A rectangular sheet can be divided into two parts by breaking it along its length or its width. What is the least number of steps required to divide a rectangular sheet of size m × n into equal sheets of size 1 × 1?
a' and 'b' are the roots of the equation 2x2 – 7x – 10 = 0, where a > b. If Zn = a^n– b^n for n >0, then find the value of (2Z6 - 10Z4)/Z5
In ΔABC, D, E, F and G are the midpoints of the sides BC, AD, BE and FD respectively. What is the ratio of the area of ΔEGD to that of ΔAEC?
A natural number consists of only 0's and 1's. If the number is divisible by 375, then what is the least possible number of 0's and 1's in the number respectively?
A man is running in a railway tunnel. When he has covered exactly two-fifth of the length of the tunnel he sees a train approaching the tunnel from behind. He realises that irrespective of the direction in which he runs he will be hit by the train at one of the ends of the tunnel. If the speed of the man is 10 km/hr, find the speed of the train.
a) 60 km/hr
b) 50 km/hr
c) 40 km/hr
d) 30 km/hr
If a, b and c are the sides of a triangle, and a^2 + b^2 + c^2 = bc + ca + ab, then the triangle is
a. equilateral
b. isosceles
c. right-angled
d. obtuse-angled
How many arrangements of the seven digits 0, 2, 3, 3, 4, 4 and 5 will result in an even number greater than 40,00,000?
In how many ways can 73 identical chocolates be stuffed into three boxes – B1, B2 and B3 – such
that B1 contains more chocolates that B2 and B2 contains more chocolates than B3?
(a) 888 (b) 444 (c) 222 (d) 666
Rohan and five of his friends contributed equal money and hired a car to Goa. At least one of his friends pulled out of the trip at the last moment and so they decided to divide the expenses between the rest of the people. During the journey the car required some minor repair for which they paid 250 extra. The total travelling expenses, including the repair charges, amounted to 410 per person. If each of the six friends had contributed an integral amount more than 100 initially, then what was their total initial contribution?
a) 1800
b) 570
c) 2460
d) Cannot be determined
If a, b, c and d are integers and n is a prime number, then which of the following is always a factor of (a + b – c – d)^n – (a^n + b^n – c^n – d^n)?
a) n
b) a + b – c – d
c) n – 2
d) n + 2
A society of 380 people organized a tournament comprising three different games. The number of people who participated in at least two games was 42% more than those who participated in exactly one game. At least one person participated in exactly n games, where n = 1, 2, 3. If the number of people who did not participate in any of the three games was minimum possible, then what was the maximum possible number of people who participated in exactly two games?
a) 149
b) 150
c) 212
d) 213
In triangle ABC, D is the midpoint of BC. E is a point on AC such that AE : EC = 2 : 1 and F is a point on AB such that AF : FB = 3 : 1. Line segments AD and FE intersect at point O. What is the ratio of the area of triangle DOF to the area of triangle DOE?
If 13x + 17y = 555, where x and y are natural numbers, what is the maximum possible value of the product of x and y?
a) 657
b) 250
c) 324
d) None of these
Please share your solution with the answer.
There are two points A (0,2) & B (6,0) and the origin be denoted as O, find the locus of a point P such that Area of Triangle APO = 2*(area of tr BPO)
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A square floor area of 27x27 cm is to be covered with tiles of 1x1cm , 2x2cm, and 3x3cm. Find the minimum no of 1x1cm tiles used
. A) 0 B ) 1 C) 4 D) 27
Important Pythagoras triplets (integers) to remember.
(3,4,5)
(5,12,13)
(7,24,25)
(8,15,17)
(9,40,41)
(11,60,61)
(12,35,37)
(13,84,85)
(15,112,113)
(16,63,65)
(17,144,145)
(19,180,181)
(20,21,29)
(20,99,101)
500! + 505! + 510! + 515! is completely divisible by 5n, where n is a natural number. How many
distinct values of n are possible?
I am stuck with this ques.Can someone please explain the solution in detail?
Can someone give me a formula to find triplets
Hi,
I found this file and thought it might be useful to you all.