MIXED QUESTIONS . COM
PAPER - 1
find the length of CR. 5.5cm
find the length of CR. 5 cm
If AB =2cm, BC= 4cm, and CD =9 cm, calculate EB and AF. AEF and CED, AFC and BEC, ABE and ACD, 3, 4.5
Calculate
If BO: OD= 4:7, find
1) A shopkeeper buys a box of 10 dozen apples for Rs180. He estimates the 20% of them would be rotten. He intends to sell each apple so as to make a profit of 60% on his cost. Assuming that 20% of the apples turn out to be rotten, find:
a) the number of goods apples in the box. 96
b) the sum of money for which he should sell the good apples so has to make a profit 60% on his cost, Rs288
c) the selling price of each apple in order to earn the said profit. Rs3
2) A merchant bought 40 kg tea and sold it for Rs3225.60, thereby making a profit of 12%.
a) At what rate per kg was a tea bought. Rs72
b) If the cost price of the tea is the raised by 8% for the merchant, and the selling price per kg remains the same, find his profit and loss on selling 50 kg tea. Rs144
3) A man bought 150 articles, the price of each being the same. He sold 30% of these articles at a profit 30%, 48% of the articles at a profit of % and the remaining at a loss of 16%, thus making a profit of Rs4071.60 on the whole . Find the cost price of each article. Rs180
4) 150 articles, the price of each being the same kind were bought by a supplier for Rs12750 and Rs12.50 per article were spent on its packaging, transporting etc.
if 60% of the articles was sold for Rs115 each and remaining for Rs120 each ; find the profit percent. 20%
5) A certain number of eggs are bought at 4 for Rs 5 and an equal number at 9 for Rs10.
a) If 15% of eggs were broken in transaction and remaining were sold at 2 for Rs3. Find the profit percent. 8%
b) Find the number of eggs of each kind bought, if Rs510 were gained on the whole. Rs2700
6) A manufacturer is to charge Rs32000 for an article manufactured by him. These charges include the costs of material and labour in the ratio 3:5 and a profit of 60% to the manufacturer.
If the cost of material doubles and the labour becomes 20% costlier but manufacturer gets the same money (Rs32000) for the article; what loss or profit percent does he make? 1%
7) A trader gives two successive discount of 15% and 10% on the marked priced of an article.
a) if the marked price was Rs100, what would be the selling price ? Rs76.50
b) The actual selling price is Rs7650. Calculate the actual marked price ? 10000
c) The actual marked price is 25% more than the cost price. Calculate
i) the cost price, Rs8000
ii) the profit or loss percent. 4.375%
8) A trader gives 25% discount on his articles and still makes a profit of 25%. Find his profit percent, if he sells his articles at
a) 10% discount. 50%
b) their marked price . 200/3%
9) The catalogue price of an article is Rs3600 and a manufacturer sell it to the distributor at 20% off the catalogue price. The distributor, in turns, sells it to the retailer at 10% off the catalogue price.
a) What profit percent is made by the retailer , If he sells the article to a customer at the catalogue price ? 100/9%
b) What profit percent is made by a manufacturer , if the catalogue price is 40% above the cost? 20%
10) A trader adds 40% of the price he pays for his goods to give a selling price. He later a reduces the price of goods, in a sale , by 25%.
a) if the trader buys an article for Rs640; find its sale price. Rs672
b) Find the price paid by the trader for an article whose sale price is Rs1575.
In both the cases, given above, find the profit percent made by the trader. Rs1500; 5% in each case
11) A man is 15 barrls, all of same capacity, of oil. If heyou sells oil at Rs25 per litre, he loses Rs1500 on the whole and if he sales oil at Rs27 per litre, he gains Rs300 on the whole. Find the quantity, in litres, of oil in each barrel and the cost price of oil per barrel. 60 litres; Rs1600
12) The population of a town increases every year at a certain fixed rate. If its population at the end of years 1994 and 1995 be 46000 and 52900 respectively. Find its population at the beginning of the 1994 and at the beginning of 1997. 40000, 60835
13) The cost of machine depreciated by Rs4752 during the second year by Rs4181.76 during the third year. Calculate
a) its rate of depreciation. 12%
b) its original cost. 45000
c) its cost at the end of the third year. Rs30666.24
14) A sum of Rs30000 is invested at 10% per year compound interest.
