 and 4

j) Sum is multiple of 3 or 4.

k) Sum is atleast 8

l) Sum is Atmost 7

m) The product of the faces is 12.

n) Sum of the faces is more

     than 12

44) There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a

a)A Boy

b) A girl.

45) Seventeen cards numbered 1,2,3...16,17 are put in a box and mix thoroughly. One person draw a card from the box. Find probability that the number on the card is

a)A prime

b) Divisible by 3

c) Divisible by 2 and 3 both

d) Not divisible by 2

e) Divisible by 2 but not by 3

f) Divisible by 3 but not by 2

g) Divisible by either 3 or 2

h) Neither Divisible by 2 nor 3

i) multiple of 4

10) A bag contains 6 Red,8 white balls, 5 green and 3 black balls . One ball is drawn at random from the bag. Find the probability that the ball is:

a) White

b) Red or White

c) Not green

d) Neither white nor black

e) A pink ball

46) From a pack of cards jacks, queens,kings and aces of red colours are removed. From the remaining, a card is drawn random. Find the probability:

a)A black queen

b) A red card

c) A picture card

47) The probability that will rain today is 0.84. what is the probability that will not rain today ?

48) What is the probability that an ordinary year has 53 Sundays

49) Find the probability of getting 53 Friday in a leap year

50) In a lottery there are 10 prizes and 25 blanks . What is the probability of getting a prize ?

51) It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out random from the box. What is the probability that the bulb drawn is

a) Defective

b) not defective.

52) A bag contains 3 green and 8 white balls. If one ball is drawn at random. Find the probability that:

a)It is green

b) It is white

53) There are 17 numbered 1 to 17 in a bag, If a person selects one ball is drawn randomly. Find the probability that the number printed on the ball will be an even number greater than 9.

54) One card is drawn from a pack of cards. Find the probability that

a)Either a spade or a diamond

b) Either a spade or a king.

c) Neither king nor diamond.

d) Either red or queen.

55) One counter is drawn at random from a bag contain 70 counters marked with the first 70 numerical. Find the chance that:

a) multiple of 8 or 9

b) either multiple of 3 or 4

56) What is the probability that in a group of 3 people

a) 3 people having same Birthday

b) 2 people have same birthday

c) All have different birthdays

d) atleast one have same birthday

e) Atleast 2 have same birthday

f) Atmost 2 have same birthday.

57) the face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random.find probability that they belong to different suits?

58) In a throw of two dice, find the probability of getting one prime and one composite number?          ⅓

59) Find the probability that a leap year chosen at random will have 53 Sundays.                                     2/7

60) An integer is chosen at random from the first 100 integers. What is the probability that this number will not be divisible by 5 or 8?         7/10

61) In throwing a fair dice, what is the probability of getting the number' 3'                                      ⅙

62) Find the probability of throwing atleast one ace in a sample throw with two dice.  11/36

63) From a pack of 52 Cards, two are drawn at random. Find the probability that one is a knave and the other a queen.                  8/663

64) If a card is picked up at random from a pack of 52 Cards. Find the probability that it is

A) a spade.                               1/4

B) a king or queen.                    2/23

C) a spade or king or a queen. 19/52

65) Three coins are tossed. What is the probability of getting

A) 2 Tails and 1 Head..               3/8

B) 1 tail and 2 heads.                  3/8

C) neither 3 heads nor tails.         3/4

D) three heads.                             1/8

E) atleast one tail.                         ⅞

66) Two fair dice are thrown. Find the probability of getting

A) a number divisible by 2 or 4.  1/2

B) a number divisible by 2 & 4.   1/4

C) a prime no. less than 8.      13/36

67) What is the probability of throwing a number greater than 2 with a fair dice.                           ⅔

68) Two fair coins are tossed. Find the probability of getting

A) 2 heads.                                1/4

B) 1 head and 1 tail.                   1/2

C) 2 tails.                                     ⅔

69) In rolling two dices, find the probability that

A) atleast one '6'.                   11/16

B) the sum is 5.                      22/36

70) Two fair dice are thrown. What is the probability of

A) throwing a double.                  1/6

B) the sum is greater than 10.   1/12

C) The sum is less than 10.        ⅚

71) From a pack of 52 Cards, three cards are drawn at random. Find the probability of drawing a king, a queen and Jack.              16/5525

72) A bag contains 20 balls marked 1 to 20. One ball is drawn at random. Find the probability that it is marked with a number multiple of 5 or 7.  

