#tcs 2nd december with solutions
1)Esha ran 224m in 27 sec and Usha in 17 sec.AT what distance did Esha
cross Usha.?
Ans:formula is : x(t2-t1) /t2
224(27-17) /27
2)a series 1234123441234441234444.....n what is the value on 200th position..?
Ans:1234 => 4 times
12344 => 5 times
123444 => 6 times
.
.
.
4 + 5 + 6 + ...n < 200
n(n+1)/2 - 6 = 200
So n = 19
i.e. 4+5+6+...19 = 184
After the 184th term,the sequence has 20 terms
12344444444444444444 = 20 terms
=> 200th term = 4
3)Star mark question(most tricky) How many squares are there between
2011 to 2300 which follows 2013,2020,2027.......2300
Ans; there are 3 squares 45.,46,47 but 47^2 follows the pattern.
answer 1 many given 3 (note:-but it is completely wrong
)
4)If a pipe can fill the tank within 6hrs.But due to leak it takes 30
min more. Now
the tank is full then how much time will it take to empty the tank through the
leak?
Ans;
given that it takes 6 hours for the pipe to fill the tank
so in 1 hour it can fill =1/6
but because of leak it takes 30 min more i.e (6+1/2) hours =13/2.
so in 1 hour pipe+ leak can fill= 2/13
finally pipe=1/6
pipe+leak=2/13
leak=1/6-2/13 =1/78
leak can alone do in 78 hours.
5)
There was a question of train. 2 trains crossing each other in 23
seconds. A man standing on the platform.. Find the ratio of speeds of
2 trains.i cannot completely recall that question
Ans:Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
27x + 17y / x+ y = 23
27x + 17y = 23x + 23y
4x = 6y
x/y = 3/2
(the question is from rs agaarwal)
6)the numbers from 1 to 20 are written in the below order, sum of any
two adjacent numbers is prime number.
20;A;16;15;4;B;12:C;10;7;6;D;2;17;14;9;8;5;18;E
then find value at A ?
Ans:
A=3
B=19
C=1
D=11
E=13
7)if a(b+c)=33
b(c+a)=40
c(a+b)=49
then find ab
Ans:a(b+c)=33
so a=11 or 3
b+c=11 or 3
c(a+b)=49
c=7
a+b=7
so a=3
and b=4
and c=7
abc=84
8)#(most dangerous ) a spider web consists of 3 concurrent lines
forming radial support for 20 concentric regular hexagon .the hexagon
vertices are 5mm from their immidiate neighbour. if the innermost
hexagon has a side length 3mm how many meters is the length of the
entire web including the 3 diagonals ?
Ans;side of innermost hexagon = 3mm
side of next hexagon = 8mm
it goes on as series 3,8,13... 20th terms
total length of smallest hexagon = 6 * 3= 18mm
next hexagon length = 6 * 8= 48mm
sum of all hexagon sides = 20/2 * (2*18 + 19 * 30) = 6060mm
but the sum length of diagonals is 6*98=588
so 6.060+0.588=6.648 meters
9)the diagnal of a square field is 266.66(some value i dont remember
exactly), then find the area of a square
ANs:ans- a. 2*10^4
10)Rs.7791 is divided among shills=a ,beena and chris in such a way
that if Rs.34 Rs.32 and Rs.29 be deduced from their respective shares
they are left with money in the ratio 8:6:12 find shilas share in
rupees a)2402 b)1798 c)1808 d)239
Ans:7791-(34+32+29)=7696
s:b:c=8:6:12
share of s=8/26*76976 + 34=2402
11)123412344123444123444412344444... now the last two terms of 200th number
Ans:1st group 1234 number of digit 4
2nd group 12344 number of digit 5
3rd group 1234444 number of digit 6
so at the end of each group there will be series of 4s.
So the answer is 44
12)HOW MANY NUMBERS ARE THERE FROM 1 TO 400 HAVING EXACTLY THREE
INTEGRAL FACTORS
ANs:there are total 8 nos. less than 400 having three integral factors
4 , 9 , 25 , 49 , 121 , 169 , 289 , 361
13)(1-1/3^2) (1-1/4^2) (1-1/5^4)----------(1-1/2015^2) = x/2015 then x value
Ans:(1+1/3)(1-1/3)(1+1/4)(1-1/4)......(1-1/2015)(1+1/2015)=x/2015
2/3*4/3*3/4*5/4.......................2014/2015*2016/2015=x/2015
2/3*2016/2015=x/2015
after solving
x=1344.