a) What is the sum due at the end of the wnd year. Rs36300
b) What is the sum due at the end of 3rd year ? Rs39930
c) Find the difference between the answer in (b) and (a) and find the interest on this sum for 1 year. Rs3630 and Rs363
d) Find the compound interest for the 4th year. 3993
15) A sum of money lent out at 12% CI, compounded yearly earns an interest of Rs4704 in the 2nd year. Find :
a) compound interest in first year. Rs4200
b) compound interest in 3rd year. Rs5268.48
c) the sum lent. 35000
16) Find the difference between the simple interest and compound interest on Rs24000 for 2 years at 15% per annum. Rs540
17) 3 years ago, the population of a town was 900000. It increased by 5% the in first year and by 6% in the 2nd year but it. decreases by 10% in the third year . find its present population. 901530
18) A man borrowed Rs14000 for 3 years under the following terms--
15% simple interest for first two years.
16% CI for the last year on the amount due after 2 years. The intrest being compounded semiannually.
Find the amount to be paid after 3 years. Rs21228.48
19) A sum of money lent out at CI per year amounts to Rs5292 in 2 years and to Rs5556.60 in 3 years. Find
a) the rate of interest. 5%
b) the sum lent out. Rs4800
20) The scale of a map 1: 20000. A plot of land of area 20 km² is to be represented on the map. Find :
a) the number of kilometres on the ground which is represent by 1 cm on the map. 2km
b) the area, in km², that can be represented by 1cm². 4km²
c) the total area of the map that represents the whole plot of land . 5cm²
21) A model of a building is made to a scale of 1: 50.
a) The height of the model is 1 m, calculate the height of the building. 50m
b) The area of the land used for the building is 1600m², find the area of the base of the model. 0.64m²
c) The volume of the model is 20 litres, calculate the volume of the building. 2500 m³
22) In a size transformation, the area of the image of an object of area 4.8m² is 30 cm². Calculate the scale factor. 1:40
also, find the volume of an object, if the volume of its image is 180cm³. 11.52m²
23) A model of a ship is made to a scale of 1:160. Find
a) the length of the ship , if the length of its model is 1.2m. 192
b) the area of the deck of the ship, if the area of the deck of its model is 1.2m². 30720 m³
c) the volume of the ship , if the volume of its model is 1.2m³. 4915200m³
24) ABC is a right angle triangle with the right angle at B. BD is the altitude through B. Given BD= 12cm and AD= 9cm,
a) calculate AB. 15
b) Name the two triangle which are similar to Triangle ADB. ABC, BDC
c) find AC. 25cm
d) find BC. 20cm
25) In the given figure, if AC =3cm, CB =6cm,
26) in the given figure AC =8cm and CB=4 cm,
27) In triangle ABC, angle ABC= 90°, and CD perpendicular to AB , Find
a) CD, if AB =18cm and DB= 6cm. 6√2=8.5 app
b) DA, if CA=7 cm and BA= 9cm. 49/9cm
c) BC, id BD= 3cm and AD= 6cm. 3√3= 5.2cm app
28) In the given figure, name three pair of similar triangles.
29) in the figure of question number 28, if AF =7.5cm, CD =12.5cm and EF= 5cm, calculate the measure of EC and EB. 25/3cm, 75/16cm
30) In the given figure : ABCD is a parallelogram and AP : PB= 3:5.
a) area(∆PBN): area(trapezium APND). 25:39
b) PN: BC and area (∆PMN): area(∆BMC). 5:8 and 25:64
c) BM: DM and BM: BD. 5:8 and 5:13
d) area(∆BMC) : area (∆DMC) and area(∆BDA): area (∆DMC). 5:8 and 13:8
31) in the given figure shows a trapezium in which AB is parallel to DC and diagonals AC and BD interesected at point O.
