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Chapter – 5 Tests – 1

- Find
the numbers of diagonals and triangles formed in a decagon.
- Out of
18 points in a plane, no three are in straight line except five which are
collinear. How many straight lines can be formed?
- 16c2 –
5c2+1
- 18c2 –
6c8+1
- 18c2 –
5c2+1
- none
of these
- Arjit
being a party wants to hold as many parties as possible among his 20
friends. However, his father has warned him that he will be financing his
parties under the following conditions only:
- The
invitees have to be among his 20 best friends
- He
cannot call the same set of friends to a party more than once
- The
number of invitees to every party have to be the same
- Given
these constraints, Arjit wants to hold the maximum number of parties. How
many friends should he invite to each party
- 11
- 8
- 10
- 12
- There
are 10 subjects in the school day at St. Vincent’s High School, but the 6
^{th}standard students have only 5 periods in a day. In how many ways can we form a time-table for the day for the 6^{th}standard students?

a

- A class
perfect goes to meet the principal every week. His class has 30 people
besides him. If he has to take groups of 3 every time he goes to the
principal, in how many weeks will he be able to go to the principal
without repeating the group of same 3 which accompanies him?
- several
teams take part in a competition, each of which must play one game with
all the other teams. How many teams took part in the competition if they
played 45 games in all?
- 5
- 10
- 15
- 20
- There
are V lines parallel to the x-axis and ‘W’ lines paralled to y-axis. How
many rectangles can be formed with the intersection of these lines?
- 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 occupy odd places only?
- There
are 7 pairs of black shoes and 5 pairs of white shoes. They all are put
into a box and shoes are drawn one at a time. To ensure that at least one
pair of black shoes are taken out, what is the number of shoes required to
be drawn out?
- 12
- 13
- 7
- 18
- On a
triangle ABC, on the side AB 5 points are marked, 6 points are marked on
the side BC and 3 points are marked on the side AC (none of the points
being the vertex of the triangle). How many triangles can be made by using
these points?
- 90
- 333
- 328
- none
of these
- The
number of circles that can be drawn out of 10 points of which 7 are
collinear is
- 130
- 85
- 45
- cannot
be determined
- In how
many ways a cricketer can score 200 runs with fours and sixes only?
- 13
- 17
- 19
- 18
- There
are 20 people among whom 2 are sisters. Find the number of ways in which
we can arrange them around a circle so that there is exactly one person
between the 2 sisters?
- 18!
- 2!.19!
- 19!
- 2!18!
- how
many rectangles can be formed out of a chessboard?
- 204
- 1230
- 1740
- 1296
- 5 boys
and 3 girls are sitting in a row of 8 seats. In how many ways can they be
seated so that not all girls sit side by side?
- 36000
- 45000
- 24000
- none
of these
- There
are 5 bottles of sherry and each have their respective caps. If you are
asked to put the correct cap to the correct bottle then how many ways are
3 so that not a single cap is no the correct bottle?
- In how
many ways can 8 boys and 3 girls be made to sit in a row, so that a boy is
seated at each end and no 2 girls sit together?
- 120(7!)
- 210(8!)
- 180(3!)
- 140(11!)
- In his
wardrobe, Timothy has three trousers. One of them is black, the second is blue
and the third is brown. He also has 4 shirts. One of them is black and the
other 3 are white. He opens his wardrobe in the dark and picks up one up
shirt – trouser pair without examining the color. What is the likelihood
that both the shirts as well as the trouser are non – black?
- 1/12
- ½
- ¼
- 1/3
- Coomar
is given the digits 2, 4, 9 and asked to make a 3 – digit number using
these digits, without repeating any of them. What is the likelihood that
the number he makes will be greater than 450 but lesser than 900?
- 1/12
- 1/6
- ¼
- 1/3
- 3
identical dice are rolled. The
probability that the same number will appear on each of them is
- 1/6
- 1/36
- 1/216
- 3/28
- What is
the ratio of the number of 3 letter words to the number of four – letter
words that can be formed from the letters of the word ‘TERMINAL’ using at
least one vowel in each?
- 12:17
- 23:130
- 28:97
- 2:15
- Identical
spherical balls are spread on a table top so as to form on equilateral
triangle. How many balls are needed so that a side of the equilateral
triangle contains n balls?

a.

- Ram and
Shyam stand in a line for tickets with 10 other people. What is the
probability that there are 3 people in between them?
- 8/38
- 4/33
- 16/55
- 8/55
- There
are 5 lines in a plane. The maximum number of points at which they may
intersect is
- 6
- 8
- 10
- none
of these
- In a
room there are 3 lamp holders and there are 12 bulls of which 5 are
defective. If 3 bulbs are selected at random to be put into the holders,
what is the probability that the room is lighted?
- 21/22
- 1/22
- 1/18
- 17/18
- An
integer X is chosen at random from the numbers 1 to 50. The probability
that X + 336/X ≤ 50 is
- 7/10
- 17/25
- 19/50
- 13/50
- For the
BCCI, a selection committee is to be chosen consisting of 5 ex-cricketers.
Now there are 10 representatives from four zones. It has further been decided
that if Kapil Dev is selected, Sunil Gavaskar will not be selected and
vice versa. In how many ways can this be done?
- 140
- 112
- 196
- 56
- 2 real
numbers X and Y are chosen at random and such that │X│≤3 and │Y│≤5. What
is the probability of the fraction X/Y being positive?
- 0.25
- 0.5
- 0.75
- 0.66
- In
CAMPUS exam paper there are 3 sections, each containing 5 questions? A
candidate has to solve 5, choosing at least one from each section. The
number of ways he can choose is
- 2500
- 2250
- 2750
- 3250
- A
committee is to be formed comprising of 7 members such that there is a
majority of men and at least 1 woman in every committee. The shortlist
consists of 9 men and 6 women. In how many ways can this be done?
- 3724
- 3630
- 3526
- 4914
- To form
a single cube, 27 identical wooden cubes are arranged. They are held
together tightly and the cube so formed is pained black on all faces. When
the paint has dried up, the smaller cubes are detached and one of them is
picked up at random. What is the probability that the cube that has been
picked up will be painted black on 2 of its sides?
- 4/9
- 8/27
- 2/9
- 1/3

For
Q 32 & 33: Answer the questions based on the following information:

There
are 6 boys and 4 girls sitting for a photo session. They were posing for the
photograph standing in 2 rows one behind the other. There were 5 people sitting
in the front row and 5 standing in the black row.

