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Pattern 1:
Q) (1/2) of a number is 3 more than the (1/6) of the same number?
a) 6 b)7 c)8 d)9
Sol: Let the number be x,
((1/2)*x)=3+(1/6)*x,
Then solve x
Q) (1/3) of a number is 3 more than the (1/6) of the same number?
a) 6 b)16 c)18 d)21
Q) (1/3) of a number is 6 more than the (1/6) of the same number?
a) 6 b)18 c)36 d)24
Q) (2/3) of a number is 4 more than the (1/6) of the same number?
a) 6 b)8 c)36 d)24
Q) (1/3) of a number is 5 more than the (1/6) of the same number?
a) 6 b)36 c)30 d)72
Pattern 2:
Q)There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled
up like, 10, 20, 40,80, 160…..in tank B. (At the end of first hour, B has 10 liters, second hour it has 20 liters and so on). If tank B is
1/32 filled of the 21 hours, what is total duration of hours required to fill it completely?
a) 26 B)25 c)5 d)27
Sol: Given that B fills up at the rate 10,20,40 etc...
This is a geometric progression where a = 10 r = 2
so after 21 hrs lts in B = a*r
21
= 10 * 2
21
This is equal to 1/32 volume of B
SO TOTAL VOLUME OF B = 32 * 10 * 2
21
which is =10 * 2
26
So hrs required to fill up B is 26
Or
for every hour water in tank in B is doubled,
Let the duration to fill the tank B is x hours.
x/32 part of water in tank of B is filled in 21 hours,
Next hour it is doubled so,
2*(x/32) part i.e (x/16) part is filled in 22 hours,
Similarly (x/8)th part in 23 hours,(x/4)th part is filled in 24 hours,
(x/2)th part is filled in 25 hours, (x)th part is filled in 26 hours
So answer is 26 hours.
Q)There are two pipes A and B. If A filled 10 liters in an hour, B can fill 20 liters in same time. Likewise B can fill 10, 20, 40, 80,
160…... If B filled in 1/16 of a tank in 3 hours, how much time will it take to fill the tank completely?
a) 9 B)8 c)7 d)6
Q)There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled
up like, 10, 20, 40,80, 160…..in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tank fully?
a) 26 B)25 c)5 d)27
Q)A tank is filled with water. In first hour 10 liters, second hours 20 liters, and third hour 40 liters and so on…If time taken to fill ¼
of the tank if 5 hours. What is the time taken to fill up the tank?
a) 5 B)8 c)7 d)12.5
Q)If a tank A can be filled within 10 hours and tank B can be filled ¼ in 19 hours then, what is the time taken to fill up the tank
completely?
a) 21 B)38 c)57 d)76
Pattern 3:
Q)6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with
them. Hence the current average age has become 45. Find the age of seventh person?
a) 43 b)69 c)52 d)31
Sol: a+b+c+d+e+f+ Z = 45*7 =315
a+b+c+d+e+f+ 12 = 43*6 = 258
therefore : a+b+c+d+e+f = 246
so age of seventh person "Z" is = 315 - 246 = 69
Q)In a market 4 men are standing. The average age of the four before 4years is 45, after some days one man is added and his age
is 49. What is the average age of all?
a) 43 b)45 c)47 d)49
Sol: Avg 4 yrs ago = 45
so avg now = 49
a person of age 49 is added
so avg remains 49
Q)In a shopping mall with a staff of 5 members the average age is 45 years. After 5 years a person joined them and the average
age is again 45 years. What‟s the age of 6th person?
a) 25 b)20 c)45 d)30
Sol: After 5 years average age becums 50
Total age = 250
new member joins suppose age x
so (250 + x) / 6 = 45
x = 20
Q)In a market 4 men are standing .The average age of the four before 2 years is 55, after some days one man is added and his age
is 45. What is the average age of all?
a) 55 b)54.5 c)54.6 d)54.7
Sol: After 2 years average age becomes 57
Total age=228
New member joins, his age is 45
So, (228 + 45)/6 = 54.6 ans
Pattern 4:
Q)In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed
around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are
36 readers, how many reading spots do not have even a single reader?
a)8 b)none c)16 d)15
Sol: There are some readers such that in each
occupied reading spot there are different numbers of
readers.
1+2+3+4+5+6+7+8= 36 readers
so ,8 spots have different readers.
remainings are 23-8= 15.
15 spots are empty.
Or
he just said that in each different spot there are different
number of readers. So there will be many possibilities...