14)x,y,z are positive integers if x(y+z)=63, y(z+x)=40, z(y+x)=33.
what is the value of x+y+z ( please check ,not sure)
ans: answer is 14 but not sure please check as this is not in my slot as x=7
y=4
z=3
15) Given sequence 91011....33 .what is the remainder when divided by 9?
a)2
b)0
c)3
d)7
ans:c)3
(9+10+11+12.......33)-(1+2+3...8)
so here
n(n+1)/2-n(n+1)/2
(33x34)/2-(8x9)/2
33x17-4x9
561-36=525
now 525/9=3
16)when sum of the numbers from 9 to 33 divided by 9 the remainder is
a)7
b)5
c)3
d)1
ans:sum from 1 to 33 =561 i.e. (n(n+1)/2)
sum from 1 to 8= 36
561-36= 525
525/9 remainder is 3.....option C
17)x,y,z are positive integers if x(y+z)=63, y(z+x)=40, z(y+x)=33.
what is the value of x+y+z?
ans: do not have time,please solve
answer is 24 not sure .not in my slot
18)
In a tank 7/13 th part contains fuel. 22 liters of fuel is taken out
from the tank, Themn its showing 1/5th mark in tank.
ans:Let X ltr is total capacity,
then
(7/13)x-(1/5)x=22
(35x-13x)/65=22
x=65
19)A 4*4 Table was given first row contains number 1,2,3,4.We have to
find value of x which is in third row such that no number should
repeated diagonally or row-wise/column-wise.
ans:ans is =3(status: very tricky,do not attempt)
1 2 3 4
3 4 1 2
1 2 3 4
3 4 1 2
20)there are 2 man one old and one young work in the same office and
live in same apartment.
The old man takes 30 minutes to reach office and young man take 20
minutes to reach the office . If old man starts at 10:00 a.m for
office and the young man at 10:05 a.m then at what time will they
meet?
ans:et speed of old man=vo
let speed of young man=vy
vo*30=vy*20
vo/vy = 2/3.....................(1)
now let they will meet after t time of 10:00 am
vo*t = vy*(t+5).........................(2)
from eq(1) and eq(2) we get
vo*t = 15*vo
so, t=15 mints
now we can say that they will meet at 10:15 am
21)
in what ratio 50 rs and 60 rs wheat is to be mixed such that after
selling it at 70 rs a profit of 20% is made
ans:ans-1:5
let 50rs be x and 60rs be y
so,cost price=50x+60y
selling price=70(x+y)
gain%=sp-cp/cp*100
20/100=70(x+y)-(50x+60y)/50x+60y
x:y=1:5
22)a number decreases successively. for eg. 9876543210. How many such
5- digits numbers are possibe?
ans:ans 13/18
probability of not getting same no
1st person:6/6
2nd person:5/6
3 : 4/6
4: 3/6
probability of not getting similar is 6/6*5/6*4/6*3/6=5/18
probabilty of getting is:1-5/18=13/18 (ans)
23)do not remember the question but i remember f(1)=5 and f(a+b)=
F(a)+f(b)+ a*b someting like that
it is last option that i remember
24)
A series of book was published at seven year intervals. When the
seventh book was published the total sum of publication year was 13,
524. First book was published in?
a. 1911
b. 1910
c. 2002
d. 1932
Answer:
Explanation:
Let the years be n, n+7, n+14, ...., n+42. (∵ use formula Tn=a+(n−1)d
to find nth term)
Sum = Sn=n2(2a+(n−1)d) = 72(2n+(7−1)7) = 13,524
⇒7n+147=13,524
⇒ n = 1911
25)
Assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1). For all natural
numbers (Integers>0)m and n. What is the value of f(17)?
a. 5436
b. 4831
c. 5508
d. 4832
Explanation:
f(1) = 0
f(2) = f(1+1) = f(1)+f(1)+4(9×1×1 – 1) = 0+0+4×8 = 32
f(4) = f(2+2) = f(2)+f(2)+4(9×2×2 – 1) = 32+32+4×35 = 204
f(8) = f(4+4) = f(4)+f(4)+4(9×4×4 – 1) = 204+204+4×143 = 980
f(16) = f(8+8) = f(8)+f(8)+4(9×8×8 – 1) = 980+980+4×575 = 4260
f(17) = f(1+16) = f(16)+f(1)+4(9×16×1 –1) = 4260+0+ 4×143 = 4832
26)Ram and Shakil run a race of 2000 meters. First, Ram gives Shakil a
start of 200 meters and beats him by one minute. If, Ram gives Shakil
a start of 6 minutes Ram is beaten by 1000 meters. Find the time in
minutes in which Ram and Shakil can run the races separately.