73) Two fair dice are thrown. Given that the sum of the dice is less than or equal to 4, find the probability that only one dice shows two.            ⅓

74) Out of all the 2digit Integers between 1 to 200, a 2digit number has to be selected at random. What is the probability that the selected number is not divisible by 7 ?    77/90

75) Two dice are thrown. If the total on the faces of the two dices are 6, find the probability that there are two odd numbers on the faces.        ⅗

Matrix

1) if A=2x+ 3y   a- 2b and B= 3      8

              2a+ b   3x - 2y            6     11

And A= B then find x,y a, b.

2) Construct a 2x2 matrix whose elements are a= i+ j

3) If A= x- 2       y   and B= 3       1

             a+ 2b   3a - b          5       1 then find the value of a,b, x,y

4) If A= 2    x & B=4     3 & C= z     -3

              1    0          y    2         15     4 and 3A + 2B = C then find x,y and z.

5) If A= 2   -1 & B= -3    2 & C=1    0

              2    0           4    0         0     2 and A+ X = 2B + C then find the matrix X.

6) If A= 2   4 & B=1    3 & C=-2    5

              3   2        -2    5          3     4 then find 3A - 2B + 4C

7) If A= 4     6 & B= 3      1 

             -3     7          5     -2 then find the matrix X such that X+ A= B

8) If A= 6     2 & B= 1    2 

              5     4         -5    1 then find the matrix X such that 2A + 3B - 5X = O

9) If Y=1      2 & 2X+ Y=5     0    

            -1      5               -3     3 then find the matrix X 

10) IfA + B=5      4 & A - B= 11    2  

                     7      3               -1      7 then find the matrix A and B

11) If A= cos t         sin t 

               - sin t        cos t and

B= sin t          - cos t

     Cos t            sin t then prove that A cos t + B sin t= I (I is unit matrix)

12) If A=a    3 & B=2     b & C=1      1

               4    2         1    -2        -2      c

 and D= 5     0

               7     3 and A+ B - C= D then find a, b, c.

13) If A=3   -2 & B= 2x & C=-4   

              -1   4             1          5   

And D= 2

              y and the relation AB+ 2C = 4D, then find x and y.

14) If B=3     4 & C =9        2 

              -1     2         14       2 

And A. B = C. Find the matrix A.

15) If A= 1       1

                8       3 evaluate A² - 4A.      

16) If A=3    7 & B=0     2 & C=1    -5  

               2    4         5     3        -4     6

And A. B+ 2X= C. Then find the matrix X.

17) If X =4      1

               -1      2 show that 6X - X² = 9I. I is unit matrix 

18) If A =2    -2

               -3     4 evaluate - A²+6A

19) If A =3    1

               -1    2 show A²-5A+7I= 0

20) If A=1    2 & B=2    1 & C=1    3 

               2    3         3    2         3    1 find the matrix C(B - A).

21) If A=1         0   

               0        -1 find A² and A³. Also state which of these is equal to A.

22) If A=1     1  

               x      x find the value of x that A² = O.

23) If A=2     1 & B= -3       1

               4     2           0      -2 Find

A) A² + 2AB+ B²

B) (A+ B)²

Is A² + 2AB+ B² = (A+ B)² ?

24) If A=4     -5 & B= 10      -11

              -2      1          12      -15 Find the matrix A such that AB = C.

BANKING

1) Ram has a 5 years recurring deposit account in Bank of Baroda and deposits 2400 a month. If he receives ₹186090 at the time of maturity, find the rate of simple interest.

2) On depositing ₹200, every month in a cumulative time deposit account, paying 9% p.a. intrest, a person collected ₹2517 at maturity. Find the period.