a) ∆ABD: ∆AOB. 7:4
b) ∆AOB: ∆ACB. 4:11
c) ∆DOC: ∆AOB. 16:49
D) ∆ABD : ∆ BOC. 11:7
32) The perimeter and area of each of the following figures. (All dimensions are in centimetre and the curved parts are arcs of the circle whose centres are marked ).
a)
76cm, 358.75cm²
b)
60.95cm, 209.52cm²
c)
66.19cm, 230.95cm²
d)
63cm, 244.125cm²
e)
60.57cm, 57.46cm²
33) Calculate the area and the perimeter of a remaining, after quadrants of radius 4 cm and cut from the four corners of a rectangle measure 18cm by 10cm. 129.71cm², 49.14cm
34) A piece of wire in the form of an Arc of a circle of radius 20cm, subtending an angle 150° at the centre of the circle. If it is bent into the form of a complete circle, find the radius of the circle. 25/3cm
35) The area enclosed between two concentric circle is 2464cm² and the difference between their perimeters. is 88cm, calculate the circumference of the inner circle and the area of the outer circle. 132, 3850
36) The radii of three concentric circles are 14cm, xcm, 56cm, where 14< x < 56. if four times the area enclosed between the two inner circles is equal to the area enclosed between the two outer circles , calculate the value of x. 28
37) The pulley on the jib of a crane has a diameter of 56 cm. Find :
a) the circumference of the pulley . 176
b) the number of revolutions made by the pulley when the crane raises a load through a verticle height of 44m. 25
38) A square is inscribed in a circle of radius 21√2 cm. Calculate the area enclosed between the circle and the square. 1008cm²
39) A circle running track, 4.2 m wide, is bounded by two concentric circles . A sum of Rs20314.80 is spent in constructing this track at the rate of Rs45 per m²; calculate the length of the diameter of the outer edge of the running track. 38.4m
PAPER - 2
1) Find the number of permutations of 6 things taken 4 at a time .
a) 120 b) 240 c) 360 d) 720 e) 840
2) How many 3 digit numbers can be formed out of the digit 1,2,3,4 and 5 .
a) 60 b) 120 c) 240 d) 360 e) 480
3) In How many ways can the 7 letters M,N,O, P,Q,R,S be arranged so that P and Q occupy continuous position ?
a) 720 b) 360 c) 180 d) 120 e) 24
4) What would happen if the letters PQR to be together from M,N,O,P,Q,R,S.
a) 720 b) 360 c) 180 d) 120 e) none
5) Of the different words that can be formed from the BEGINS, how many begins with B and end with S.
a) 24 b) 48 c) 60 d) 72 e) 144
6) In how many ways can the letters of the word VALEDICTORY be arranged so that all the vowels are adjacent to each other ?
a) 8! b) 4! c) 4. 8! d) 4!. 8! e) 8. 4!
7) If there are two kinds of hats-- red and blue -- and at least 5 of each kind, then in how many ways can the hats be put in each of 5 different boxes.
a) 2 b) 2² b) 2³ c) 2⁴ d) 2⁵ e) none
8) In how many ways can 4 Indians and 4 Nepalese people be seated around a round table so that no two Indians are in adjacent positions?
a) 72 b) 144 c) 182 d) 720 e) 840
9) How many number greater than a million can be formed from the digit 1, 2, 3, 0, 4, 2 3 ?
a) 120 b) 240 c) 620 d) 740 e) 1080
10) In how many numbers of 3 digits can be formed with the digit 1, 2, 3, 4, 5 (repetition of digits not allowed)
a) 125 b) 120 c) 60 d) 150 e) 140
11) How many numbers between 2000 to 3000 can be formed with the digit 0, 1, 2, 3, 4, 5, 6, 7 repetition of digits not allowed .
a) 42 b) 210 c) 336 d) 440 e) 500
12) If there are 5 routes to go from Allahabad to Patna and 4 ways to go from Patna to Calcutta, then how many ways are possible for going from Allahabad to Kolkata via Patna ?
