29/5/22
A. P
1) If the sum of the three numbers in A. P be 18 then what is the middle term? 6
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? Y
4) Find the 8th term of an AP., 13, 10, 17, 24...... 52.
5) Which term of the AP. 7, 11, 15, 19, ....... is 103? 25th
6) If the 7th term of an AP be 20 and the 10th term be 29 then find the first and the common difference. 2, 3
7) Can be any term of the AP 5, 10, 15..... N
8) In an AP 1st term be -5, last term be 25 and number of terms be 10. Find the sum of the terms. 100
9) What do you mean by natural numbers? Find the sum of first 100 natural numbers. 5050
10) a²+ 3a + 2, 3a²+ 2a+5, 4a²+ 5a + 4 are in AP, then find a. 2
11) Find the arithmetic progression of which nth term is 3n -1. 2, 5, 8.......
12) If the pth term of an AP be q and qth term be p, then find the p+ q th term. 0
13) The sum of first n terms of an AP is n². Find the common difference. 2
14) Find the sum of the first 20 terms of the AP. 20, 17, 14... -170
15) 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. 55, 825/2
16) The sum of p th term of an AP is 3p²+ 5p; show that it is an AP.
17) Insert five A. M between 2 and 20.
18) The n th term of an AP is p. Show that the sum of first (2n -1) terms is (2n -1)p.
19) The p th term of an AP is a, and the q th term is b. Show that the sum of first (p+ q) terms is 1/2 (p+ q)(a+ b + (a- b)/(p - q)).
20) The sum of how many terms of the series 27 + 24+21+...... will be equal to 132 ? 8 or 11
21) 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.
22) Find the sum upto n terms of the following series. 1+ 5 + 12+ 22+ 35+ ....... {n²(n+1)/2}
23) If the sum of the p, q and r terms of an AP be x, y, z respectively then prove that:
x/p (q- r)+ y/q (r- p)+ z/r (p- q)= 0
24) Find the following sum:
1²+ 3² + 5²+ ...... upto n terms. n/3 (4n² - 1).
25) The middle term of an AP having 11 terms is 12. Find the sum of the 11 terms of that progression.
26) Find the sum of n terms of 2.4 + 6.8 + 10.12+ ..... 4n/3 (n+1)(4n -1)
27) The p th, q th and r th terms of an AP are P, Q , R respectively. Prove p(Q - R) + q(R - P) + r(P - Q)= 0.
28) The sum of the three numbers in AP is 21 and their product is 231. Find the numbers. 3, 7,11 or 11, 7, 3
29) There are n arithmetic means between 4 and 31. If the second mean: last mean= 5: 14 then find the value of n. 8
30) 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.
31) The sum of n, 2n and 3n of an AP are a, b, c respectively. Show that c= 3(b - c).
32) Find the sum of 1² - 2²+ 3²- 4² + 5² - 6²+ ...... n/2 (n+ 1).
33) If the sum of p terms of an AP is to the sum of q terms as p² : q², show that (p th term)/(q th term)= (2p -1)/(2q -1).
34) If the
15/2/22
Reasoning
1) Choose the odd one:
A)a)13-22 b) 24-76 c)16-52 d)17-62
B) a)6-16 b)18-48 c)21-56 d)27-76
C)a)39-77b)51-119 c)33-88 d)52-91
D)a)26-4 b)226-14 c)274-16 d)82-8
E) a)2-4 b) 4-5 c)6-18 d)8-32
F) 82, 15., 65, 26
G) a)4-44 b) 6-64 c)3-30 d)5-35
H) 37, 47, 17, 27.
I) New Delhi, Kolkata, Chennai, Mumbai
2) 7: 32 :: 28 : ?
A) 128 B) 228 C) 328 D) 428
3) BCFG: HILM :: NORQ: ?
A) TUXW B) TXUW C) TWXU D) TWUX
4) ACEG: ZXVT:: BDFH: ?
A) SUWY B) YEUS C) YUES D) N
5) 8: 9:: 56 : ?
