Linear equation
3) 2(2p+1) - 30% 8 (5p -2) = 76
4) (3p-2)/7 - (p -2)/4 = 2.
5) (x+5)/2 - (x -2)/3 = 4.
6) (2x -3)/6 - (x -5)/2 = x/6.
7) (x -4)/7 - (x +5)/5 = (x+3)/7
8) (x-1)/5 + (x -2)/2 = x/3 + 1
9) 2(x-5)+ 3 (x -2) = 8+ 7(x -4)
10) 3(2x -5)/4 - 5(7 - 5x)/6 = 7x/3.
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
3) 6x² + 5x -6.
4) 3x² - x - 4
5) x³ - 2x² - x + 2
6) x³ - 3x² - 9x -5
7) x³ + 13x² - 32x + 20.
8) 2x³ + x² - 2x - 1
9) x² - 5x + 6
10) x³ - 23x² + 142x + 120
11) 9x² + 6xy + y²
12) 4x² - 4x + 1
13) x² - y²/100
14) 8a³ + b³ + 12a²b + 6ab²
15) 8a³ - b³ - 12a²b + 6ab².
16) 27 - 125a³ - 135a + 225a²
17) 64a³ - 27b³ - 144a²b + 108ab².
18) 27p³ - 1/216 - 9p²/2 + p/4
19) 27y³ + 125z²
20) 64m³ - 34n³
21) x² + 1/x² - 2x - 2/x +2
22) a(a- 1)- b(b- 1)
23) 8x³ - 27y³ + 36x²y +54xy².
24) 8x³ + y³ + 27z³- 18xyz
25) (2x+ 3y)³ - (2x - 3y)³.
26) a³ - b³ + 1 + 3ab
27) (p -q)³ + (q - r)³ + (r - p)³
28) 9x³ - 9y³ + 6x + 1
29) x² - 5x/12 + 1/24
30) x⁶ - y⁶
31) 1 + x³
32) x¹² - y¹²
33) 54a³ - 250b³
34) 8x³ + 27y³ + 36x²y +54xy².
9/5/22
29) 64¹⁾³
30) 8⁵⁾³
31) 9³⁾²
32) 125⁻¹⁾³
33) 243 ⁻³⁾⁵
34) (9/16)⁻¹⁾²
35) (0.01) ⁻¹⁾²
36) (64/25)⁻³⁾²
37) √36
38) ³√125
39) ⁴√81
40) ⁵√32
41) √50
42) ³√40
43) 125 ¹⁾³
44) 8 ²⁾³
45) (1/5) ⁻²
46) 16 ⁻³⁾⁴
47) 32 ⁻⁴⁾⁵
48) (8/125)⁻¹⁾³
49) (-27)²⁾³
50) (0.001)⁻¹⁾³
8/5/22
Exponent
Simplify:
1) 64¹⁾².
2) 32 ¹⁾²
3) 125 ¹⁾³
4) 9³⁾²
5) 32²⁾⁵
6) 16 ³⁾⁴
7) 125⁻¹⁾³
8) 2²⁾³. 2¹⁾⁵
9) (1/3³)⁷
10) 11 ¹⁾² /11¹⁾⁴
11) 7 ¹⁾² . 8¹⁾²
12) 4³⁾²
13) (8¹⁾⁵)⁴
14) (1/3⁵)⁴
15) 7 ¹⁾⁵/7 ¹⁾³
16) 13¹⁾¹⁵+ 13 ¹⁾³⁰
17) 2²⁾³ . 2²⁾³
18) 13 ¹⁾⁵ . 17¹⁾⁵
19) 16 ³⁾²
20) 8¹⁾³ /8 ¹⁾⁶
21) 3²⁾³x 8 ²⁾³
22) (2³)²
23) (625)¹⁾⁴
24) (64) ⁻¹⁾³
25) ³√(64) ⁻²
26) (√x³) ²⁾³
27) If (2/6)⁶ x (9/4)⁵= (3/2)ⁿ⁺² then find the value of n
28) (-1/27)²⁾³.