a) 20 b) 5⁴ c) 4⁵ d) 5⁴+4⁵ e) none
13) How many ways can the letters of the word DELHI be arranged
a)119 b) 120 c) 60 d) 24 e) 59
14) In how many ways can the letters of the word PATNA be rearranged
a) 60 b) 120 c) 119 d) 59 e) none
15) How many words would be there which would start with the letter P with the letters PATNA
a) 24 b) 12 c) 60 d) 18 e) 30
16) How many words start with P and end with T with the word PATNA
a) 3 b) 6 c) 11 d) 12 e) 10
17) 10Pr= 720, find r
a) 4 b) 5 c) 3 d) 6 e) 7
18) How many numbers of 4 digits can be formed to with the digit 0,1, 2, 3 (repetition of digit is not allowed)
a) 16 b) 24 c) 64 d) 18 e) 32
19) how many numbers of 4 digits can be formed with the digits 0, 1,2 ,3 (repetition is not allowed)
a) 12 b) 108 c) 256 d) 192 e) 132
20) How many numbers between 200 and 1200 can be formed with the digits 0,1,2,3 (repetition of digit is not allowed)
a) 6 b) 8 c) 2 d) 14 e) 16
21) from above question, numbers can be formed with the same digits if repetition of digits is allowed?
a) 48 b) 63 c) 32 d) 14 e) 20
22) ²ⁿ⁺¹Pₙ₋₁ : ²ⁿ⁻¹Pₙ =7:10, find n
a) 4 b) 6 c) 3 d) 7 e) 5
23) How many four digit numbers are possible criteria being that all the four digits are odd ?
a) 125 b) 625 c) 4⁵ d) 120 e) none
24) how many new words are possible from the letters of the word PERMUTATION ?
a)11!/2! b) (11!/2!)-1 c) 11!-1 e) none
25) In how many ways can 12 papers be arranged if the best and the worst paper never come together?
a) 12!/2! b) 12!-11! c) (12!-11!)/2 d) 12!-2.11!
26) In how many ways can the letters of the word EQUATION be arranged so that all the vowels come together ?
a) 4!5! b) 9!/5! c) 9!-4!5! d) 9!/5! e) none
27) How many motor vehicle registration number of four digits can be formed with the digit 0,1,2,3,4,5 (no digit being repeated )
a) 1080 b) 120 c) 300 d) 360
28) How many motorbike registration number plates can be formed with the digits 1,2,3,4,5 (no digits being represted) if it given that registration number can have 1 to 5 digits ?
a) 100 b) 120 c) 325 d) 205
29) How many distincts words can be formed out of the word PROWLING that starts with R and end with W ?
a) 8!/2! b) 6!2! c) 6! d) none
30) How many 7 digit numbers are there having 3 three times and the digit 5 four times ?
a) 7!/(3!.5!) b) 3³x5⁵ c) 7⁷ d) 35
31) How many 7 digit numbers are there having the digit 3 three times and digit 0 four times?
a) 15 b) 3³ x 4⁴ c) 30 d) none
32) How many Even Numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetition of digits are allowed)
a) 648 b) 180 c) 1296 d) 540 e) 600
33) How many 4 digit numbers divisible by 5 can be formed with the digit 0 ,1, 2, 3, 4, 5 ,6 and 6 ?
a) 220 b) 588 c) 432 d) 216 e) 288
34) There are six pups and 4 cats. In how many ways can they be seated in a row so that no cats sit together ?
a) 6⁴ b) 10!/(4!6!) c) 6! X 7P4 d) 6!7! e) n
35) How many new words can be formed with the word MANAGEMENT all ending in G ?
a) 10!/(2!)⁴ - 1 b) 9!/(2!)⁴ c) 10!/(2!)⁴ d) 9!/(2!)⁴ - 1 e) none
36) Find the total number of 9 digit number that can be formed all having different digits ?
a) 10P9 b) 9! c) 10!-9! d) 9.9!
