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141 / 362
If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of 'a' in 2 ^ a = a ^ 3 ?
A-2
B-1
C0
D1
Answer: Option D
Explanation:2^a = 2*2 + a ......(i)
=> a^3 = 2*a + 3 .....(ii)
=> 4 + a = 2a + 3
=> a=1.
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142 / 362
If a,b,c be in GP and p,q be respectively AM between a,b and b,c then
A2/b=1/p+1/q
B2/b=1/p-1/q
C2=a/p-c/q
DNone of the above
Answer: Option A
Explanation:p=(a+b)/2; q=(b+c)/2
=> 1/p+1/q = 2*((1/(a+b))+(1/(b+c))
=> 2*(a+2b+c)/(a+b)(b+c)
=> 2*(a+2ar+a(r^2))/(a+ar)(ar+a(r^2)) because b=ar; c= a(r^2).
where r = common ratio.
On Solving, we get
=> 1/p + 1/q = 2/ar = 2/b.
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143 / 362
Thirty litres of water is added to 150 litres of 20% solution of alcohol in water.The resulting strenght of alcohol is
A16.67%.
B17.2%.
C18.3%.
DNone of these
Answer: Option A
Explanation:As per question, 20% solution of alcohol in water => 30 litres of alcohol & 120 litres of water.
Then 30 litres of water is added, so the solution now contains 150 litres of water and 30 litres of alcohol.
Therefore, the resulting strength of alcohol = 30*100/180 = 16.67%.
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144 / 362
Find the difference of minimum number of number required to form every number from 1 to 1234 and 1 to 4321.
A9
B7
C4
D3
Answer: Option D
Explanation:In 1234,
Unit place 1 to 1234 can be formed using 0 to 9 digits. i.e., 10 digits.
10's can be formed using 0 to 9 digits. i.e., 10 digits.
100's can be formed using 0 to 9 digits. i.e., 10 digits.
1000's can be formed using only one digit, 1. i.e., 1 digit.
Total no. of numbers required is 10 + 10 + 10 + 1 = 31.
In 4321, it is 10 + 10 + 10 + 4 = 34.
Therefore, difference = 34-31=3.
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145 / 362
The average age of 30 students of a class is 12 years. The average age of a group of 5 of the students is 10 years and that of another group of 5 of them is 14 years. What is the average age of the remaining students ?
A8 years
B10 years
C12 years
D14 years
Answer: Option C
Explanation:Given average of 30 students = 12 years.
So Total age of 30 students = 30*12 = 360 years.
First group total age = 5*10 = 50 years.
Second group total age = 5*14 = 60 years.
Remaining = 360-(50+70)=240
So, Average = 240/20 = 12 years.
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146 / 362
A 10 Liter mixture of milk and water contains 30 percent water. Two liters of this mixture is taken away. How many liters of water should now be added so that the amount of milk in the mixture is double that of water?
A1.4
B0.8
C0.4
D0.7
Answer: Option A
Explanation:Two liters were taken away So we have the only 8L of the mixture.
Amount of milk in 8 L of mixture = 8 * 70% = 5.6 liters
Amount of water in 8 L of mix = (8 - 5.6) = 2.4 L.
Half of milk i.e half of 5.6 = 2.8 L.
We need (2.8 - 2.4)L water more = 0.4 L
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147 / 362
Mr verma has 4 different paintings that he wishes to divide among his 3 children. In how many ways can he do this if each child must get at least 1 painting and all paintings are different ?
A72
B46
C36
D34
Answer: Option A
Explanation:First child could get 1 out of 4 paintings: 4
Second can get 1 out of remaining 3: 3
Third will get 1 out of remaining 2: 2
Now the last painting could be given to any of the three child in 3 diff ways:
Thus, total number of ways: (4 * 3 * 2) * 3 = 72.
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148 / 362
The minimum number of numbers required to form a number from 9 to 9000 which are multiples of 5 is:
A31
B41
C42
D32
Answer: Option A
Explanation:The multiples of 5 must end with 0 or 5.
Therefore, units place of a number from 9 to 9000 can be filled by only two digits 0 and 5. i.e., 2 digits.
10's place of a number from 9 to 9000 can be formed by 0 to 9 digits. i.e., 10 digits.
100's place of a number from 9 to 9000 can be formed by 0 to 9 digits. i.e., 10 digits.
1000's place of a number from 9 to 9000 can be formed by by 1 to 9 digits 1. i.e., 9 digits.
Therefore, total number of numbers required is 2 + 10 + 10 + 9 = 31.
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149 / 362
if it is 00.45,then what be the time corresponds to 12 hour watch?
A12.45 AM
B12.45 PM
C11.45 am
DNone of these
Answer: Option A
Explanation:24 hr clock-12=12 hr clock.
therefore 00.00 in 24 hr clock corresponds to 12 am in 12 hr clock.
so 00.45= 12.45 am
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150 / 362
Atul bought a machine for 4,50,000 and sold it to Irrfan who later sold the machine to Danish at a loss of 10% for rs.4,95,000. The profit earned by atul is:
A23%
B21%
C25%
D22.22%
Answer: Option D
Explanation:cost price of irfan is : 90x/100=4,95,000 => x=5,50,000;
profit =(5,50,000-4,50,000)/4,50,000; = 1,00,000/4,50,000
profit % for atul = .2222 * 100 = 22.22%
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