3) Sumit paid ₹300 per month in a cumulative time deposit for 2 years. He received ₹7875 as the maturity amount. Find the rate of interest.

4) Sujata deposited, a certain sum of money, every month, for 5/2 years in a cumulative time deposit account. At the time of maturity she collected ₹4965. If the rate of interest was 8% p.a. find the monthly deposit.

5) Amar deposits ₹1600 per month in a recurring deposit for 3 years at the rate of 9% p a. Simple interest. Find the amount Amar will get at the time of maturity.

6) Miss Anshu Gupta deposited ₹350 for 20 months under recurring deposit scheme. Find the total amount payable by the bank on maturity of the account if the rate of interest is 11% per annum.

7) Shyam opens a recurring deposit account with the bank of Rajasthan and deposits ₹600 per month for 20 months. Calculate the maturity value of this account, if the bank pays intrest at the rate of 10% per annum.

8) Mamta has a cumulative time deposit account in a bank. She deposits ₹800 per month and gets ₹15198 as maturity value. If the rate of interest be 7% p.a, find the total time for which the account was held.

9) Manisha has a recurring deposit account for 2 years at 10% p.a. if she receives ₹1900 as intrest, find the value of the monthly installment paid by her.

10) Shalini has a cumulative time deposit account of ₹340 per month at 6% p.a., If she gets ₹7157 at the time of maturity, find the total time for which the account was held.

Revision XII(Maths) 22/23

Tangent and Normal

1) Write down the equation of the tangent at a point (4,3) on the ellipse 9x²+ 16y²= 288.

2) Write down the equation of the tangent of the parabola y²= 4x at (1,2).

3) write down the value of slope of the tangent to the parabola y² = 8(x - 6) at the point (8,-4).

4) Determine the points on the curve y= x+ 1/x, where the tangent is parallel to x-axis.

5) Find the gradient of the tangent to the parabola y² = 4x at the point (1,2).

6) Show that the equation of the normal to the hyperbola x = a sec t, y= b tan t at the point (a sec t, b tan t) is . ax cos t + by cot t= a²+ b².

7) At a point P(x,y) on the parabola y= x²/4 + 1, the tangent makes an angle 45° with the positive direction of the x-axis. Find the coordinates of the point P.

8) Find the condition that the straight line lx + my = n touches the ellipse x²/a² + y²/b² = 1.

9) Write down the equation of the tangent and normal of the parabola y²= 4ax at (0,0).

10) Obtain the equation the normal to the hyperbola x²/a² - y²/b² = 1 at (a sec t, b tan t).

11) If the straight line lx + my = 1 is a normal to the parabola y²= 4ax, then show that al³+ 2alm² = m².

12) Find the coordinates of the point on the curve y= 1+ 2x- 3x² at which the tangent make an angle of 45° with the positive direction of the x-axis.

13) Find the equation of the tangent to the hyperbola x²/a² - y²/b² = 1 at (a sec t, b tan t).

14) find the equations of the tangent and normal to the ellipse 4x² + 9y² = 72 at the point (3,2).

15) Find the equation of the tangent to the parabola y² = 4x + 5, which is parallel to the straight line y= 2x+ 7.

16) Find the equation of the normal to the curve y= x² - x at the point (3,6). Show that this normal touches the parabola x² + 660y = 0.

17) If the straight line lx + my = n is normal to the hyperbola x²/a² - y²/b² = 1, then show that a²/l² - b²/m² = (a² + b²)²/n².

18) If the straight line x cos t+ y sin t= p touches the ellipse x²/a² + y²/b² = 1, then prove that a² cos²t + b² sin²t = p².

19) Prove that the straight line x+ y= 2+ √2 touches the circle x²+ y² - 2x - 2y+ 1= 0. Find the point of contact.

20) If the straight line lx + my + n= 0 touches the parabola y²= 4ax then prove that am² = nl.

21) tangent are drawn from origin to the curve y= sinx. Prove that their points of contact lie on x²y² = x² - y².

22) Find the equation of the tangent and the normal to the curve y= x³ - 3x at the point (2,2).