- If the
boys were divided equally among the front and back rows, in many ways can
the photo sessions be arranged?

a.

- In how
many ways could the photos be taken such that no two boys and no two girls
are standing or sitting together?
- There
are 4 married couples in a cube. The number of ways of choosing a
committee of 3 members so that no couple appears on the committee is
- 4
- 8
- 16
- 32
- A bag
contains 80 envelops of which 30 are airmail and the rest are ordinary.
Out of the 80 envelops in the bags, 48 are stamped and the rest are
unstamped. There are 20 unstamped ordinary envelops in the bag. If one
envelope is chosen at random from the bag, then the probability that this is
an unstamped airmail envelope is
- 12/80
- 18/80
- 20/80
- 30/80
- A bag
contains 5 tickets numbered 1, 2,3,4,5. In a lottery, one ticket was drawn
at random from the bag and was kept in the bag after noting down its
number. Then a second ticket was drawn at random and its number was noted.
Let X and Y be the two numbers so observed. Then the probability that X+Y
equal 7 is given by
- 1/25
- 1/20
- 4/25
- 4/20
- 4 boxes
of 4 different colors are to be wrapped up in 4 sheets of similar colors.
Find the probability that every box is wrapped in a sheet of its own
color?
- 1/18
- 1/24
- 1/54
- 1/216
- Sethi
and Wilson participate in the finals of a snooker tournament consisting of
9 games. The winner is decided by the method of ‘Race to 5’ i.e., the
first person to win 5 games is declared the winner. In how many ways can
the winner be decided?
- 270
- 62
- 252
- 76
- The
eccentric scientist, who lives at the end of our block, showed me his
latest invention, a time – machine. To start the time – machine, one must
press, in any order, exactly seven buttons, each of which is of different
color. 3 of the buttons are circular, 2 are triangular and the rest are
square in shape. The time – machine would travel in the past, if any
square button is pressed before the first triangular button to be pressed.
Else, it would travel into the future. In how many distinct ways can I
start the time – machine and travel in the future, given that I can press
only one button at a time?
- 3080
- 4180
- 2520
- 1880
- One red
flag, three white flags and 2 blue flags are arraged in a line such that,
- No 2
adjacent flags are of the same color.
- The
flags at the 2 ends of the line are of different colors.

In how many different ways can the flags be arranged?

- 6
- 4
- 10
- 2
- A test
has 2 sections, the first section consisting of 3 questions and the second
section consisting of four questions. Further, each question in the first
question has three answer choices and each question in the second section
has two answer choices. In many different ways can a student answer the
test?
- 432
- 5184
- 1296
- 972
- Each
face of a cubical die is numbered with a distinct number from among the
first six odd numbers, such that the sum of the two numbers on any pair of
opposite side is 12. if 10 such dice are thrown simultaneously, then find
the probability that the same of the numbers that turn up is exactly 55.

a

- A box
contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a
different size. One ball is selected and it is found to be red. What is
the probability that it is the smallest red ball?
- 1/18
- 1/3
- 1/6
- 2/3
- In a
group, 3 are 15 men and 12 women. The men exchange roses among themselves,
and the women also do the same. ( an exchange is one person giving another
a rose, and the other then giving another rose to the first person.) each
woman gives one rose to only one man, and each man gives one rose to only
one women. How many rose are exchanged?
- 300
- 369
- 394
- 342
- What is
the probability that a four – digit number formed by using 3,9,2 and 7
without repetition is divisible by 33?
- ½
- 1/3
- ¼
- 1/6
- 3 men
and 3 women are sitting at a round table, each women being flanked by 2
men and vice versa. How many different seating arrangements are possible
such that in no arrangement, every man is flanked by the same women?
- 12
- 720
- 6
- 120
- A cube
is divided into four equal cubes. Each of these cubes is further sub
divided into four equal cubes. If the original cube’s sides are painted
blue, then what is the probability that exactly two sides of a small cube
is painted blue?
- 3/8
- 1/16
- ¼
- 3/4
- What is
the probability of finding exactly 33 multiples of 3 when 100 consecutives
natural numbers are selected?
- 1/3
- 2/3
- 1
- none
of these
- A
machine produces 10 units of an article in a day of which 4 are defective.
The quality inspector allows releases of the products if he finds none of
the 3 units chosen by him at a random to be defective. What is the
probability of quality inspector allowing the release?
- 1/5
- 6/10
- 1/6
- 5/6
- A
growth of investigation took a fair sample of 1972 children from general
population and found that there are 1000 boys and 972 girls. If the
investigators claim that their research is so accurate that the sex of a
new born child can be predicted based on the ratio of the sample of the
population, then what is the expectation in terms of the probability that
a new child born will be a girl?
- 243/250
- 250/257
- 9/10
- 243/493

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ReplyDeletecan u provide the solution of the CHAPER 5 TEST1 paper if availabel.

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