37) the number of positive numbers of not more than 10 digits formed by using digit 0,1, 2, 3 is
a) 4¹⁰-1 b) 4¹⁰ c) 4⁹-1 d) 4⁹ e) none
38) Find the number of numbers that can be formed using all the digits 1,2,3,4, 3, 2, 1 only once so that the Odd digits occupied odd places only ?
a) 4!/(2!)² b) 7!(2!)³ c) 1!3!5!7! D) 3!5! E) none
39) There is a 7 digit telephone number with all different digits. If the digits at extreme right and extreme left are 5 and 6 respectively. Find how many such telephone numbers are possible ?
a) 120 b) 100000 c) 6720 d) 30240 e) n
40) How many six digit numbers have their digits either all odd or all even?
a) 31250 b) 28125 c) 15625 d) none
41) How many 6 digit numbers have at least one even digit ?
a) 884375 b) 3600 c) 880775 d) 15624
42) if we have to make 7 boys seat alternatively with 7 girls around a round table which is numbered, then the number of ways in which this can be done is
a) 2.(7!)² b) 7!6! C) 7!7! d) none
43) how many 6 digit even numbers can be formed from the digits 1, 2,3,4,5,6 and 7 so that the digits should not repeat ?
a) 720 b) 1440 c) 2160 d) 6480
44) How many 6 digit even numbers can be formed the digit 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even ?
a) 720 b) 320 c) 2160 d) 1440
45) How many 5 digit numbers that do not contain identical digits can be written by means of the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9.
a) 6048 b) 7560 c) 5040 d) 15120
46) How many different four digit numbers are there which have the digits 1, 2, 3, 4, 5, 6, 7 and 8 such that the digit 1 appears exactly once ?
a) 7(8P4) b) 8P4 c) 4.7³ d) 7³
47) How many different 7 digit numbers can be written using only 3 digits 1, 2 and 3 such that the digits 3 occurs twice in each number?
a) 7!/2! b) 7!/(2!)³ c) 7! d) none
48) How many different four digit number can be written using the digits 1, 2, 3, 4, 5, 6, 7, 8 only once such that the number 2 is contained once.
a) 360 b) 840 c) 760 d) 1260
49) How many different 9 digit numbers can be formed from the number 223355888 by rearranging its digit so that the odd digits occupy even positions ?
a) 120 b) 9!/(2!)³ . 3! C) 4!(2!)³.3! D) 60 e) none
50) the number of permutations of the letters a, b, c, d, e,f, g such that neither the pattern 'beg' nor 'acd' occurs is:
a) 4806 b) 420 c) 2408 d) 140 e) none
TEST PAPER - 3
A) The cost price of an article is ₹2400 which is 20% of below the Marked price. It is sold at a discount of 16% on the marked price. Find
1) The marked price
A) 2000 B) 3000 C) 4000 D) 5000 E) n
2) the selling price
A) 2220 B) 2320 C) 2420 D) 2520 E) n
3) the profit%
A) 5% B) 6 % C) 7% D) 8% E) n
B) A man invests ₹15000 for two years at compound interest. After 1 year his money amounts to ₹16800. Find
4) the rate of interest
A) 5% B) 6 % C) 7% D) 12% E) n
5) the interest for the second year
A) 2000 B) 2010 C) 2016 D) n
6) In what time will it amount to ₹ 18816 ?
A) 3yrs B) 2 yrs C) 5 yrs D) n
7) A copper wire when bent in the form of a square encloses an area of 121cm². If the same wire is bent into the form of a circle, find the area of the circle.
A) 120 B) 134 C) 154 D) n
8) A tradesman marks his goods at 50% above the cost price. If he allows two successive discounts of 20% and 10%, find his profit percent
A) 6% B) 7% C) 8% D) 9 % E) n
9) the compound interest on a sum of money for 2 years is ₹410 and the simple interest on the same sum for the same period and at the same time rate is ₹400, find the sum and the rate of interest.
A) 5%, 4000 B) 10%, 4000 C) 5%, 5000 D) 20%, 5000 E) none
10)solve the following in equation:
x - 3 < 2x -2 ≤ 9 - x, x belongs to natural number
A) {1,2,3} B){2,3,4} C) {3,4,5} D) none
D) From a solid cylinder of height 12cm and base radius 5cm, a conical cavity of the same height and base is hollowed out, find
11) the volume of the remaining solid.
A) 650 B) 628.57 C) 768 D) n
12) the surface of the remaining solid.
