Find how number(s) less than 100 which have exactly 8 divisors..
94 humans take 87 days to complete a work.A robot as efficient as human starts working,after each day a new robot joins,where capcaity of ith robot is twice that of (i-1) where i>1 .find in how many days will robots finish the job ?
Find the value of a^3 + b^3 + c^3 – 3abc when a = 225, b = 236, c = 227.
PQRS is a square with side 2a units. A circle of radius a is drawn with P as the centre. Two tangents are drawn from Q and S to the circle which meet at X. Which of the following cannot be the length of XP?
a(root 6 - root 2)
a(root 6 + root 2)
a(root 2)
Any of the above can be the length of XP.
How many divisors of 21600 are perfect squares?
A positive integer is bold if it has 8 positive divisors that sum up to 3240.
For example, 2006 is bold because its 8 positive divisors, 1, 2, 17, 34, 59, 118, 1003 and 2006, sum up to 3240. Find the smallest positive bold number.
if x,y ,z are three distinct positive real numbers such that x+y+Z=1, then the value of (1/x-1)(1/y-1)(1/z-1) is:
soln
(1/x-1)(1/y-1)(1/z-1)= y+z/x.z+x/y.x+y/z
but y+z/2 is greater then or equal to yz etc.
LHS>= 8xyz/xyz
"but y+z/2" and LHS>= 8xyz+8 (in solution part i am not able to find how this both steps have come) CAn anyone helpme out,,,,
It is given that the system of equations x^2 +ax +1 =0 & x^2 +bx + c = 0 have a common real root.Also the system of equations x^2 +x+a = 0 & x^2+ cx +b = 0 have a common real root. what are the two roots of the equation x^2 +ax+1 = 0
1) - 1 & -1
2) 1 & 1
3) 1/2 & 2
4) 1 & -1
5) 1/3 & 3
Find the number of solutions of x1+x2+x3+x4 = 20 ; also given that2 ≤ x1 ≤ 73≤x2 ≤8 5≤x3 ≤ 70≤ x4≤ 10a) 208 b) 104 c) 122 d) 80
Not a right triangle angle ,if you are given 2 sides of triangle. how can you find the third side ? Here the question :
Area=300
AB=100
BC=20
AC =?
10 engine consume 80 lit of petrol running 9 hrs a day. How much petrol is required for 10 engines each running 15 hrs a day , whereas 6 engines of the former type consume as much as 5 engines of latter type
- 75
- 160
- 111.1
- 80
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A takes twice the time that B and C together need to complete a certain work,whereas B takes thrice the time that A and C together take to do the same work.If A increases his rate of doing worky by 50% and C increases his rate of doing work by 80%,then find in how many days A,B and C working together can do four times the work that B alone took 72 days to complete?
- 12 days
- 24 days
- 36 days
- 48 days
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Two cars start at the same time around a circular path of area 100pie sq. miles .one car travels at 20pie mph and the other travels at 16pie mph to complete 1 round of the circular path. if they start at 1 pm today , at what time will they will meet again at starting point ???
arrange 6 people in a line ABCDEF such that B always comes in front of C, who always comes in front of D. approach plz
A man rows upstream in a river . when he covered 1 km from starting point his hat fell down and started to move downstream the man kept swiming upstream for 5 min. but realised he has droped his hat then rows down stream to catch the hat. finally the hat and man meet at start . find the speed of the river.
Q12) The central park is 40 meters long and 30 meters wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small rectangle formed at the intersection of the two roads. Further the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?
(A) 10 meters (B) 12.5 meters (C) 14 meters (D) 15 meters (E) 16 meters
Consider a function f(x) = x^4+x^3+x^2+x+1, where x is a positive integer greater than 1. What will be the remainder if f(x^5) is divided by f(x)?
(A)1 (B) 4 (C) 5 (D) a monomial in x (E) a polynomial in x
€‹In a plane thr r two families of lines, y=x+r and y= -x+r where r£ {1,2,3,4,5}
1)find the no. Of quadrilaterals formed by the lines
2) find the no. Of squares formed by the lines?
No of positive integral solutions of
1/a + 1/b =1/6 ????
A = set of all divisors of 8100 and B = set of all divisors of 21600. What is the product of the elements of AUB?