It is same as number of ways in which you can make a sum of
9 using only digits from 1 to 9 each at most once...
Consider
1+2+3+6+7+8+9 = 36
In this case answer is: 23-7 = 16
but different answers are possible depending on case u choose
Q)In the reading room of a library, there are 10 tables, 4 chairs per table. In each table there are different numbers of people
seated. How many tables will be left out without at least 1 person?
a) 8 b)6 c)2 d)7
Q)In the reading room of a library, there are 10 tables, 4 chairs per table. In each table there are different numbers of people
seated. How many ways they will sit in the library so that no chair would be blank?
a) 8 b)6 c)2 d)7
Sol: 10 tables, each with 4 chairs
Each table has a different number of persons sitting....This is not possible as there are only 4 chairs..
The different combinations can be 0, 1, 2, 3 and 4...the sixth table would have one of the above combinations..Thus the rule is
violated..
Plus, if different numbers of people occupy a table, there would be blank spaces...so how can we calculate the possibilities of the
library being fulling occupied..
This is an ambiguous question!
Pattern 5:
Q)A man jogs at 6 mph over a certain journey and walks over the same route at 4 mph. What is his average speed for the journey?
a) 2.4 mph b) 4.8 mph c) 4 mph d) 5 mph
Sol: Average speed=2*x*y/(x+y)=2*6*4/(6+4)=4.8 kmph
Q)A man travels from A to B at 4 mph over a certain journey and returns over the same route to A, at 5 mph. What is his average
speed for the journey?
a) 4.44 mph b) 4.8 mph c) 4.887 mph d)5 mph
Q)A person is rock climbing at an altitude of 800 m. He go up by 7 mph. and come down by 9 mph. what was his average speed?
a) 7.875 mph b) 7.125 mph c) 7mph d) 7.5 mph
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of 200m?
a) 28.8 mph b) 27.8 mph c) 27.5mph d) 30 mph
Q)Person travels to a hill, if he goes from A to B with speed of 4kmph and returns back to B with speed of 5kmph. What is his
average speed of journey?
a) 4.5kmph b) 4.44kmph c) 9kmph d) 4.245kmph
Q)A man travels from A to B at 70 mph over a certain journey and returns over the same route to A, at 80 mph. What is his average
speed for the journey?
a) 74.66 b)75 c)74.33 d)74.99
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of 200m.
a) 28.8 b)28 c)27 d)28.6
Pattern 6
Q)Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small
cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer
number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes
that she needs to make the block?
a) 114 b) 135 c) 21 d) 71
Sol: dimensions of small cube = 2*2*2
Length of cube = 3 small cubes long = 6 cm
Breadth = 9 small cubes wide = 18 cm
Height = 5 small cubes deep = 10 cm
Volume = 6*18*10 = 1080cm^3
Volume of hollow cube = (6-4)(18-4)(10-4)
= 168 cm^3
total number of blocks needed = 1080-168 /8 = 912/8 = 114
Q)A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same
cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?
a) 2000 b) 5000 c) 3000 d) 7000
Sol: Total volume of cube = 5 * 6 * 7 = 210 m cube
volume of smaller cube 0.03
Total cubes reqd = 7000
for hollow cube no. of small cubes reqd = 5/0.03 *4 + 6/.03 * 4 + 7/0.03 *4
which is approx 2000 so 5000 cubes have to be removed
Note:4 sides of 5,6 and 7 in the cube...so multiplied by 4
Q)Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube
looking of the same shape?
a) 98 b) 104 c) 100 d) 61
Sol: Jst count the no. of cubes for each face
take the 1st one 25 small cubes reqd
now for 2 faces adjacent to it 20 are reqd
2 faces adjacent to all these 12 are reqd
and for the last one 9 are reqd
so 98
Q)Leena cut small cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm, width 50 cm and depth 50 cm.
How many more cubes does she need to make a perfect cube?
a)500 b)250 c)750 d)650
Sol: Volume left for perfect cube = 100*100*100 - 100*50*50
No. of cubes reqd = (100*100*100 - 100*50*50)/10*10*10 = 750
Q)Leena cut small cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm and depth 3 cm. How many
more cubes does she need to make a perfect cube?
a) 910 b) 250 c) 750 d) 650
Q)A lady builds 9cm length, 10cm width,3cm height box using 1 cubic cm cubes. What is the minimum number of cubes required to
build the box?
a) 730 b) 270 c) 720 d) 310
Sol: no. of cubes required = 9*10*3 /1 = 270
Pattern 8:
Q) (40*40*40 – 31*31*31)/(40*40+40*31+31*31)=?