a. 12, 18
b. 10, 12
c. 11, 18
d. 8, 10
Answer: d (folow campusgate for story )
27)
Of a set of 30 numbers, average of first 10 numbers = average of last
20 numbers. Then the sum of the last 20 numbers is?
a. Cannot be determined.
b. 2 x sum of last ten numbers
c. 2 x sum of first ten numbers
d. sum of first ten numbers
Answer: c
Explanation:
We know that sum = average x number of observations.
Let the common average = x
Now sum of first 10 numbers = 10x
Sum of the last 20 numbers = 20x.
So sum of the last 20 numbers = 2 × sum of the first ten numbers.
Question updated today :
28)According to the stock policy of a company , each employee in the
technical division is given 15 shares of the company and each employee
in the recruitment division is given 10 shares. Employees belonging to
both Communities get 25 shares each. There are 20 employees in the
company and each one belong to at least one division. The cost of each
share is $10. If the technical division 15 employees and the
recruitment division has 10 employees, then what is the total cost of
the shares given by the company?
a. 3120
b. 3250
c. 2650
d. 3180
Ans:total emp-20
10-recruitmnt
15-tech
so 5 - both
so only recruimnt -5
only tech -10
(5*25*10)+(5*10*10)+(10*15*10)
=1250+500+1500=3250
29)there is a networking questions,if one goes to A it is rs 100 and
one goes to B it is rs 200,follow dijakstra algorithm to get the
answer. the answer is rs 800
Email writing with phrases I remember :
Write an email in 50 words to a organization called 'helping hand' to
request them to help an old man who is an orphan not able to
speak...suffering from diseases and requesting him to accomodate .Sign
as Anthony. there are many ,i Remembered few of them.
Homeless-bus stand- reticent - rags - bus stand - help - care-
obliged-no shelter- food-accomodation-destitute home.
1)Esha ran 224m in 27 sec and Usha in 17 sec.AT what distance did Esha
cross Usha.?
Ans:formula is : x(t2-t1) /t2
224(27-17) /27
2)a series 1234123441234441234444.....n what is the value on 200th position..?
Ans:1234 => 4 times
12344 => 5 times
123444 => 6 times
.
.
.
4 + 5 + 6 + ...n < 200
n(n+1)/2 - 6 = 200
So n = 19
i.e. 4+5+6+...19 = 184
After the 184th term,the sequence has 20 terms
12344444444444444444 = 20 terms
=> 200th term = 4
3)Star mark question(most tricky) How many squares are there between
2011 to 2300 which follows 2013,2020,2027.......2300
Ans; there are 3 squares 45.,46,47 but 47^2 follows the pattern.
answer 1 many given 3 (note:-but it is completely wrong
)
4)If a pipe can fill the tank within 6hrs.But due to leak it takes 30
min more. Now
the tank is full then how much time will it take to empty the tank through the
leak?
Ans;
given that it takes 6 hours for the pipe to fill the tank
so in 1 hour it can fill =1/6
but because of leak it takes 30 min more i.e (6+1/2) hours =13/2.
so in 1 hour pipe+ leak can fill= 2/13
finally pipe=1/6
pipe+leak=2/13
leak=1/6-2/13 =1/78
leak can alone do in 78 hours.
5)
There was a question of train. 2 trains crossing each other in 23
seconds. A man standing on the platform.. Find the ratio of speeds of
2 trains.i cannot completely recall that question
Ans:Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
27x + 17y / x+ y = 23
27x + 17y = 23x + 23y
4x = 6y
x/y = 3/2
(the question is from rs agaarwal)
6)the numbers from 1 to 20 are written in the below order, sum of any
two adjacent numbers is prime number.
20;A;16;15;4;B;12:C;10;7;6;D;2;17;14;9;8;5;18;E
then find value at A ?
