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A person's present age is twofifth of the age of his mother. After 8 years, he will be onehalf of the age of his mother. How old is the mother at present?
Let the mother's present age be x years
Then, the person's present age = ( 2/5 x) years
∴ ( 2/5 x + 8) = 1/2 (x + 8)
⇒ 2(2x + 40) = 5(x + 8)
⇒ x = 40
If 2^{2x} + 2^{x+1} = 4 − 2^{x} , then x =
Given equation 2^{2x} + 2^{x+1} = 4 − 2^{x} Let 2^{x} = y
If 2 sin^{2} x + cos^{2} 45^{o} = tan 45^{o} and 0^{o} ≤ x ≤ 90^{o} , then the value of tan x is
What is the momentum of a man of mass 75 kg when he walks with a uniform velocity of 2m/s?
Given : m = 75 kg
v = 2m/s
p = ?
we know that momentum p = m x v
∴ p = 75 x 2
= 150 kg m/s.
The value of [(3.6 x 0.48 x 2.50)/(0.12 x 0.09 x 0.5)] is :
Each internal angle of a regular hexagon is :
Study the following diagram :
The value of 'x' is
3 x 4 = 12
12 x 5 = 60
3 x 5 = 15 = x
If A stands for Addition , S stands for Subtraction, M stands for Multiplication, D stands for Division, G for Greater Than and L for Less than Then which of the following alternatives will be logically correct.
16 A 3 M 2 G 16 A 2 M 3
= 16 + 3 x 2>16+2x 3
= 16+6 >16+6
= 22>22
Its logically wrong
16 A 3 M 2 G 16 M 2 A 3
= 16 + 3 x 2>16x 2+3
= 16+6 >32+3
= 22>35
Its logically wrong
16 M 3 A 2 L 16 A 2 M 3
= 16 x 3 +2<16+2x 3
= 48+2 <16+6
= 50<22
Its logically wrong
16 M 3 A 2G 16 A 2 M 3
= 16 x 3 +2>16+2x 3
= 48+2 >16+6
= 50>22
Its logically True
When a girl wrongly measures 97 metres for actual length of 100 metres,what is the percentage of error in the measurement?
percentage of error in the measurement is 100  97/100 x 100 = 3
Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?
Work done by the third pipe in 1 min. = 1/50  ( 1/60 + 1/75 )
= ( 1/50  3/100 )
=  1/100
Therefore, the third pipe alone can empty the cistern in 100 min
A person purchased a chair at Rs 70 and spent Rs 17 on its repair and 50 paise on carritage. If he sold the chair at Rs 100, then his approximate margin of profit was
Total C.P. = 70 + 17 + 0.5 = Rs. 87.50,
S.P. = Rs. 100
Gain = 100  87.50 = Rs. 12.50
∴ Gain% = 12.50/87.50 x 100 = 14.30(app.)
A certain sum was put at a certain rate of interest for 3 yrs. Had it been put at 2% higher rate, it would have fetched Rs 72 more. Find the sum.
At 2% more rate, the increase in SI for 3 years = Rs 72 (given)
So at 2% more rate the increase in SI for 1 year = 72/3 = Rs 24
i.e., Rs 24 is 2% of the invested sum
So 1% of the invested sum = 24/2 = 12
Therefore, the invested sum
= 12 x 100 = Rs 1200
Given n = 10, ∑x = 4, ∑y = 3, ∑x^{2 }= 8, ∑y^{2} = 9 and ∑xy = 3, then coefficient of correlation is
Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answerkey. All the others create their answerkey from one or two people who already possess the same. These people are called his/her "sources". If the person has two sources, then he/she compares the answerkeys obtained for both sources. If the key to a question from the both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source's answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.
The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.
Q. Which one among the following must have two sources ?
Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answerkey. All the others create their answerkey from one or two people who already possess the same. These people are called his/her "sources". If the person has two sources, then he/she compares the answerkeys obtained for both sources. If the key to a question from the both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source's answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.
The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.
Q. How many people (excluding the mastermind) needed to make answer keys before C could make his answer key ?
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