For a set of numbers T, we say that T has distinct subset sums if all distinct subsets of T have distinct sums. How many subsets of {1,2,3,4,5,6,7,8} have distinct subset sums?
A simple graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have?
Rajesh walked down a descending escalator and took 40 steps to reach bottom. Sunil started simultaneously from the bottom taking 2 steps for every one step taken by Rajesh. The time taken by Rajesh to reach the bottom from the top is same as the time taken by Sunil to reach thr top from bottom. How many steps more than Rajesh did Sunil take before they crossed each other on the escalator
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A contest consisted of 11 multiple choice questions, each having 11 possible choices, of which only 1 of the choices is correct. Suppose that 111 students actually wrote the exam, and no two students have more than one answer in common. The highest possible average mark for the students is ?
A man rows 135 km upstream in 2.7 hours. He rows the same distance downstream in 2.5 hours . However for downstream, he reduces his speed by 9%, while speed of the current gets reduced by 20%. Find the speed of the man.
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Each of the numbers x1; : : : ; x2007 can be 0,1, or -1. Let S = x1x2 + x1x3 + + x1x2007 + x2x3 + + x2005x2007 + x2006x2007; which is the sum of all products xixj with i
a. -1003 b. -1 c. -2006 d. -2005 e. None of the preceding.
A milkman sell the milk at cost price but he mixes the water in it thus he gain 9.09%.the quantity of water in the mixture of 1L is??
If x,y,z are integers and |x-3|+|y-5|+|z-7|=3 then find the max possible value of (x+3)(y+5)(z+7)?👍
For how many integral values of x is (x^2-8x+24)/(x^2-8x+16) is a prime no?👍
What is the smallest number which when divided by 7, 8, 9 leaves a remainder of 2, 4, 6 respectively?
What is the area of a square whose vertices lie on the sides of an equilateral triangle of side 1 unit?
A,B,C,D bought a certain no of apples from Market. D bought half the no of apples bought by the other 3,C bought 1/3 the no of apples bought by the other 3 and A bought 2/5 the no of apples bought by other 3. What is the ratio of the total no of apples bought by B to the total no of apples bought by all 4?( All of them bought a distinct no of apples)
Amar has 5 Butter naans and 10 rotis and Bharat has 9 butter naans and 8 rotis. Suman Joined them and they shared the butter naans and rotis equally based on the calorific value. The cost of naan as well as roti is proportional to its calorific value.Suman paid Rs10 and Rs30 to Amar and Bharat respectively. If the calorific value of one butter naan is 150 calories then what is the calorific value of 1 roti?
60 250 200 50👍
A man arrives at a railway station 1.5 hours before the time at which he had ordered his carriage to meet him.He walks at the rate of 4 kmph and meets the carriage 8 km from his house and reaches 1 hour earlier than usual time.What's the speed of the carriage and distance from station to his house?
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Adarsh starts in car from Mumbai towards Bangalore.After some time he realizes that he will cover only 3/4th of the distance in the scheduled time.He, therefore, doubles his speed immediately and thus he manages to reach Bangalore exactly on time.Find the time from start, after which Adarsh changed his speed, given that he would have been late by 3 hours if had not changed his speed.
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Smallest integer K is a perfect square when divided by 2 and a perfect cube when divided by 3. Find K
N! is completely divisible by 13^52 . What is sum of the digits of the smallest such number N? (a) 11 (b) 15 (c) 16 (d) 19