A) 27 B) 63 C) 72 D) 36
6) 25: 37: : 49: ?
A) 26 B) 62 C) 56 D) 65
7) JkL, AbC, MnO, DeF, PqR, Gh?
A) A B) D C) I D) K
8) 6, 24, 60, 120, 210, ?
A) 6 B) 33 C) 36 D) 336
9) Y X H G W V F E U T D C S R B ?
A) A B) B C) C D) D
10) R Q O L H ?
A) A B) B C) C D) D
11) 2, 6, 12, 20, 30, ?, 56
A) 2 B) 4 C) 24 D) 42
12) 1, 4, 10, 19, 31, ?
A) 4 B) 6 C) 46 D) 64
13) A husband and a wife had five married sons and each of them had four children. How many members are there in the family.
A) 32 B) 44 C) 30 D) 16
14) Two squads of soldiers A and B facing North and South respectively received the following command-- right turn, left turn, left turn, left turn, which direction could the squads A and B face at the end.
A) East, west B) West, East
C) South, North D) north, south
15) 9: 26:: 81: ?
A) 2 B) 4 C) 42 D) 242
16) 3: 26: : ? : 124
A) 142 B) 124 C) 241 D) 214
17) 4: 27:: 9: ?
A) 46 B) 64 C) 83 D) 38
18) 4, ? 144, 400, 900, 1764
A) 69 B) 96 C) 102 D) 44
19) 2, 10, 30, 68, ?
A) 110 B) 120 C) 130 D) 140
20) Odd one out: 9,16,25,36,49,61
A) 9 B) 25 C) 61 D) N
21) Fatima while introducing Mustafa to her husband said, his brother's father is the only son of my grandfather. How is Fatima related to Mustafa ?
A) brother B) sister C) aunt D) niece
22) Tarun's age is the cube of a whole number. It was square of another whole number two years ago. How long must wait before his age is again the cube of a whole number.
A) 13 B) 23 C) 32 D) 39
23) If GERMANY is written as 7, 5, 18, 13, 1, 14, 25. How can FRANCE be written.
A) 6,18,1,14,3,5
B) 6,8,1,14,3, 5
C) 6,18,1,4,3,5
D) 16,18,1,14,3,5
24) A man starts from a point 'X' and walks 3 km southwards, then he turns left and walks 6 km. In which direction is he from the starting point?
A) south-east. B) south-west
C) Northeast D) northwest
25) C is to the west B and south west of A, D is to the North of C and is in line with AB. In which direction from the point of A, B is located?
A) south-east. B) south-west
C) Northeast D) northwest
26) Veena walked 5m towards north, took a left turn and walked 7m. She took a left turn again and walked 8m before taking a left turn and walking 7m. She then took a final
11/5/22
1) x² + 6x + 5= 0.
2) 8x² - 22x -21 = 0.
3) 8x² +15 = 26x.
4) x(2x +5)= 25.
5) (x -3)(2x+5)= 0
6) x² - 7x +10= 0
7) 9x² - 3x - 2 = 0.
8) x² - 8x + 16 = 0.
9) (x² - 5x)/2 = 0.
10) 2x²= 3x + 35
8/7/22
Probability
1) In a cricket match, a boatman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
2) 1500 families with two children are selected randomly, and the following data were recorded:
No of girls in a family No of fam.
2 475
1 814
0 211
Compute the probability of a family, chosen at random, having
A) two girls
B) one girl
C) no girl
3) Three coins are tossed simultaneously 200 times with the following frequency of different outcomes:
Outcomes Frequency
3 heads 23
2 heads 72
1 head 77
No head 28
If the three are simultaneously tossed again, compute the probability of two heads coming up.
4) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:
Monthly inc. vehicles for fam.
0 1 2 above2
Less than 7000 10 160 25 0
7000-10000 0 305 27 2
10000-13000 1 535 29 1
13000-16000 2 469 59 25
16000 or more 1 579 82 88
Suppose a family is chosen. Find the probability that the family chosen is
A) earning ₹10000-13000 per month and owning exactly 2 vehicles.
