1.
Rate at which A fill is 1/42 per min
A filled for 12 min so tank filled by A will be 12/42
Similarly B empty the tank for 6 min
now the volume will be (18/42) -(6/30) = 8/35 because at the 6 min A has also filled.
Now the amount left to be filled is (1-8/35) = 27/35
Now C comes it fills 1/35 per minute.
So from now the amount will be filled is (1/42+1/35-1/30) = 2/105 per minute
So to fill the required amount it will take 105/2 * 27/35 = 40.5 min
So total time is 12+6+40.5 = 58.5 min
2.
Total no of cubes = 5*6*7/0.03=7000
for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.
3.
To make cube we need 10*10*10=1000.
Now we have only 10*3*3=90.
So the more cube we need are 1000-90=910.
4.
square root of (d/a)^2 + (d/c)^2
5.
none of these
6.
Proper Selections:
A B C
A C B
C B A
B A C (i.e. total 4)
Improper selection:
B C A
C A B (i.e. total 2)
Probability for improper selection= 2/6 = 1/3
7.
Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!
20 because their invitees are with their spouses.
Also 1 of them can stand with other so 18 places
So total is 18*19!
8.
60
9.
m+d+i=74 (1)
m=46+(d+i) (2)
i=0.4d (3)
solving we get d = 10
11.
Cost price= 24*X,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200 =3200
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=400/9 =44 4/9
12.
exp(10, m) = n * exp(2, 2) = n*(2^2) = 4*n
10^m=4*n ; where m,n integers
m=2, n=25 satisfies for the least value
13.
Let the income x, so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,
on house rent he spends rs 700-balance.
14.
L=12,N=11,J=27,M=14,K=36
Given,
K+M+J+L+N=100 ———(i)
K,M,J,L,N>10 ———(ii)
K?M?N?J?L ———(iii)
K+M=J+L+N ———(iv)
L=3 + X^3 , where X is an integer ———(v)
J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)
K=Z^2 or Z^3, where Z is an integer ———(vii)
Now from the ques value of J can be 27 or 64
but if we take 64 then eqn iv would not satisfy so J=27
Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50
Now from eqn v the value of L must be 11, thus L=11
That conclude N = 12
Now from the questio part 3,
The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
Considering the fact M-L=any of those values
Now M=L+any of those values
M=11+any of those values
Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies
again M=13, value = 2; K=37 which is neither square or cube of any integer
M=16, value = 5; K=34 which is neither square or cube of any integer
M=20, value = 9; K=30 which is neither square or cube of any integer
Thus M = 14 & K = 36.
15.
4
16. Modified:
17.
Given diagonal of square (a)= 2* side of triangle;
Area of square =1/2 a^2 where a = length of diagonal
Area of triangle = v3/4 * a^2/4
Ratio of triangle to square: v3/8
18.
Possible events
(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
Total no. of possible event = 27
So probability = 27/216 = 1/8
answer (1/8)
19.
40
20.
(3.14*5.4*5.4)*10/60 = 15.26 cm2
21.
40
22.
Number of step must be 2^n where n= no. of buckets
8ltr 5ltr 3ltr
5 0 3
5 3 0
2 3 3
2 5 1
7 0 1
7 1 0
4 1 3
4 4 0
Total 8 steps are required.
24.
Well Keep a single red ball in 1 box and move 38 red balls to the other
1st box = 1R
2nd box = 38R + 26G
p(red) = 1/2 * 1 + 1/2 * 38/64 ˜ 0.8
25.
16:15
26.
7:5
27.
1:5
28.
x=0
29. Modified:
?
Quantity of water to be added to 60 lts of milk =
[1/5 X 60]
litres =12 litre.
30.
Total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros
31.
2
for odd = 2
for even =1
32.
a=2 , d=2,a.p formula find nth term i.e.. tn=a+(n-1)d
where tn=100
100=2+(n-1)2 gives n=50.
now sum of n terms n/2(a+l)=2550(ans).
33.
55!
Rate at which A fill is 1/42 per min
A filled for 12 min so tank filled by A will be 12/42
Similarly B empty the tank for 6 min
now the volume will be (18/42) -(6/30) = 8/35 because at the 6 min A has also filled.
Now the amount left to be filled is (1-8/35) = 27/35
Now C comes it fills 1/35 per minute.
