What is the value of \((469 + 174)^2 - (469 - 174)^2\) / \((469 \times 174)\)?
Find the value of \(\frac{1}{2\times3} + \frac{1}{3\times4} + \frac{1}{4\times5} + ... + \frac{1}{9\times10}\).
The mean of 5 numbers is 20. If one number is excluded, the mean of the remaining numbers becomes 23. What is the excluded number?
In an exam, 49% students failed in English and 36% students failed in Hindi, while 15% failed in both. If the total number of students who passed the exam in both subjects was 675, what was the total number of students who appeared in the exam?
A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of C.
A ball is dropped from a height of 120 meters. It rebounds two-thirds of the height from which it falls. What is the total distance it travels before coming to rest?
The product of two co-prime numbers is 117. Their LCM should be:
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
What will be the possibility of drawing a jack or a spade from a well shuffled standard deck of 52 playing cards?
If three coins are tossed simultaneously, than the probability of getting at least two heads, is
In Daya’s bag there are 3 books of History, 4 books of Science and 2 books of Maths. In how many ways can Daya arrange the books so that all the books of same subject are together?
How many leap years do 300 years have?
The last day of a century cannot be
A can run 1 km in 4 min.54 sec. and B in 5 min. How many meters start can A give B in a km race so that the race may end in a dead heat?
Jammu Express is 1.2 km long and is running along the Kerala express at speed of 80km/hr. Kerala express is 2/3rd the length of Jammu express and runs at 60 km/hr. How much time will it take for Jammu express to overtake the Kerala express?
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Statement 7a divided by 8b can be expressed algebraically as
\(3889 + 12.952 - ? = 3854.002\)
The smallest prime number is?
The largest 4 digit number exactly divisible by 88 is:
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
What is the value of \((469 + 174)^2 - (469 - 174)^2\) / \((469 \times 174)\)?
Your Answer : (Not Answered)
Correct Answer : B
This is based on algebraic identities. The numerator is in the form \((a+b)^2 - (a-b)^2\), which simplifies to \(4ab\).
Here, a=469 and b=174.
The expression becomes \(\frac{4ab}{ab} = 4\).
Find the value of \(\frac{1}{2\times3} + \frac{1}{3\times4} + \frac{1}{4\times5} + ... + \frac{1}{9\times10}\).
Your Answer : (Not Answered)
Correct Answer : B
This is a telescoping series. Each term can be split using partial fractions: \(1/(n(n+1)) = 1/n - 1/(n+1)\).
The series becomes: \((\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + ... + (\frac{1}{9} - \frac{1}{10})\).
All the intermediate terms cancel out.
We are left with \(\frac{1}{2} - \frac{1}{10} = \frac{5-1}{10} = \frac{4}{10} = \frac{2}{5}\).
The mean of 5 numbers is 20. If one number is excluded, the mean of the remaining numbers becomes 23. What is the excluded number?
Your Answer : (Not Answered)
Correct Answer : A
The sum of the original 5 numbers = Mean × Count = 20 × 5 = 100.
After one number is excluded, there are 4 numbers left, and their mean is 23.
The sum of the remaining 4 numbers = 23 × 4 = 92.
The excluded number is the difference between the original sum and the new sum.
Excluded number = 100 - 92 = 8.
In an exam, 49% students failed in English and 36% students failed in Hindi, while 15% failed in both. If the total number of students who passed the exam in both subjects was 675, what was the total number of students who appeared in the exam?
Your Answer : (Not Answered)
Correct Answer : C
Let F(E) be the percentage of students who failed in English and F(H) be the percentage who failed in Hindi.
Given: n(F(E)) = 49%, n(F(H)) = 36%, n(F(E) ∩ F(H)) = 15%.
The percentage of students who failed in at least one subject is n(F(E) ∪ F(H)).
n(F(E) ∪ F(H)) = n(F(E)) + n(F(H)) - n(F(E) ∩ F(H)) = 49 + 36 - 15 = 70%.
The students who passed in both subjects are those who did not fail in any subject. This is the complement of failing in at least one subject.