B) earnings ₹16000 or more per month and owning exactly 1 vehicle.
C) earning less than ₹7000 per month and does not own any vehicle.
D) earning ₹13000-16000 per month owning more than 2 vehicles.
E) owning not more than 1 vehicle.
5) Marks No. Of students
00-20 7
20-30 10
30-40 10
40-50 20
50-60 20
60-70 15
70 and above 8
Total 90
A) Find the probability that a student obtained less than 20% in Mathematics test.
B) Find the probability that a student obtained 60 marks or above.
6) To know the opinion of the students about subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.
Opinion Number of students
like 135
Dislike 65
Find the probability that a student chosen at random
A) likes statistics
B) does not like it.
7) 11 bags of wheat flour, each marked 5 kg, actually contain the following weights of flour(in kg):
4.97, 5.05, 5.08, 5.03, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
find the probability that any of these bags chosen at random contains more than 5 kg of flour.
8) A dice is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:
Outcome Frequency
1 179
2 150
3 157
4 149
5 175
6 190
9) On one page of a telephone directory three were 200 telephone numbers. The frequency distribution of their unit place digit (for example, in the number 25828573, the unit place digit is 3) is given the following table:
Digit frequency
0 22
1 26
2 22
3 22
4 20
5 10
6 14
7 28
8 16
9 20
Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is 6 ?
10) The record of a weather station shows that out of the past 250 consecutive days, its weather forecast were correct 175 times.
A) what is the probability that on a given day it was correct?
B) what is the probability that it was not correct on a given day?
11) A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of 1000 cases.
Distances(in km). Frequency
Less than 4000 20
4000 to 9000 210
9001 to 14000 325
More than 14000 445
if you buy a tyre of this company, what is the probability that:
A) it will need to be replaced before it has covered 4000 km?
B) it will last more than 9000 km.
C) it will need to be replaced after it has covered some where between 4000 km and 14000 km ?
12) The percentage of marks obtained in the monthly unit tests are given by the following table:
Unit tests % of marks obtained
I 69
II 71
III 73
IV 68
V 74
Based on this data, find the probability that the student gets more than 70% marks in a unit test.
13) An Insurance Company selected 2000 drivers at random (i.e. without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:
Age of drivers accident in 1 yr
0 1 2 3 over 3
18-28 440 160 110 61 35
30-50 505 125 60 22 18
Above 50 360 45 35 15 9
Find the probability of the following events for a driver chosen at random from the city:
A) 18-29 years of age having exactly 3 accidents in 1 year.
B) being 30-35 years of age having one or more accidents in a year.
C) having no accidents in one 1 year.
14) 50 seeds were selected at random from each of 5 bags of seeds, and were kept under standardized conditions favorable to germinate. After 20 days, the number of seed which had germinated in each collection were counted and recorded as follows:
Bag No of seeds germinated
1 40
2 48
3 42
4 39
5 41
what is the probability of germination of:
A) more than 40 seeds in a bag?
B) 49 seeds in a bag more than 35 seats in the bag?
C) more than 35 seeds in a bag?
15) A die is thrown once. Find the probability of getting a prime number.
16) A coin is tossed once. Find the probability of getting a head.
17) From a group of two boys and 3 girls, we select a child. Find the probability of this child being a girl.
18) if we throw a die, then the upper face shows 1 or two; or three or four; or five or six. Suppose we throw a die 150 times and get 2 for 75 times. What is the probability of getting a '2'?
19) A coin is toss 200 times and is found that a tail comes up for 120 times. Find the probability of getting a tail.
20) if a coin is tossed for a certain number of times. How many times the coin was tossed, if the probability of getting a head is 0.4 and it appeared up for 24 times ?
21) In a cricket match, if the probability (P(E)) of hitting the boundary is 0.3, then find the probability of not-hitting the boundary.
22) In a G K test a student was given 50 questions one by one. He gave the correct answer for 30 questions. Find the probability of giving correct answers.