Ans:
A=3
B=19
C=1
D=11
E=13
7)if a(b+c)=33
b(c+a)=40
c(a+b)=49
then find ab
Ans:a(b+c)=33
so a=11 or 3
b+c=11 or 3
c(a+b)=49
c=7
a+b=7
so a=3
and b=4
and c=7
abc=84
8)#(most dangerous ) a spider web consists of 3 concurrent lines
forming radial support for 20 concentric regular hexagon .the hexagon
vertices are 5mm from their immidiate neighbour. if the innermost
hexagon has a side length 3mm how many meters is the length of the
entire web including the 3 diagonals ?
Ans;side of innermost hexagon = 3mm
side of next hexagon = 8mm
it goes on as series 3,8,13... 20th terms
total length of smallest hexagon = 6 * 3= 18mm
next hexagon length = 6 * 8= 48mm
sum of all hexagon sides = 20/2 * (2*18 + 19 * 30) = 6060mm
but the sum length of diagonals is 6*98=588
so 6.060+0.588=6.648 meters
9)the diagnal of a square field is 266.66(some value i dont remember
exactly), then find the area of a square
ANs:ans- a. 2*10^4
10)Rs.7791 is divided among shills=a ,beena and chris in such a way
that if Rs.34 Rs.32 and Rs.29 be deduced from their respective shares
they are left with money in the ratio 8:6:12 find shilas share in
rupees a)2402 b)1798 c)1808 d)239
Ans:7791-(34+32+29)=7696
s:b:c=8:6:12
share of s=8/26*76976 + 34=2402
11)123412344123444123444412344444... now the last two terms of 200th number
Ans:1st group 1234 number of digit 4
2nd group 12344 number of digit 5
3rd group 1234444 number of digit 6
so at the end of each group there will be series of 4s.
So the answer is 44
12)HOW MANY NUMBERS ARE THERE FROM 1 TO 400 HAVING EXACTLY THREE
INTEGRAL FACTORS
ANs:there are total 8 nos. less than 400 having three integral factors
4 , 9 , 25 , 49 , 121 , 169 , 289 , 361
13)(1-1/3^2) (1-1/4^2) (1-1/5^4)----------(1-1/2015^2) = x/2015 then x value
Ans:(1+1/3)(1-1/3)(1+1/4)(1-1/4)......(1-1/2015)(1+1/2015)=x/2015
2/3*4/3*3/4*5/4.......................2014/2015*2016/2015=x/2015
2/3*2016/2015=x/2015
after solving
x=1344.
14)x,y,z are positive integers if x(y+z)=63, y(z+x)=40, z(y+x)=33.
what is the value of x+y+z ( please check ,not sure)
ans: answer is 14 but not sure please check as this is not in my slot as x=7
y=4
z=3
15) Given sequence 91011....33 .what is the remainder when divided by 9?
a)2
b)0
c)3
d)7
ans:c)3
(9+10+11+12.......33)-(1+2+3...8)
so here
n(n+1)/2-n(n+1)/2
(33x34)/2-(8x9)/2
33x17-4x9
561-36=525
now 525/9=3
16)when sum of the numbers from 9 to 33 divided by 9 the remainder is
a)7
b)5
c)3
d)1
ans:sum from 1 to 33 =561 i.e. (n(n+1)/2)
sum from 1 to 8= 36
561-36= 525
525/9 remainder is 3.....option C
17)x,y,z are positive integers if x(y+z)=63, y(z+x)=40, z(y+x)=33.
what is the value of x+y+z?
ans: do not have time,please solve
answer is 24 not sure .not in my slot
18)
In a tank 7/13 th part contains fuel. 22 liters of fuel is taken out
from the tank, Themn its showing 1/5th mark in tank.
ans:Let X ltr is total capacity,
then
(7/13)x-(1/5)x=22
(35x-13x)/65=22
x=65
19)A 4*4 Table was given first row contains number 1,2,3,4.We have to
find value of x which is in third row such that no number should
repeated diagonally or row-wise/column-wise.
ans:ans is =3(status: very tricky,do not attempt)
1 2 3 4
3 4 1 2
1 2 3 4
3 4 1 2
20)there are 2 man one old and one young work in the same office and
live in same apartment.