a)8 b)9 c)71 d)51
Q) (98*98*98 – 73*73*73)/( 98*98*98 – 73*73*73)=?
a).171 b).4 c).420 d).415
Q) (209*144)^2 + (209*209)+(209*144)+(144*144) = ?
a)905863729 b)905368729 c)905729368 d)65
Pattern 9:
Q) ((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16 d)15
Q)x/2y = 2a,then 2x/x-2ay=?
a)4 b)8 c)16 d)2
Q)3X/5Y = 5Y/3X…..Find the value of X/Y
a)3/5 b)5/3 c)2/5 d)5/2
Q)What is the value of (3X+8Y)/(X-2Y), if X/2Y=2
a)8 b)none c)10 d)13
Q) (4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)48/5 b)46/5 c)47/5 d)49/5
Q) ((4x+2y)/(4x-2y)= ? as (x/2y) = 2
a)8/7 b)9/7 c)11/7 d)6/7
Pattern 10:
Q)A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2
different toppings?
a)16 b)56 c)112 d)28
Sol: The number of ways of choosing r distinct objects from n distinct objects is given by the formula
C(n, r) = n!/r!*(n-r)!
where n! = n(n-1)(n-2).......3*2*1
If order was important, the number of arrangements is
P(n,r) n!/(n-r)!
Now suppose you wanted to display one topping in the middle and the other around the edge, you would be considering arrangements
and the answer would be
P(8, 2) = 8!/6!
= 8*7
= 56
However, suppose that you wish to sprinkle toppings randomly over the pizza base. Since it does not matter what the arrangements
are, the number of ways is
C(8, 2) = 8! / 2!*6!
= 8*7 / 2*1
= 56/2
= 28
This is correct.
Q)A pizza shop made pizzas with many flavors. There are 10 different flavors, in that 7 flavors are taken to make pizza. In how
many ways they can arrange?
a)240 b)120 c)65 d)210
Sol: 10c7=10c3=120
Q)A pizza shop made pizzas with many flavors. There are 9 different flavors, in that 2 flavors are taken to make pizza. In how many
ways they can arrange?
a)16 b)26 c)36 d)46
Sol: 9c7=9c2=36
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Pattern 1:
Q) (1/2) of a number is 3 more than the (1/6) of the same number?
a) 6 b)7 c)8 d)9
Sol: Let the number be x,
((1/2)*x)=3+(1/6)*x,
Then solve x
Q) (1/3) of a number is 3 more than the (1/6) of the same number?
a) 6 b)16 c)18 d)21
Q) (1/3) of a number is 6 more than the (1/6) of the same number?
a) 6 b)18 c)36 d)24
Q) (2/3) of a number is 4 more than the (1/6) of the same number?
a) 6 b)8 c)36 d)24
Q) (1/3) of a number is 5 more than the (1/6) of the same number?
a) 6 b)36 c)30 d)72
Pattern 2:
Q)There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled
up like, 10, 20, 40,80, 160…..in tank B. (At the end of first hour, B has 10 liters, second hour it has 20 liters and so on). If tank B is
1/32 filled of the 21 hours, what is total duration of hours required to fill it completely?
a) 26 B)25 c)5 d)27
Sol: Given that B fills up at the rate 10,20,40 etc...
This is a geometric progression where a = 10 r = 2
so after 21 hrs lts in B = a*r
21
= 10 * 2
21
This is equal to 1/32 volume of B
SO TOTAL VOLUME OF B = 32 * 10 * 2
21
which is =10 * 2
26
So hrs required to fill up B is 26
Or
for every hour water in tank in B is doubled,
Let the duration to fill the tank B is x hours.
x/32 part of water in tank of B is filled in 21 hours,
Next hour it is doubled so,
2*(x/32) part i.e (x/16) part is filled in 22 hours,
Similarly (x/8)th part in 23 hours,(x/4)th part is filled in 24 hours,
(x/2)th part is filled in 25 hours, (x)th part is filled in 26 hours
So answer is 26 hours.