So from now the amount will be filled is (1/42+1/35-1/30) = 2/105 per minute
So to fill the required amount it will take 105/2 * 27/35 = 40.5 min
So total time is 12+6+40.5 = 58.5 min
2.
Total no of cubes = 5*6*7/0.03=7000
for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.
3.
To make cube we need 10*10*10=1000.
Now we have only 10*3*3=90.
So the more cube we need are 1000-90=910.
4.
square root of (d/a)^2 + (d/c)^2
5.
none of these
6.
Proper Selections:
A B C
A C B
C B A
B A C (i.e. total 4)
Improper selection:
B C A
C A B (i.e. total 2)
Probability for improper selection= 2/6 = 1/3
7.
Mr and Mrs smith never be together so out of 20 (with both them) 19 can b any place so total = 19!
20 because their invitees are with their spouses.
Also 1 of them can stand with other so 18 places
So total is 18*19!
8.
60
9.
m+d+i=74 (1)
m=46+(d+i) (2)
i=0.4d (3)
solving we get d = 10
11.
Cost price= 24*X,
spoiled= 24*1/3=8 kg, now total amount= (24-8)=16 kg
selling price= 16*200 =3200
profit= (3200-24*X)
profit=2* cost , (3200-24*X)= 2*24*X, x=400/9 =44 4/9
12.
exp(10, m) = n * exp(2, 2) = n*(2^2) = 4*n
10^m=4*n ; where m,n integers
m=2, n=25 satisfies for the least value
13.
Let the income x, so in petrol he spends 3x/10 rs,remaining x-3x/10=7x/10 on house rent and balance on.now 3x/10=300,so x=1000,
on house rent he spends rs 700-balance.
14.
L=12,N=11,J=27,M=14,K=36
Given,
K+M+J+L+N=100 ———(i)
K,M,J,L,N>10 ———(ii)
K?M?N?J?L ———(iii)
K+M=J+L+N ———(iv)
L=3 + X^3 , where X is an integer ———(v)
J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)
K=Z^2 or Z^3, where Z is an integer ———(vii)
Now from the ques value of J can be 27 or 64
but if we take 64 then eqn iv would not satisfy so J=27
Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50
Now from eqn v the value of L must be 11, thus L=11
That conclude N = 12
Now from the questio part 3,
The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
Considering the fact M-L=any of those values
Now M=L+any of those values
M=11+any of those values
Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies
again M=13, value = 2; K=37 which is neither square or cube of any integer
M=16, value = 5; K=34 which is neither square or cube of any integer
M=20, value = 9; K=30 which is neither square or cube of any integer
Thus M = 14 & K = 36.
15.
4
16. Modified:
- 1. How many kgs. of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by Belling the mixture at Rs. 7.20 per kg ?
17.
Given diagonal of square (a)= 2* side of triangle;
Area of square =1/2 a^2 where a = length of diagonal
Area of triangle = v3/4 * a^2/4
Ratio of triangle to square: v3/8
18.
Possible events
(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
Total no. of possible event = 27
So probability = 27/216 = 1/8
answer (1/8)
19.
40
20.
(3.14*5.4*5.4)*10/60 = 15.26 cm2
21.
40
22.
Number of step must be 2^n where n= no. of buckets
8ltr 5ltr 3ltr
5 0 3
5 3 0
2 3 3
2 5 1
7 0 1
7 1 0
4 1 3
4 4 0
Total 8 steps are required.
24.
Well Keep a single red ball in 1 box and move 38 red balls to the other
1st box = 1R
2nd box = 38R + 26G
p(red) = 1/2 * 1 + 1/2 * 38/64 ˜ 0.8
25.
16:15
26.
7:5
27.
1:5
28.
x=0
29. Modified:
- 1. How much water must be added to 60 litres of mixture of milk? 1 ½ litres of milk for Rs. 20. So as to have a mixture worth Rs.10? a litre ?
?
Quantity of water to be added to 60 lts of milk =
[1/5 X 60]
litres =12 litre.
30.
Total zeros at the end of product 5^5 x 10^10 x 15^15 x 20^20 x 25^25 x 30^30 x 35^35 x 40^40 x 45^45 will be 5+10+15+20+50+30+35+40+45 = 250 zeros
31.
2
for odd = 2
for even =1
32.
a=2 , d=2,a.p formula find nth term i.e.. tn=a+(n-1)d
where tn=100
100=2+(n-1)2 gives n=50.
now sum of n terms n/2(a+l)=2550(ans).
33.
55!
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