The old man takes 30 minutes to reach office and young man take 20
minutes to reach the office . If old man starts at 10:00 a.m for
office and the young man at 10:05 a.m then at what time will they
meet?
ans:et speed of old man=vo
let speed of young man=vy
vo*30=vy*20
vo/vy = 2/3.....................(1)
now let they will meet after t time of 10:00 am
vo*t = vy*(t+5).........................(2)
from eq(1) and eq(2) we get
vo*t = 15*vo
so, t=15 mints
now we can say that they will meet at 10:15 am
21)
in what ratio 50 rs and 60 rs wheat is to be mixed such that after
selling it at 70 rs a profit of 20% is made
ans:ans-1:5
let 50rs be x and 60rs be y
so,cost price=50x+60y
selling price=70(x+y)
gain%=sp-cp/cp*100
20/100=70(x+y)-(50x+60y)/50x+60y
x:y=1:5
22)a number decreases successively. for eg. 9876543210. How many such
5- digits numbers are possibe?
ans:ans 13/18
probability of not getting same no
1st person:6/6
2nd person:5/6
3 : 4/6
4: 3/6
probability of not getting similar is 6/6*5/6*4/6*3/6=5/18
probabilty of getting is:1-5/18=13/18 (ans)
23)do not remember the question but i remember f(1)=5 and f(a+b)=
F(a)+f(b)+ a*b someting like that
it is last option that i remember
24)
A series of book was published at seven year intervals. When the
seventh book was published the total sum of publication year was 13,
524. First book was published in?
a. 1911
b. 1910
c. 2002
d. 1932
Answer:
Explanation:
Let the years be n, n+7, n+14, ...., n+42. (∵ use formula Tn=a+(n−1)d
to find nth term)
Sum = Sn=n2(2a+(n−1)d) = 72(2n+(7−1)7) = 13,524
⇒7n+147=13,524
⇒ n = 1911
25)
Assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1). For all natural
numbers (Integers>0)m and n. What is the value of f(17)?
a. 5436
b. 4831
c. 5508
d. 4832
Explanation:
f(1) = 0
f(2) = f(1+1) = f(1)+f(1)+4(9×1×1 – 1) = 0+0+4×8 = 32
f(4) = f(2+2) = f(2)+f(2)+4(9×2×2 – 1) = 32+32+4×35 = 204
f(8) = f(4+4) = f(4)+f(4)+4(9×4×4 – 1) = 204+204+4×143 = 980
f(16) = f(8+8) = f(8)+f(8)+4(9×8×8 – 1) = 980+980+4×575 = 4260
f(17) = f(1+16) = f(16)+f(1)+4(9×16×1 –1) = 4260+0+ 4×143 = 4832
26)Ram and Shakil run a race of 2000 meters. First, Ram gives Shakil a
start of 200 meters and beats him by one minute. If, Ram gives Shakil
a start of 6 minutes Ram is beaten by 1000 meters. Find the time in
minutes in which Ram and Shakil can run the races separately.
a. 12, 18
b. 10, 12
c. 11, 18
d. 8, 10
Answer: d (folow campusgate for story )
27)
Of a set of 30 numbers, average of first 10 numbers = average of last
20 numbers. Then the sum of the last 20 numbers is?
a. Cannot be determined.
b. 2 x sum of last ten numbers
c. 2 x sum of first ten numbers
d. sum of first ten numbers
Answer: c
Explanation:
We know that sum = average x number of observations.
Let the common average = x
Now sum of first 10 numbers = 10x
Sum of the last 20 numbers = 20x.
So sum of the last 20 numbers = 2 × sum of the first ten numbers.
Question updated today :
28)According to the stock policy of a company , each employee in the
technical division is given 15 shares of the company and each employee
in the recruitment division is given 10 shares. Employees belonging to
both Communities get 25 shares each. There are 20 employees in the
company and each one belong to at least one division. The cost of each
share is $10. If the technical division 15 employees and the
recruitment division has 10 employees, then what is the total cost of
the shares given by the company?
a. 3120
b. 3250
c. 2650
d. 3180
Ans:total emp-20
10-recruitmnt
15-tech
so 5 - both
so only recruimnt -5
only tech -10
(5*25*10)+(5*10*10)+(10*15*10)
=1250+500+1500=3250
29)there is a networking questions,if one goes to A it is rs 100 and
one goes to B it is rs 200,follow dijakstra algorithm to get the
answer. the answer is rs 800
Email writing with phrases I remember :
Write an email in 50 words to a organization called 'helping hand' to
request them to help an old man who is an orphan not able to
speak...suffering from diseases and requesting him to accomodate .Sign
as Anthony. there are many ,i Remembered few of them.
Homeless-bus stand- reticent - rags - bus stand - help - care-
obliged-no shelter- food-accomodation-destitute home.
No comments:
Post a Comment