A) 120π B) 210π C) 230π D) π E) n
13) A well is to be dug with 6m inside diameter and 20 m in depth. Find the volume of the earth to be excavated. The earth taken out is spread all around to a width of 3m to form an embankment. find the height of the embankment
A) 6 B) 6.67 C) 7 D) 7.76 e) n
14) find the value of: (sin⁴30° + 2 sin²30° . Cos²30° + cos⁴30°) (sin²90 + cos²90° + tan²45).
A) 0 B) 1 C) 2 D) 3 E) 4
15) A man bought a horse and a carriage for ₹3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.
A) 1200 B) 1100 C) 300 D) 600
16) The mean temperature of Monday to Wednesday was 37° and of Tuesday to Thursday was 34°C. What was the temperature on Thursday?
i) The temperature on Thursday was 4/5th that of Monday
ii) The mean temperature of Monday and Thursday was 40.5°C
iii) The difference between the temperature on Monday and that on Thursday was 9°C
A) i and ii only B) ii and III only
C) either i or ii D) either i, ii or III
17) In an examination, 65% students passed in civics and 60% in history, 40% passed in both of these subjects. If 90 students failed in history and civics both, then what is the total number of students?
A) 600 B) 650 C) 700 D) 750
18) Two stations A and B are 110km apart on a straight line. One train starts from A at 7 a.m and travels towards B at 20kmph. Another train starts from B at 8 a.m and travels towards A at a speed of 25 kmph. At what time will they meet?
A) 9a.m B) 10a.m C) 10.30a.m D) 11a.m
19) Tea worth ₹126 per kg and ₹135 per kg mixed with a third variety in the ratio 1:1:2. If the mixture is worth ₹153 per kg, the price of the third variety per kg will be
A) 169.50 B) 170 C) 175.50 D) 180
20) A sum of ₹53 is divided among A, B, C in such a way that A gets ₹7 more than what B gets and B gets ₹8 more than what C gets. The ratio of their shares is
A) 16:9:18 B) 25:18:10
C) 18:25:10 D) 15:8:30
21) There is 60% increase in an amount in 6 years at simple interest. What will be the compound Interest of ₹12000 after 3 years at the same rate
A) 2160 B) 3120 C) 6240 D)3972
22) Three partners shared the profit in a business in the ratio 5:7:8. They had partnered for 14 months, 8 months and 6 months respectively. What was the ratio of their investments?
A) 5:7:8 B) 28:49:64 C) 38:28:21 D) n
23) A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternatively, A beginning, in how many days, the work will be completed?
A) 41/4 days B) 10 days C) 21/2 days D) 43/4 days
24) A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the good train in 4 hours. Find the speed of the goods train
A) 36B) 37 B) 34 C) 40
TEST PAPER - 4
I) A,B ,C,D,E,F and G are brothers. Two brothers had an argument and A said to B, "You are as old as C was when I was twice as old as D, and will be as old as E when he was as old as C is now". B said to A, "You may be older than F" but G is as old as I was when you were as old as G is, and D will be as old as F was when F will be as old G is."
1) Who is the eldest brother?
A) A B) E C) C D) can't determined
2) who is the youngest brother
A) B B) D C) F D) can't determined
3) which two are probably twins
A) D and G B) E and C C) A and B D) cannot determined
4) which of the following is false
A) G has four elder brothers
B) A is older than G but younger than E.
C) B has three elder brothers
D) There is a pair of twins among the brothers.
* A is the father of C. But C is not his son.
* E is the daughter of C. F is the spouse of A.
* B is the brother of C. D is the son of B
* G is the spouse of B. H is the father of G
5) who is the grandmother of D?
A) A B) C C) F D) H
6) Who is the son of F?
A) B B) C C) D D) E
7) If C is A's father's nephew. D is A's cousin but not the brother of C. How D related to C ?
A) father B) sister C) mother D) aunt
** In each questions given below a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.
a) if only conclusion II follows
b) if either I or II follows
c) if neither I nor II follows
d) if both I and II follows
8) Statement: The cabinet of state X took certain steps to tackle the milk glut in the state as the cooperatives and government dairies failed to use the available milk- A news profit
Conclusion: (I): The milk production of state X is more than its need
II): The government and co-operative dairies in state X are not equipped in terms of resources and technology to handle such excess milk.
