How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000 ?

An alloy P has copper and zinc in the proportion of 5: 2 (by weight), while another alloy Q has the same metals in the proportion of 3: 4 (by weight). If these two alloys are mixed in the proportion of a : b (by weight), a new alloy R is formed, which has equal contents of copper…

There are numbers \(a_1,a_2,a_3,\ldots,a_n\) each of them being +1 or -1. If it is known that \(a_1a_2+a_2a_3+a_3a_4+\cdots+a_{n-1}a_n+a_na_1=0\) then

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

From the passage: Analyze the given data for exports and imports of rubber in Rs. crores...

Average annual exports for the given period 2006-2017 was approximately

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 31), and (31, 0) is

Determine the greatest number among the following four numbers

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 \(cm^2\). Then the possible values of the sum of their volumes are________

The inequality…