23) Find the equation of the tangent and normal of the curve y(x - 2)(x -3) - x +7= 0 at the point of intersection with the x-axis.

24) Find the equation of the common tangent to the parabola y² = 4ax and x²= 4by.

25) Show that the normal at any point on the curve x= a(cos t+ t sin t), y= a(sin t - t cos t) is a constant distance from the origin.

Continuity

1) A function f(x) is defined as:

        =   x²        when x< 1

 f(x)=  2.5       when x= 1

       =  x²+2     when x> 1

Is f(x) continuous at x= 1?

2) A function f(x) is defined as:

        = 3+ 2x        when -3/2≤x< 0

 f(x)=  3- 2x       when 0≤ x< 3/2

       =  -3x -2x     when x ≥ 3/2

Show that f(x) continuous at x= 0 and discontinuous at x=3/2.

3) A function f(x) is defined as:

        =(Sin 3x)/2x        when x≠ 0

 f(x)=  2/3       when x= 0

Is f(x) continuous at x= 0 ?

4) Find the points of discontinuity of the function (x²+2x+5)/(x²-7x+12).

5) A function f(x) is defined as:     

 f(x)=(x⁴+4x³+2x)/sin x  when x≠0

       And f(0)=0

Show that f(x) continuous at x= 0

6) A function f(x) is defined as:

 f(x)= x sin(1/x)       when x≠ 0

       =  0                     when x = 0

Show that f(x) continuous at x= 0

7) The function f(x) is defined as:

        =x²-2x+3       when x< 1

 f(x)=  2                 when x= 1

       =2x²-5x+5      when x> 1

Is f(x) continuous at x= 1 ?

8) f(x)= (x²-1)/(x³-1) is undefined at x= 1. What should be the value of f(x) at x= 1 such that f(x) may be continuous at x= 1 ?

9) For what value of f(4), the function f(x) = (x²-16)/(x-4) is continuous at x= 4 ?

10) Examine the continuity of the function f(x) at x= 1.

 f(x)= |x-1|/(x-1)      when x≠1

       =  0                    when x = 1

Is f(x) continuous at x= 1?

11) Test whether the following function is continuous at x= 0 :

 f(x)= |x|/x         when x≠ 0

       =  1             when x = 0

12) A function f(x) is defined as:

        = x+1        when x≤ 1

 f(x)= 3- ax²     when x > 1

Find the value of a for which f(x) will be continuous at x= 1 ?

13) A function f(x) is defined as:

 f(x)=(x³+x²-16x+20)/(x-2)² at x≠2

       =  K                      at x= 2

If f(x) continuous for all values of x then find the value of K.

14) Determine the values of a so that the following function is continuous at x= 1

 f(x)= ax+3,       when x ≥ 1 

       = x²+a²       when x < 1

15) Two function f(x) and g(x) are defined as:

 f(x)= x²+4      when x ≤ 2

       = x+6       when x > 2 

And g(x)= 2x      when x ≤ 2

               = 4        when x > 2

Show that f(x). g(x) is continuous at x = 2.

16) The function f(x)={log(1+ax) - log(1- bx)}/x is not defined at x= 0. Find the value of f(0), so that f(x) is continuous at x= 0.

_________________________________

Answers

1) no 3) no 4) 4,3 7) yes 8) 2/3 9) 8 

10) continuous at x= 1

11) discontinuous at x= 0  12) 1

13) 7      14) 2, -1  16) a+ b

DIFFERENTIATION

1) logₑ x

2) log₁₀x

3) x ⁻³⁾²

4) x + 1/x

5) x⁴ +6

6) sin 4x

7) sin(x²)

8) ₑ√x

9) log(sin x)

10) cos ⁻¹(ₑ√tanx)

11) a |sinx| + 2x

12) 3x⁵+ 7x⁴ - 2x² - x + 6

13) 1+ x + x²/2! + x³/3! + x⁴/4!

14) √x + 2√x² + 3√x³ + 4√x⁴ + 5√x⁵

15) 5x³/⁵√x² - 3x/³√x⁴ + 7x/⁷√x² + 12 ⁴√/³√x.