Q)There are two pipes A and B. If A filled 10 liters in an hour, B can fill 20 liters in same time. Likewise B can fill 10, 20, 40, 80,
160…... If B filled in 1/16 of a tank in 3 hours, how much time will it take to fill the tank completely?
a) 9 B)8 c)7 d)6
Q)There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled
up like, 10, 20, 40,80, 160…..in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tank fully?
a) 26 B)25 c)5 d)27
Q)A tank is filled with water. In first hour 10 liters, second hours 20 liters, and third hour 40 liters and so on…If time taken to fill ¼
of the tank if 5 hours. What is the time taken to fill up the tank?
a) 5 B)8 c)7 d)12.5
Q)If a tank A can be filled within 10 hours and tank B can be filled ¼ in 19 hours then, what is the time taken to fill up the tank
completely?
a) 21 B)38 c)57 d)76
Pattern 3:
Q)6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with
them. Hence the current average age has become 45. Find the age of seventh person?
a) 43 b)69 c)52 d)31
Sol: a+b+c+d+e+f+ Z = 45*7 =315
a+b+c+d+e+f+ 12 = 43*6 = 258
therefore : a+b+c+d+e+f = 246
so age of seventh person "Z" is = 315 - 246 = 69
Q)In a market 4 men are standing. The average age of the four before 4years is 45, after some days one man is added and his age
is 49. What is the average age of all?
a) 43 b)45 c)47 d)49
Sol: Avg 4 yrs ago = 45
so avg now = 49
a person of age 49 is added
so avg remains 49
Q)In a shopping mall with a staff of 5 members the average age is 45 years. After 5 years a person joined them and the average
age is again 45 years. What‟s the age of 6th person?
a) 25 b)20 c)45 d)30
Sol: After 5 years average age becums 50
Total age = 250
new member joins suppose age x
so (250 + x) / 6 = 45
x = 20
Q)In a market 4 men are standing .The average age of the four before 2 years is 55, after some days one man is added and his age
is 45. What is the average age of all?
a) 55 b)54.5 c)54.6 d)54.7
Sol: After 2 years average age becomes 57
Total age=228
New member joins, his age is 45
So, (228 + 45)/6 = 54.6 ans
Pattern 4:
Q)In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed
around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are
36 readers, how many reading spots do not have even a single reader?
a)8 b)none c)16 d)15
Sol: There are some readers such that in each
occupied reading spot there are different numbers of
readers.
1+2+3+4+5+6+7+8= 36 readers
so ,8 spots have different readers.
remainings are 23-8= 15.
15 spots are empty.
Or
he just said that in each different spot there are different
number of readers. So there will be many possibilities...
It is same as number of ways in which you can make a sum of
9 using only digits from 1 to 9 each at most once...
Consider
1+2+3+6+7+8+9 = 36
In this case answer is: 23-7 = 16
but different answers are possible depending on case u choose
Q)In the reading room of a library, there are 10 tables, 4 chairs per table. In each table there are different numbers of people
seated. How many tables will be left out without at least 1 person?
a) 8 b)6 c)2 d)7
Q)In the reading room of a library, there are 10 tables, 4 chairs per table. In each table there are different numbers of people
seated. How many ways they will sit in the library so that no chair would be blank?
a) 8 b)6 c)2 d)7
Sol: 10 tables, each with 4 chairs
Each table has a different number of persons sitting....This is not possible as there are only 4 chairs..
The different combinations can be 0, 1, 2, 3 and 4...the sixth table would have one of the above combinations..Thus the rule is
violated..
Plus, if different numbers of people occupy a table, there would be blank spaces...so how can we calculate the possibilities of the
library being fulling occupied..
This is an ambiguous question!
Pattern 5:
Q)A man jogs at 6 mph over a certain journey and walks over the same route at 4 mph. What is his average speed for the journey?
a) 2.4 mph b) 4.8 mph c) 4 mph d) 5 mph
Sol: Average speed=2*x*y/(x+y)=2*6*4/(6+4)=4.8 kmph
Q)A man travels from A to B at 4 mph over a certain journey and returns over the same route to A, at 5 mph. What is his average
speed for the journey?
a) 4.44 mph b) 4.8 mph c) 4.887 mph d)5 mph
Q)A person is rock climbing at an altitude of 800 m. He go up by 7 mph. and come down by 9 mph. what was his average speed?
a) 7.875 mph b) 7.125 mph c) 7mph d) 7.5 mph
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of 200m?
a) 28.8 mph b) 27.8 mph c) 27.5mph d) 30 mph
Q)Person travels to a hill, if he goes from A to B with speed of 4kmph and returns back to B with speed of 5kmph. What is his
average speed of journey?
a) 4.5kmph b) 4.44kmph c) 9kmph d) 4.245kmph
Q)A man travels from A to B at 70 mph over a certain journey and returns over the same route to A, at 80 mph. What is his average
speed for the journey?