9) Statement: The manager humiliated Sachin in the presence of his colleagues
Conclusion I: The manager did not like Sachin
II: Sachin was not popular with his colleagues
10) In each questions given below a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.
a) if only conclusion II implicit
b) if either I or II implicit
c) if neither I nor II implicit
d) if both I and II implicit
11) Statement: The regulatory authority has set up a review committee to find out the reasons for unstable stock prices
Conclusion: (I): The investors may regain confidence in stock market by this decision.
II): The review committee has the expertise to find out the causes for volatile in the stock market.
12) Statement: "Avon Cycles - fast, easy to ride, impressive, reliable, crafted and up-to-date automation."- An advertisement.
Conclusion: (I): There is no other cycle with any of these feat6.
II): People do not bother about the cost.
13) You are standing at the top of a church tower, and you drop a tennis ball over the parapet. The ball reaches the ground after 4 seconds. How high is the tower.
A)250 ft B) 256 ft C) 262ft D) 247 ft
14) If A={5, 6, 9, 10}, B={7,8,9,11} and C={9,10, 11, 12} then show that A U(B UC)= (A UB) U C.
15) If A={1,2,3,4}, B={2,4,6,8} and C={3,4, 5,6} then prove that A ∩ (B ∩C)= (A ∩B) ∩ C.
16) If A={5,6,7,8,9}, B={2,4,6,8,10,12} and C={3,6,9,12} then show that (A U B ∩C) = (A UB)∩ (A U C).
17) If A={1, 3,5}, B={1,3,4} and C {3, 5, 7} then prove A ∩(B U C) = (A∩ B) U ( A ∩ C).
18) If U= {1,2,3,4,5,6,7,8}, A={1,2,3,4} and B={3,4,5,6} then prove that (AUB)' = A'∩ B'
19) If U={a,b,c,d,e,f}, A={a, b, c} and B={b, c, d} then prove that (A ∩B)' = A' U B'.
20) If A={1, 2, 5}, B={2, 4, 6} and C={5,7} then prove that A - (BUC)= (A - B)∩ (A - C).
21) If A={1,2}, B={2,3} and C={3,4} are three given sets then find the following sets.
a) (A x B) U (A x C)
b) (A x B)∩ (A x C).
22) In an examination out of 100 student 70 passed in mathematics 65 passed in physics and 55 passed in chemistry. Of these students 50 passed in mathematics and physics, 45 passed in Mathematics and Chemistry, 40 passed in physics and chemistry and 35 passed in all three subjects
a) how many students passed in exactly two of the three subjects
b) how many student passed in exactly one of the three subjects.
c) how many students failed in all three subjects? 30, 25, 10
23) In an examination 60% students passed mathematics, 68% passed in statistics 52% passed in both the subjects. If 42 students failed in both the subjects, find the total number of students. 175
24) Out of 20 members of a family 15 prefer tea and 9 prefer tea but not coffee. Each number of the family prefers at least one drink. Find the number of members who
a) prefer both drinks. 6
b) prefer coffee but not tea. 5
25) Out of 150 students of a school 35 students prefer Bengali and 25 students prefer both Bengali and English. Each students prefer atleast one subject. Find the number of students who
a) prefer English. 40
b) prefer English but not Bengali. 15
26) In a survey of 150 students, it was found that 40 students studied Economics, 50 students studied mathematics, 60 students studied accountancy and 15 students studied all the three subjects. It was also found that 27 students studied economics and accountancy, 35 students studied accountancy and Mathematics and 25 students studied Economics and mathematics. Find the number of Students who studied only economics and the number of students who studied none of these subjects. 3, 72
27) Out of 1600 students in a school, 390 played cricket,580 played football, 450 played hockey, 90 played cricket and hockey, 125 played hockey and football and 155 played cricket and football, 50 played all the three games. How many student did not play any game? 500
28) In an Engineering college 80 students get chance for computer science, 75% for information technology, 72 for electronics. If 60 students get chance in computer science and information technology. 50 in Information Technology and electronics, 40 in computer science and electronic and 30 get chance in all three branches. How many seats are there in the engineering College? (the College has only 3 disciplines). 107
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