23) A coin is tossed 150 times and it is found that heads comes 115 times and tell 35 times. If a coin tossed at random, what is the probability of a getting
A) a head
B) a tail
24) A dice thrown 270 times and the outcomes are recorded as in the following table:
Outcome frequency
1 36
2 45
3 33
4 18
5 75
6 63
if a dice is thrown at random, find the probability of getting:
A) 1
B) 2
C) 3
D) 4
E) 5
F) 6
25) In a sample study of 640 people, it was found that 512 people have a high school certificate. If a person selected at random, the probability that he has a high school certificate is:
A) 0.50 B) 0.65 C) 0.80
26) In a survey of 360 children, it was found that 90 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is:
A) 0.25 B) 0.50 C) 0.75
27) The probability of a sure event is:
A) 0 B) 1 c) 100
28) The probability of an event cannot be less than
A) 0 B) 1 C) -1
29) The probability of an event can not be more than:
A) 0 B) 1 C) -1
30) A common dice has
A) one face B) four faces C) six faces
31) When a die is thrown once, the least possible score must be
A) 0 B) 1 C) 6
32) when a die is thrown once, the greatest possible score must be
A) 0 B) 1 C) 6
33) the sum of the probabilities of all possible outcomes is always equal to
A) 0 B) 1 C) 100
34) if two dice are thrown together, then the least possible total score must be
A) 0 B) 1 C) 2
35) If two dies are thrown together, then the greatest possible score must be
A) 1 B) 6 C) 12
36) the probability of the occurrence of an event is 1/4. what is the probability of the non occurrence of that event?
A) 0 B) 3/4 C) 1/4
37) a coin is tossed 100 times and a head is got 63 times. The probability of getting a head is:
A) 6.3 B) 63.0 C) 0.63
38) In a medical examination of students of a class, the following blood groups are recorded:
Blood group No of students
A 15
B 20
AB 23
O 12
A student is selected at random from the class. The probability that he/she has blood group B, is
A) 1/20 B) 3/4 C) 2/7
39) 80 bulbs are selected at random from a lot and their life time ( in hours is recorded as given below:
lifetime(hrs) No. of bulbs
400 10
500 3
600 12
700 20
800 14
900 11
one bulb is selected at random from the lot. The probability that its life is less than 800 hours is:
A) 1/80 B) 1/4 C) 11/16
40) A dice is thrown once. The probability of getting a number greater than 6 is:
A) 0. B) 1 C) 1/6
41) In a class of 10 students, 4 are or girls. The probability choosing a boy is :
A) 2/5 B) 3/5 C) 1/10
42) Cards are marked 1 to 20. The probability of drawing a card marked with a multiple of 3 is:
A) 3/10 B) 3/20 C) 1/20
43) The probability of getting a number '0' is one throw of a die is
A) 0 B) 1/6 C) 1
44) The probability of getting a number 6 is one throw of a die is
A) 0 B) 1/6 C) 1
------------
1) Fifth term of a G.P is 2; then the product of its first 9 terms is-
2) The Number of Numbers that can be formed using the digits 1,2,3,4,5 repetition is not allowed.
3) The Number of Numbers that can be formed using the digits 1,2,3,4,5 repetition is not allowed such that the ten's digit is greater than thousand's digit is -
4) If the first term of an A. P is 2 and common difference is 4, then the sum of its first 40 terms is-
5) a≠b but a²=5a-3 and b²=5b-3, then the Equation whose roots are
a/b and b/a is-
6) If log₄(x-1)=log₂(x-3)
then x is-
7) find k if (k-2)x²+8x+k+4=0 has
real roots.
8) How many words can be formed from the letters of the word COMMITTEE ?
9) Value of log₈log₁₅16 .log₂15 is-
10) log₂log₂log₄256+2log₂2 is
11) If nth term of the G. P is
-5/2,5/4,-5/8,... is 5/1024 find n.