a) 74.66 b)75 c)74.33 d)74.99
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down at an altitude of 200m.
a) 28.8 b)28 c)27 d)28.6
Pattern 6
Q)Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small
cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer
number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes
that she needs to make the block?
a) 114 b) 135 c) 21 d) 71
Sol: dimensions of small cube = 2*2*2
Length of cube = 3 small cubes long = 6 cm
Breadth = 9 small cubes wide = 18 cm
Height = 5 small cubes deep = 10 cm
Volume = 6*18*10 = 1080cm^3
Volume of hollow cube = (6-4)(18-4)(10-4)
= 168 cm^3
total number of blocks needed = 1080-168 /8 = 912/8 = 114
Q)A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same
cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?
a) 2000 b) 5000 c) 3000 d) 7000
Sol: Total volume of cube = 5 * 6 * 7 = 210 m cube
volume of smaller cube 0.03
Total cubes reqd = 7000
for hollow cube no. of small cubes reqd = 5/0.03 *4 + 6/.03 * 4 + 7/0.03 *4
which is approx 2000 so 5000 cubes have to be removed
Note:4 sides of 5,6 and 7 in the cube...so multiplied by 4
Q)Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube
looking of the same shape?
a) 98 b) 104 c) 100 d) 61
Sol: Jst count the no. of cubes for each face
take the 1st one 25 small cubes reqd
now for 2 faces adjacent to it 20 are reqd
2 faces adjacent to all these 12 are reqd
and for the last one 9 are reqd
so 98
Q)Leena cut small cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm, width 50 cm and depth 50 cm.
How many more cubes does she need to make a perfect cube?
a)500 b)250 c)750 d)650
Sol: Volume left for perfect cube = 100*100*100 - 100*50*50
No. of cubes reqd = (100*100*100 - 100*50*50)/10*10*10 = 750
Q)Leena cut small cubes of 3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm and depth 3 cm. How many
more cubes does she need to make a perfect cube?
a) 910 b) 250 c) 750 d) 650
Q)A lady builds 9cm length, 10cm width,3cm height box using 1 cubic cm cubes. What is the minimum number of cubes required to
build the box?
a) 730 b) 270 c) 720 d) 310
Sol: no. of cubes required = 9*10*3 /1 = 270
Pattern 8:
Q) (40*40*40 – 31*31*31)/(40*40+40*31+31*31)=?
a)8 b)9 c)71 d)51
Q) (98*98*98 – 73*73*73)/( 98*98*98 – 73*73*73)=?
a).171 b).4 c).420 d).415
Q) (209*144)^2 + (209*209)+(209*144)+(144*144) = ?
a)905863729 b)905368729 c)905729368 d)65
Pattern 9:
Q) ((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16 d)15
Q)x/2y = 2a,then 2x/x-2ay=?
a)4 b)8 c)16 d)2
Q)3X/5Y = 5Y/3X…..Find the value of X/Y
a)3/5 b)5/3 c)2/5 d)5/2
Q)What is the value of (3X+8Y)/(X-2Y), if X/2Y=2
a)8 b)none c)10 d)13
Q) (4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)48/5 b)46/5 c)47/5 d)49/5
Q) ((4x+2y)/(4x-2y)= ? as (x/2y) = 2
a)8/7 b)9/7 c)11/7 d)6/7
Pattern 10:
Q)A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2
different toppings?
a)16 b)56 c)112 d)28
Sol: The number of ways of choosing r distinct objects from n distinct objects is given by the formula
C(n, r) = n!/r!*(n-r)!
where n! = n(n-1)(n-2).......3*2*1
If order was important, the number of arrangements is
P(n,r) n!/(n-r)!
Now suppose you wanted to display one topping in the middle and the other around the edge, you would be considering arrangements
and the answer would be
P(8, 2) = 8!/6!
= 8*7
= 56
However, suppose that you wish to sprinkle toppings randomly over the pizza base. Since it does not matter what the arrangements
are, the number of ways is
C(8, 2) = 8! / 2!*6!
= 8*7 / 2*1
= 56/2
= 28
This is correct.
Q)A pizza shop made pizzas with many flavors. There are 10 different flavors, in that 7 flavors are taken to make pizza. In how
many ways they can arrange?
a)240 b)120 c)65 d)210
Sol: 10c7=10c3=120
Q)A pizza shop made pizzas with many flavors. There are 9 different flavors, in that 2 flavors are taken to make pizza. In how many
ways they can arrange?
a)16 b)26 c)36 d)46
Sol: 9c7=9c2=36
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