Answer :
Given rope of length = 40m (radius)
Area of semi circle =(pi*r^2)/2 = (1600 * pi)/2 = 800*pi ---(1)
Area of quarter circle = (1/2 * 800 * pi) = 400*pi ----- (2)
Area of sector is = r*r*(pi/2)/2 = 25*pi ----- (3)
By adding above eq. (1) (2) & (3)
Total area = 1225*pi
As per quesiton there are 2 goats
so area = 1225*pi*2 = 2450pi.
Answer :
Total no. of families who take newspaper=80
Hindu newspaper = 60% = (80*60/100) = 48
Regional newspaper = 80% = (80*80/100) = 64
TOI newspaper = 70% = (70*80/100) = 56
Find common families take H.C.F (48,64,56) = 8
Therefore,(8/80)*100=10%
So, common families who take all newspaper = 10%.
Question 3. What Is The Simplified Result Of Following The Steps Below In Order?
Answer :
X2-X-6=0
(x-3)(X+2)=0
X=3,-2.
Answer :
Lets assume son's age = x
So, father's age = x + 30
After 5 years:
Son's age = x + 5
Father's age = x + 35
In 5 years the father is thrice as old as his son so:
3(x + 5) = x + 35
x = 10
So, current father's age = 40 Years.
Answer :
Let 10'splace digit is x and unit's place digit y
First milestone : 10x+y
Second milestone : 10y+x
Third milestone: 100x+y
Since the speed is uniform so
Distance covered in first Hr = Distance covered in Second Hr
(10y+x)-(10x+y) = (100x+y)-(10y+x)
By solving,
y=6x
but since x and y are digits so only possible combination is x=1 and y=6,
So average speed = 45 Kmph.
Question 6. If Log 0.317=0.3332 And Log 0.318=0.3364 Then Find Log 0.319 ?
Answer :
log 0.317=0.3332 and log 0.318=0.3364
then
log 0.319=log0.318+(log0.318-log0.317)
=0.3396.
Answer :
A+B=132
B+C=130
C+D=102
B+D=116
A+2B+C=262
B+C+2D=218
A+B-2D=44
132-2D=44
D=44.
Answer :
The volume of the cylinder is Pi x r^2 x h = Pi x 3^2 x 6 = 54Pi
Volume of a cylinder is 4/3 x Pi x r^3
Now 54Pi = 12 x 4/3 x Pi x r^3
54 = 16 x r^3
r^3 = 54/16 = 27/8
r = 3/2
Therefore diameter is 3 cms.
Answer :
persons who can speak English = 1 - (1/5) = 4/5
persons who can speak Hindi = 1 - (3/7) = 4/7
persons who can speak any or both = 1 - 1/10 = 9/10
so total persons speak both = 4/5 + 4/7 - 9/10 = 33/70
persons speak any = 1 - 33/70 - 1/10 = 3/7
% = 300/7% = 42.86%.
Question 10. If A - B = 3 And A^2 + B^2 = 29, Find The Value Of Ab?
Answer :
2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
ab = 10.
Answer :
If any one choose container A then prob = (1/2)*(4/10)=1/5
If any one choose container A then prob = (1/2)*(40/100)=1/5.
Question 12. Below Is A Pseudo Code Read X?
Answer :
Given Last value int seq. = 54.
and in every Loop result multiplied By 3.
So By Backward Approach
54/3=18 => 18/3=6
=> 6/3=2.
So, The Starting Value Is 2.
Question 13. If M^2+m^-2=23;then What Is The Value Of M^3+m^-3?
Answer :
m^2+m^-2=23
=> (m + m^-1)^2 - 2 = 23
=> (m + m^-1) = 5
m^3+m^-3 = (m + m^-1)^3 - 3(m + m^-1) = 5^3 - 3*5 = 110.
Question 14. If M=2- _/3 Find The Value Of: M^6+m^5+m^4+1)/m^3?
Answer :
m = (2 - ?3)
=> 1/m = (2 + ?3)
(m^6+m^5+m^4+1)/m^3
= m^3 + m^2 + m + 1/m^3
= (m + 1/m)^3 - 3(m +1/m) + m(m+1)
= 4^3 - 3*4 + (2-?3)(3-?3)
= 64 - 12 + 9 - 5?3
= (61 - 5?3).
Answer :
Let Swati's age = 2X and Varun's age = 5X
(2X + 8)/(5X + 8) = 1/2 => X = 8
Swati's age = 16 years
and Varun's age = 40 years
Difference of their ages = 24 years.
Answer :
20*10 +15*8 +x*4/20+15+x = 8.5
x= 5 child.
Question 17. When A Square Of An Odd Number Is Divided By 8?
Answer :
Let's call the odd number 2a+1, where a is an integer.
Then (2a+1)^2 = 4a^2 + 4a + 1 = 4a(a+1) + 1.
Since a is odd, a+1 is even.
So, 4a(a+1) has to be a multiple of 8
Therefore 4a(a+1) + 1 must leave a remainder of 1 when divided by 8.
Answer :
Since each one of the three numbers a, b, and c is divisible by 3, the numbers can be represented as 3p,3q, and 3r, respectively, where p, q, and r are integers.
The product of the three numbers is 3p*3q*3r =27(pqr).
Since p, q, and r are integers, pqr is an integer and therefore abc is divisible by 27.
Answer :
Number of runs made by running = 110 - (3 * 4 + 8 * 6)
= 110 - (60) = 50.
Required percentage = ({50/110}*100)% = 45{5/11}%.
Question 20. How Many Ways Can 360 Be Written As Product Of Two Numbers?
Answer :
1*360, 2*180, 3*120, 4*90, 5*72, 6*60, 8*45, 9*40, 10*36, 12*30, 15*24, 18*20
SOL 2) 360 => 2^3 * 3^2 * 5^1 [i.e. a^x * b^y * c^z)
No. of ways can be written as a prod of 2 no's is
(x+1)*(y+1)(z+1)/2
=> (3+1)*(2+1)*(1+1)/2
=> 24/2 = 12.
Answer :
Two tallest boys can be arranged in 2! ways, rest 18 can be arranged in 18! ways.
Girls can be arranged in 6! ways.
Total number of ways in which all the students can be arranged = 2! * 18! * 6! = 18! *1440.
Answer :
The order of each letter in the dictionary is ABLORU.
Now, with A in the beginning, the remaining letters can be permuted in 5! ways.
Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways.
With L in the beginning, the first word will be LABORU, the second will be LABOUR.
Hence, the rank of the word LABOUR is 5!+5!+2 =242.
Answer :
Let their marks be (x + 9) and x.
Then, x + 9 = (56/100)(x + 9 + x)
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.
Answer :
To complete a work for 6 days, 8 men require
For complete a work for 1 day = 6*8 = 48 men
For complete a work in half a day(1/2) = 48*2 = 96 men.
Answer :
length covered by 80% of the pencils =80/100 * 14000000 * 5 = 56000000 inches
Minimum length covered by remaining 20% of the pencils =20/100 * 14000000 * 3 = 8400000 inches
Maximum length covered by remaining 20% of the pencils =20/100 * 14000000 * 6 = 16800000 inches
Hence, total length spanned by the pencils is (56000000 +8400000) to (56000000 +16800000 )
ie, 64400000 inches to 72800000 inches.
Answer :
Given A works trice as much as B
So the ratio between A and B = 3:1
so 3x-x=60
and x = 30
so 1/90+1/30=221/2 days.
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