12) The Number of straight lines that can be formed by joining 20 points of which 4 are collinear is-
13) If the Equation x²+px+q=0 and x²+qx+p=0 have a common root, then the value of(p +q) is-
14) Total Number of four digit odd numbers that can be formed using the digits 0,1,2,3,4,5,6,7 are-
15) The Number of diagonals of a polygon of 20 sides is-
16) a,b,c are in A. P then
a/bc,1/c,2/b will be in-
17) value of log[1¹/⁵+(32)¹/⁵
+(243)¹/⁵] is-
18) log₅8 log₈24 log₂₄x=log₈512
find x
19) if logₙ[log₂log₇x]=0 find x
20) The least integral value of k which makes roots of the Equation x²+5x+k=0 imaginary is-
21) If n parallel lines in a plane are intersected by a family of m parallel lines, then the number of parallelogram formed in the network will be-
22) The condition that one root of the Equation ax² +bx+c=0 is three times the other is-
23) A polygon has 35 diagonals; then the number of its sides is-
24) 11 books consisting of 5 Mathematics,4 physics and 2 chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together, is-
25) Six line segments of lengths 2,3,4,5,6,7 units are given. The number of triangles that can be formed by these lines is-
26) If x,y,z are in A.P then
1/yz,1/zx,1/xy are in-
27) The condition that x³-3px+2q may be Divisible by a factor of the form x²+2ax+a² is-
28) A boy goes to school from his home at a speed of x km/hr and comes back at a speed y km/hr. Then his average speed is-
29)Numbers greater than 1000 but less than 4000 are formed using the digits 0,1,2,3,4 (repetition allowed). Total number of such Numbers is -
30) The sum of integers from 1 to 100 that are Divisible by 2 or 5 is-
31) The number of ways in which the letters of the word ARRANGE be arranged such that both R do not come together.
6/4/22
1) Value of 1³-2³+3³-4³+.....+9³ is-
2) The number of terms of the A. P. 3,7,11,15, .. to be taken so that the sum is 406, is-
3) The two G. M between 1and 64 is-
4) The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between two boys, is-
5) The number of 2-digit even Numbers can be formed using the digits 1,2,3,4,5 is-
6) If the roots of the Equation ax²+bx+c=0 are k and 2k,then find the value of a
7) If p and q are the roots of the Equation x²+px+q=0 then find p,q
8) If log₇log₅{√(x+5)+√(x)}=0 find x.
9) if ⁴³Cᵣ₋₆ =⁴³C₃ᵣ₊₁ Find r
10) value of ⁿCᵣ₊₁+ⁿCᵣ₋₁ +ⁿCᵣ is.
11) In how many ways can 7 girls be seated in a row so that 2 particular girls are next to each other ?
12) A bag contains 3 red and 5 blue balls. If one ball is drawn from the bag, what is the probability that the ball is not red ?
13) In examination paper consists of 12 questions Divided into two parts A and B. Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions, selecting atleast 3 questions from each part. In how many ways can he selected the questions ?
14) In how many ways can the letters of the word SALLOON ibe arranged so that the two O's do not together.
15) The Odds in favour of an event are 3:5. Find the probability of occurrence of this event.
5/4/22
1) A committee of 5 is to be formed from a group of 10 students consisting of 6 boys and 4 girls. In how many ways can the committee be formed if it consists of exactly 3 boys and 2 girls ?
2) A purse contains two silver and four gold coins. A second purse contains four silver and three gold coins. If a coin is taken out at random from one of the purses, what is the probability that it is a silver coins ?
3) In How many ways can the letters of the word LAUGHTER be arranged, so that the vowels are not separated ?
4) A bag contains 4 white and 3 green balls. One ball is drawn at random. Find the chance that it is a green ball.
5) If ²⁵Cᵣ₊₄ = ²⁵C₂ᵣ₋₃ find r.
6) If the roots of the Equation 5x²-7x+k=0 are reciprocal of each other, then find k .
7) How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order.
8) There are n points of which m points are collinear. How many lines can be formed from these points?
9) If the roots of the Equation (a²+b²)x² -2(ac+bd)x + c²+d²=0 are equal, find the Relation between a,b,c,d.