16) logₐx + log xᵃ + eˡᵒᵍˣ + logeˣ + e¹⁺ˣ

17) 10ˣ. x¹⁰.

18) (x²+7)(x³+10)

19) √x eˣ

20) x secx log(x eˣ)

21) (1+ sinx)/(1- sinx).

22) 2 cosx/(1- sinx)²

23) (cos x - cos 2x)/(1- cos x).

24) (x³ - 2 + 1/x³)/(x - 2 + 1/x)

25) (eˣ + e³ˣ)/(eˣ + e⁻ˣ)

26) e²ˣ(1+ 2x)

27) √(2x) - √(2/x) + (x+4)/(4 - x)

28) {f(x)}ⁿ

29) √(log x)

30) tan⁵x

31) (tan⁻¹x)²

32) ₑ(ax² + bx +c)

33) ₑ{√(x+1) - ₑ √(x -1)}

34) ₇(x²+ 2x)

35) log(sinx)

36) log(ax²+ bx +c)

37) log(secx + tanx)

38) log ₛᵢₙ ₓ 

39) logₑ{x + √(x²±a²)}

40) sin€(x)

41) cos(ax + b)

42) sinx°

43) sinx sin 2x sin 3x

44) sin⁻¹(x/a)

45) cot⁻¹(cosec x+ cotx)

46) log(cos x²)

47) 2 tan⁻¹√{(x - a)/(b - x)}

48) cot⁻¹{√(1+ x²)}

49) cos⁻¹{(1- x²)/(1+ x²)}

50) sin⁻¹{2x/(1+ x²)}

51) tan⁻¹{2x/(1- x²)}

52) tan⁻¹{1/√(x² - 1)}

53) tan⁻¹{(3x - x³)/(1- 3x²)} at x= 1

54) tan⁻¹{cosx/(1- sinx)}

55) cos(sin⁻¹x) + tan(cot⁻¹x)

56) sin(cos⁻¹x) + 1/2 sin⁻¹{2x/(1+ x²)}

57) f(logx) where f(x)= logx

58) tan⁻¹{cosx/(1+ sinx)} + sin(eˣ)

59) logₓ(tanx)

60) log √{(1- cosx)/(1+ cosx)} + aˣ.

61) sinx/(1+ cosx)

62) tan⁻¹√{(1- x)/(1+x)}

63) cos{2 tan⁻¹(cosx)}

64) x√(x² + a²)+ a² log{x+ √(x²+ a²)} at x= 0

65) eᵅˣ sin bx.

66) log₁₀ √{(1- cosx)/(1+ cosx)}

67) tan⁻¹√{(1+ cos 2x)/(1- cos 2x)}

68) ₑ√cotx.

69) ₃√(1+ x + x²)

70) log sec(ax + b)³

71) log{2x + 4 + √(4x² + 16x - 22)}

72) tan log sin(ₑx²)

73) xˣ

74) ₓ(1+ x + x²).

75) (tanx)ˢᶦⁿ ˣ at x= π/4.

76) x ᶜᵒˢˣ sin(logₑx)

77) sin⁻¹{2x/(1+ x²)} w.r.t. cos⁻¹{(1- x²)/(1+ x²)}.

78) ₓsin⁻¹x w.r.t. sin⁻¹x.

79) (tan⁻¹x)/(1+ tan⁻¹x) w.r.t. tan⁻¹x.

80) cos⁻¹{(1- x²)/(1+ x²)} w.r.t. tan⁻¹{2x/(1- x²)}.

81) cos⁻¹{(1- x²)/(1+ x²)} w.r.t. sin⁻¹{2x/(1+ x²)}.

82) log[eˣ{(x -1)/(x +1)}³⁾²].

83) {x³√(x² - 12)}/³√(20 - 3x) at x= 4.

84) [x/{1+ √(1- x²)}]ⁿ.

85) cos⁻¹{(8x⁴ - 8x²+1)}

86) xʸ = eˣ⁻ ʸ

87) log(x²+ x+1)/(x² - x +1)

88) tan⁻¹{(cosx - sinx)/(cosx + sinx)}

89) sin⁻¹{2ax √((1- a²x²)}.