Percentage Passed in both = 100% - n(F(E) ∪ F(H)) = 100% - 70% = 30%.
We are given that this number is 675. Let T be the total number of students.
30% of T = 675
0.30 × T = 675
T = 675 / 0.3 = 2250.
The total number of students was 2250.
A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of C.
Your Answer : (Not Answered)
Correct Answer : A
Wages are distributed in the ratio of the work done. A's 1 day work = 1/6. B's 1 day work = 1/8. (A+B+C)'s 1 day work = 1/3. C's 1 day work = \(1/3 - (1/6+1/8) = 1/3 - 7/24 = (8-7)/24 = 1/24\). Ratio of work done by A:B:C = 1/6 : 1/8 : 1/24. Multiplying by 24 gives the ratio 4:3:1. C's share = \(\frac{1}{4+3+1} \times 600 = \frac{1}{8} \times 600 = 75\). So, C's share is Rs. 75.
A ball is dropped from a height of 120 meters. It rebounds two-thirds of the height from which it falls. What is the total distance it travels before coming to rest?
Your Answer : (Not Answered)
Correct Answer : C
This is a trick question. The answer should be 600 m. Let's re-calculate. Initial drop distance = 120m. After that, it rebounds and falls. Rebound 1: up \(120 \times 2/3 = 80\), down 80. Rebound 2: up \(80 \times 2/3 = 160/3\), down 160/3. The total distance is \(120 + 2 \times (80 + 160/3 + ...)\). The series in the bracket is a G.P. with \(a=80, r=2/3\). Its sum is \(\frac{a}{1-r} = \frac{80}{1-2/3} = \frac{80}{1/3} = 240\). Total distance = \(120 + 2 \times 240 = 120 + 480 = 600\) m.
The product of two co-prime numbers is 117. Their LCM should be:
Your Answer : (Not Answered)
Correct Answer : B
Co-prime numbers are numbers whose Highest Common Factor (HCF) is 1.
We know that for any two numbers a and b, Product of numbers = HCF(a,b) × LCM(a,b).
Given, Product = 117 and HCF = 1 (since they are co-prime).
117 = 1 × LCM.
Therefore, LCM = 117.
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
What will be the possibility of drawing a jack or a spade from a well shuffled standard deck of 52 playing cards?
Your Answer : (Not Answered)
Correct Answer : A
No answer description available for this question.
If three coins are tossed simultaneously, than the probability of getting at least two heads, is
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
In Daya’s bag there are 3 books of History, 4 books of Science and 2 books of Maths. In how many ways can Daya arrange the books so that all the books of same subject are together?
Your Answer : (Not Answered)
Correct Answer : D
No answer description available for this question.
How many leap years do 300 years have?
Your Answer : (Not Answered)
Correct Answer : C
Given year is divided by 4, and the quotient gives the number of leap years.
Here, 300%4 = 75.
But, as 100,200 and 300 are not leap years => 75 - 3= 72 leap years.
The last day of a century cannot be
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
A can run 1 km in 4 min.54 sec. and B in 5 min. How many meters start can A give B in a km race so that the race may end in a dead heat?
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
Jammu Express is 1.2 km long and is running along the Kerala express at speed of 80km/hr. Kerala express is 2/3rd the length of Jammu express and runs at 60 km/hr. How much time will it take for Jammu express to overtake the Kerala express?
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
Statement 7a divided by 8b can be expressed algebraically as
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
\(3889 + 12.952 - ? = 3854.002\)
Your Answer : (Not Answered)
Correct Answer : D
Let \(3889 + 12.952 - x = 3854.002\)
Then,
\(x = (3889 + 12.952) - 3854.002\\
= 3901.952 - 3854.002\\
= 47.95\)
The smallest prime number is?
Your Answer : (Not Answered)
Correct Answer : C
The smallest prime number is 2
The largest 4 digit number exactly divisible by 88 is:
Your Answer : (Not Answered)
Correct Answer : A
Largest 4-digit number = 9999
\(\frac{9999}{88} = 113\tfrac{55}{88}\)
Required number \(= (9999 - 55) = 9944\)
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
We'll write only best content for you