10) If the sum of first n terms of an A. P. series is n²+2n, then the term of the series having value 201 is-
11) Everybody in a room shake hands with everybody else. If the total number of handshake is 66, then the number of persons in the room is-
12) If Log 617.2=2.7904 then find the value of log 0.0006172.
13) How many nine digit numbers can be formed using the digits 2,2,3,3,5,5,8,8,8 so that odd digits occupy even positions ?
14) If x²+px+q=0 is the Quadratic Equation whose roots are (a-2) and (b-2) where a and b are roots of x²-3x+1=0, then find p and q.
15) Number of triangles formed by joining 12 points, 7 of which are in the same straight line is-
4/4/23
1) The Number of five digits number Divisible by 3 that can be formed using the digits 0,1,2,3,4,5.
2) Find x:
a) x² 4√2 x+6=0.
b)) x² - x - a(a+1)=0
3) Find Karl Pearson's correlation
X: 20 13 18 21 11 12 17 16
Y: 17 12 22 24 20 21 18 10.
4) Find the mean of 7,9,16,24,26
5) A box contains two white, three black balls and 4 red balls. In how many ways can three balls be drawn from the box if Atleast one black ball is to be included in the draw ?
6) Age: 25-30 30-35 35-40 40-45
Class: 30 23 20 14
Find the mean.
7) Bag1 contains 5 white and 4blue balls. Another bag contains 7white and 9black balls. A ball is transferred from the first bag to the 2nd and then a ball is drawn from the 2nd bag. Find the probability that the ball is drawn is white.
8) How many words can be formed out of 5 Different consonants and 4 Different vowels if each word is to contain 3 consonants and 2 vowels.
9) From a deck of cards, one card is drawn at random. What is the probability that the card drawn is either an Ace or a king.
10) There are 3 girls and 6 boys in a club. A committee of 5 is to be selected such that there are 2 girls and 3 boys in the commitee. In how many ways can the commitee be selected? What is the number of ways if there is atleast one girl in the committee ?
11) A bag contain some white and black balls. Another bag contain 7 white and 9 black balls. A ball is transferred from 1st bag to the 2nd and then a ball is drawn from the 2nd bag. Find the total probability that the ball is white.
12) How many Numbers between 5000 and 6900 can be formed with digits 3,4,5,6,7,8?
13) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5 find b.
14) Solve:
(x+3)/(2x+3) =(x+1)/(3x+2)
15) Rs2000 is lent out for 10% compound interest, compounded annually. Calculate:
a) the amount at the end of 1st year.
b) the amount at the end of 2nd yr.
c) C. I at the end of 2 years.
3/4/22
1) Find mean and mode
Class. Age
Below 10 15
,, 20 35
,, 30 60
,, 40 80
,, 50 96
,, 60 127
,, 70 190
2) If x²+ax+10=0 and x²+bx -10=0 have a common root then the value of (a² -b²) is-
3) If the roots of the Equation
(x²- bx)/(ax- c)= (m- 1)/(m+1) are equal and of opposite signs, then the value of m is -
4) Let a,b be the roots of the Equation x²+(3-K) x - K=0. The value of K for a²+b²=5
5) A man has 10 friends. In how many ways he can invite one or more of them to a party ?
6) Out of 6 teachers and 4 boys, a committee of eight is to be formed. In how many ways can this be done when there are not less than 4 teachers ?
7) Out of two regression lines, find the line of regression
of Y on X : 3x+12y=0; 9x +3y =46.
8) A speaks the truth in 60% cases and B in 90% cases. In what% of cases are they likely to contradict each other in stating the same fact.
9) Calculate the compound interest on Rs8000 for 1 year at 12% per annum compounded half-yearly.
10) If f(x) = (2x - 7)/(x+4) find
a) f(2)
b) f(x³)
c) f(3x+1)
11) If x:y=4:3 find (5x+8y):(6x- 7y)
12) 5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15,15, 16,1618,19,20. Find Mean, Median, Mode.
14) If f(x)=225-4x² find
a) f(3)
b) x, such that f(x) =0.