90) cos⁻¹{(3 + 5 cosx)/(5+ 3 cosx)}

91) log√{(a cosx - b sinx)/(a cosx + b sinx)}.

92) sin{2 tan⁻¹√{(1 - x)/(1+ x)}.

93) tan⁻¹[√{(a - b)/(a+ b)} tan(x/2)]

94) 3x⁴ - x²y + 2y³= 0

95) x³ + y³ = 3axy.

96) eˣʸ - 4xy = 2.

97) ₓcos⁻¹x

98) xy = cos(xy) at x= π/2 ,y= 0.

99) xʸ. yˣ = 1.

100) (x+ 2)/{(x -1)(x +5)}

101) ₓcos²x

102) x= log(xy)

103) xʸ+ yˣ = 1.

104) ₐx²

105) (sinx)ᶜᵒˢ ˣ+ (cosx) ˢᶦⁿ ˣ.

106) log(xy)= eˣ ⁺ʸ + 2

107) (cosx)ʸ = (siny)ˣ.

108) xᵖ yᑫ = (x + y)ᵖ⁺ᑫ

109) ax² + by² + 2hxy + 2gx + 2fy + c= 0.

110) x= at², y= 2at.

111) x= a cos k,.y = b sin k.

112) x= sin²t, y = tan t.

113) x= a(2t + sin 2t), y = a(1- cos 2t).

114) sinx= 2t/(1+ t²), tan y = 2t/(1- t²).

115) tan⁻¹{t/√(1- t²)} and x= sec⁻¹{1/(2t² - 1)}.

116) y= sin⁻¹(3t - 4t³), x= sec⁻¹{1/(1- 2t²)}

117) y= ₑsin⁻¹t, x= ₑ⁻ cos⁻¹t, 

118) y= a sin³t, x= a cos³t.

119) y= a(sint - t cos t), x= a(cost + t sin t) at t= 3π/4.

120) tan y= 2t/(1- t²), cosx = (1- t²)/(1+ t²).

121) x= 3at/(1+ t³), y= 3at²/(1+ t³).

122) [{tanx}ᵗᵃⁿˣ] ᵗᵃⁿ ˣ at x=π/4

Prove:

1) If cos y = x cos(a+ y), then show dy/dx= (cos²(a+ y))/sin a.

2) If sin y = x sin(a+ y), then show dy/dx= (sin²(a+ y))/sin a = sin a/(1- 2x cos a + x²)

3) If √(1- x²) + √(1 - y²) = a(x - y) then show dy/dx= √{(1- y²)/(1- x²)}

4) If f(x)= {(a+ x)/(b+ x)}ᵃ⁺ᵇ⁺ ²ˣ then show f'(0) = {2 log(a/b) + (b² - a²)/ab}{a/b}ᵃ⁺ᵇ.

5) If y= x²/2 + x/2 √(x²+ 1) + log✓√{x + √(x²+1)}] then prove 2y = x dy/dx + log(dy/dx)

6) If x= a sin 2t(1+ cos 2t), y= a cos 2t(1- cos 2t), then show 1+ (dy/dx)² = sec²t

Revision/test (Standard Deviation)

1) The standard deviation of 1,2,3, ...., n is √14. What is the value of n.

A) 11  B) 13   C) 12   D) 14

2) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.
A) 2.78  B) 1.58 C) 1.48  D) 2.58

3) Find the standard deviation: 49, 63, 46, 59, 65, 52, 60, 54
A) 36.7  B) 34.9 C) 26.4  D) 36.5

4) Find the standard deviation: 20, 85, 120, 60, 40.
A) 6.78  B) 6.36 C) 6.48  D) 6.38

5) Find the standard deviation: 4, 5, 6, 6, 7, 8
A) 2.78  B) 1.29 C) 1.48  D) 1.58

6) Find the standard deviation: 3, 5, 11, 7, 8, 10, 9, 12, 14, 11.
A) 3.78  B) 3.58 C) 3.48  D) 3.16