15) An aeroplane travelled a distance of 800 km at an average speed of x km/hr. On return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:
a) the onward journey
b) the return journey
If the return journey took 40 minutes less than the onward journey, write down an equation in x and find its value.
2/4/2022
1) Two numbers are in the ratio of 7:11. If 15 is added to each Number, the ratio becomes 5:7. Find the numbers.
2) Calculate the compound interest for the 2nd year on Rs6000 invested for 3 years at 10% p.a.
3) Solve: 3x²-5x=1.
4) Ashok borrows Rs20000 at 12% C.I. per annum, interest payable every six months. He pays back Rs6200 at the end of every six months. Calculate the 3rd payment Ashok has make at the end of 18 months in order to clear the entire loan.
5) n P 5 : n P 3 = 2:1 find n.
6) How many Numbers between 5000 to 6000 can be formed with the digits 3,4,5,6,7,8.
7) A bag contains 4 white and 3 green balls. One ball is drawn at random. Find the probability that it is white.
8) A box contains 2 white,3 black balls and 3 red balls. In how many ways can 3 balls be drawn from the box if Atleast 1 black ball is to be included in the draw ?
9) The probability of X,Y,Z solving a problem are 1/3,2/7,3/8. If all the three try to solve the problem simultaneously, find the probability that Exactly one of them will solve it.
10) find the value of ¹⁰C₅+¹⁰C₄
11) What is the probability of getting 3 white balls in a draw of 3 balls from a box containing 5 white and 4 black balls.
12) If f(x) = (x-1)/(2x²-7x+5)
when ≠1 and find f'(1)
13) You are given the following results on two variables x and y: mean of X and Y is 36,85 s.d of x and y are 11,8 r is 0.66. find the two regression equation of x and y and estimate the value of x when
y=25.
14) Four persons are chosen at random from a group consisting of 3 men, 2women and 4 children. Find the probability that exactly two of them will be children.
15) In how many ways can 10 books be arranged on a shelf such that a certain pair of books should always be together.
16) What is the probability that the sum of the faces is not less than 10 when two unbiased dice are thrown
1.4.2022
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1) The mean weight of 150 students in a class 60 kg. The mean weight of boys is 70kg and that of girls is 55kg. Find the number of boys and girls in the class.
2) There are 4 questions in group A, 4 in a group B and 2 in group C. In how many ways can a student select 5 questions taking 2 from A. 2 from B and 1 from C.
3) Find correct correlation coefficient of: mean of X and Y is 30,40 and X²=220, Y²= 340, XY= 214. On subsequent verification it was detected that the pair(4,8) was copied wrongly, the correct value (2,6).
4) X: 18 20 22 23 27 28 39
Y: 23 25 27 30 32 31 36 .
Find regression equations.
5) An urn contains two silver and four gold coins. A second urn contains 4 silver and 3gold coins. If a coin is taken out randomly from one of the two urns, what is the probability that it is a silver coin?
6) A committee of 5 is to be formed from a group of 10 students consisting of 6 boys and 4 girls. In how many ways can the committee be formed if it consists of exactly 3 boys and 2 girls?
7) Calculate median and mode of 9,0,2,8,5,3,5,4,1,5,2,7.
8) Solve: 30-4(2x-1)> - 8.
9) Solve y - √(3y -6) =2.
10) If -5 is a root of the x²+ kx - 130=0. Find k, Hence find the other root.
11) The perimeter of a rectangular plot is 180m and its area is 1800m². If the length is x m, Express the breadth in terms of x. Hence, form an Equation in x. Solve the Equation and find the length and the breadth of the rectangle.
12)X:2-4 4-6 6-8 8-10 10-12 12-14
F: 6 9 16 13 4 2
Find mode.
13) g(x)=9-x² where x belongs to R,
a) find g(2)
b) find x if g(x)=0
14) Given f(x)=x³ -1, find x if f(x) is 215
15) If g(x)= (2x²-1)/(x-2), x≠ 2, x belongs to R, find the value of
g(5)/g(1/2).
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