7) Find the standard deviation: 240.12, 240.13, 240.15, 240.12, 240.17, 240.15, 240.17, 249.16, 240.22, 240.21
A) 0.0785  B) 0.0585 C) 0.0325  D) 0.0352

8) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.10
A) 2.77  B) 2.87 C) 2.47  D) 2.57

9) Find the standard deviation: 1,2, 3,4,5,6,7,8,9.10, 11
A) 3.76  B) 3.16 C) 3.46  D) 3.56

10) For a set of ungrouped values the following sums are found: N= 15, ∑x = 480, ∑x²= 15735. Find the standard deviation.
A) 3 B) 4 C) 5 D) 6

11) Calculate the variance of 1,5,6
A) 4.66 B) 4.86 C) 4.76 D) 4.96

12) Find the variance of the first n positive integers?
A) (n²-1)/12 B) 2(n²-1)/3 C) (n²- 3)/12 D) (n²-2)/12 

13) Find the standard deviation of:

X: 10    20    30    40   50    60

F:  9      18    25    27   14     7

A) 13.12 B) 13.56 C) 13.25 D) 13.52

14) Find the standard deviation of:

X: 25      36     45       55      65  
F: 60    130    150     130    30
A) 11.12 B) 11.56 C) 11.07 D) 11.52

15) Find the standard deviation of:
X: 50    55    60    65   70

F: 30    40    65    50   15   

A) 5.69 B) 5.49 C) 5.79 D)   5.59

16) Find the standard deviation of:
X: 30      40      50       60       70  
F: 64     132    153     140     51
A) 11.78 B) 11.64 C) 11.48 D) 11.58

17) Find the standard deviation of:
Height in inch   No.of students
59-61 61-63  63-65   65-67  67-69
F:  4      30        45        15        6
A) 1.58 B) 1.38 C) 1.85 D) 1.83

18) Find the standard deviation of:
X: 20-23   25-29   30-34   35-39
F:   16           28       14         12
A) 5.50 B) 13) 5.08 C) 5.05 D) 5.04

19) Find the standard deviation of:
Weight     No of students
120-124        12

125-129        25

130-134        28  

135-139       15

140-144       12

145-149        8

A) 7.58 B) 7.38 C) 7.18 D) 7.81

20) The mean of two samples of sizes 50 and 100 respectively are 54.4 and 50.3; and their SDs are 8 and 7 respectively. What is mean and SD of the combined set of observations?
A) 51.7, 7.6  B) 51.7, 7.8 C) 50.7, 7.6  D) 50.7, 7.8

21) The mean of two samples of sizes 15 and 22 respectively are 3.5 and 4.7 ; and their SDs are 3 and 4 respectively. What is mean and SD of the combined set of observations?
A) 4.21, 4.68 B) 3.21,3.68 C) 4.21, 3.68 D) 3.21, 4.68

22) The mean and SD of 20 samples is 10, and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Calculate the SD if the wrong item is replaced by 12.
A) 1.909  B) 1.099 C) 1.990 D) 1.900

23) The mean of two samples of sizes 10 were found to be 9.5 and 2.5 respectively. Later on an additional observation became available. This was 15, and it was included in the original sample. Find the SD of the 11 observations.
A) 2.68  B) 2.48 C) 2.84 D) 2.86

24) For a group containing 100 observations. The mean and SD are 8 and √10.5. For 50 observation selected from these 100 observations the mean and SD are 10 and 2 respectively. Find  mean and SD of the other half.
A) 6, 2  B) 5, 4 C) 6,3 D) 5,5

25) The mean of 20 samples is found to be 10, and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Calculate the SD if the wrong item is omitted.
A) 1.799  B) 1.997 C) 1.979 D) 1.907

26) The first of two samples has 100 items with mean 15 and SD 3. If the whole group has 250 items with mean 15.6 and SD √13.44. find the SD of the second group.
A) 3  B) 4 C) 5 D) 6

27) In a distribution of 200 boys, where 0-5, 5-10 etc. are groups, mean and SD are 40 and 15  respectively. On checking it was found that the marks obtained by one student was wrongly entered as 53 in place of 43. Find the correct SD.
A) 14.17 B) 14.77 C) 14.57 D) 14.97

28) A student obtained the mean and SD of 100 observations as  40 and 5.1 respectively. It was found later that he had wrongly copied one observation as 50, the correct figure being 40. Calculate the correct mean and SD.
A) 39.9, 5 B) 35.9, 9 C) 39.5, 9 D) 39.5, 5

29) Find the coefficient of variation: 40, 30, 80, 60, 50, 90, 70
A) 33.26 B) 33.33 C) 33.36 D) 33.44

30) Find the SD of
Marks(x)       No. Of students
00-10                  05
10-20                   10
20-30                   20
30-40                  40
40-50                  30
50-60                  20
60-70                  10
70-80                   4
A) 15.67 B) 15.65 C) 15.69 D) 15.63

31) Find the coefficient of variation
Marks(x)       No. Of students
01-10                  05
11-20                   12
21-30                   20
31-40                   25
41-50                  40
51-60                  22
61-70                  15
71-80                   6
81-90                   4
91-100                 1
A) 41.2 B) 45.2 C) 42.5 D) 52.4

32) Prices of a particular commodity in five years in two cities are given below:
Prices in City A           City B
  20                                  10
  22                                  20
  19                                  18
  23                                  12
  26                                  15
Find the City which had more stable prices.
A) A B) B C) both A and B D) N

33) Which factory has greater variability in industrial wages?
Factory-A  Average  SD employee
    A              34.5         5       476
    B              28.5        4.5    524
A) A B) B C) both A and B D) n

Revision/test (probability (x)

1) Two dice are rolled. Find the probability of getting a sum 7.

2) A number is chosen at random from the first 11 natural numbers; then the probability that the chosen number is even.

3) An unbiased coin is tossed 3 times in succession, find the probability of getting exactly one head

4) The probability of getting 11 when an ordinary die is thrown twice

5) Three children are selected at random from a group of 3 boys and 2 girls. Write down the sample space of this random experiment.

6) A number is chosen at random from the numbers 1,2,.....,15. Find the probability that the chosen number is

A) even

B) odd

C) multiple of 3.

7) From a pack of 52 cards, 1 card is drawn at random. Find the chance of drawing

A) a spade

B) not spade

8) What is the probability of getting 7 points with the rolling of two dice?

9) What is the probability of picking a spade or an ace not of spade from a pack of 52 cards?

10) A box contains 50 articles of which 4 are defective. Find the probability that an article chosen at random from the box is non defective.

11) A die is thrown. Write down the sample space. What is the probability that either an odd number or a number greater than 4 will turn up ?

12) An unbiased coin is tossed two times. Write down the sample space. Hence find the probability of getting exactly one head.

13) Given that a family of two children has a boy, what is the probability that the other also is a boy

14) It is known that a family has three children and atleast one of these three children is a girl. Find the probability that all the three children are girls.

15) A coin is tossed n times. Find the probability of odd numbers of head.

16) Two dice are rolled. Find the probability of getting a total of 5 points on these dice.

17) In a single cast with 3 dice what is the probability of getting 3 sixes.

18) In a single cast with 3 dice what is the probability of getting different digits.

19) In a single cast with 3 dice what is the probability of getting same digits in two dice and different digit in the other.

20) What is the probability of getting a sum of 8 in a single cast with two dice.

21) What is the probability of getting atleast 8 in a single cast with two dice.

22) In a family there are 4 children. Find the probability that

A) all of them will have different birthdays

B) two of them will have the same birthday

23) What is the probability that a leap year selected at random will contains 53 Mondays? Find also the probability of having 53 Mondays in a year, which is not a leap year.

24) Two fair dice are thrown simultaneously. The two scores are then multiplied together. Calculate the probability that the products is

A) 12

B) even

25) There are 52 cards with each of two boys. Each draws a card at random. What is the probability that

A) both the cards will be king of diamonds

B) both will be diamonds

C) both will be kings

26) If two numbers are selected at random from the numbers 1, 2, 3, 4 determine the probability that their sum is odd when they are selected together.