Consider the three digit numbers 301, 431, 602, 715, 842,
856, 973, 986
They ALL satisfy the following properties:
1) All the digits are different
2) When the digits are
placed along a cirlce, each digit is three times the previous digit, or one
unit more, or two units more (while doing this, keep in mind that if this
number comes out to be more than 9, only the units digit is taken). Hence 7 is followed by 1, 2 or 3. 3 is followed by 9, 0 or 1. If the number ends with the digit 8, then the
first digit can be 4, 5 or 6.
Not only the above listed numbers, their cyclic permutations
also satisfy the above properties.
Hence the above list gives 22 three digit numbers. We know, no number starts with a zero.
Now, try for four digited numbers that satisfy the above
properties. How many such numbers are
there, if we consider their cyclic permutations also as different number?
with different radii are given in the plane touching each other externally at 
. Consider points 
on 
and 
on 
, such that 
subtends right angle at 
matrices such that 
and 
. Does the matrix 
have inverse? 
for which the point 
lies in the larger segment of the circle 
made by the chord whose equation is x + y – 2 = 0 
, find the maximum and minimum values of f(x) in the interval 
to the curve 
meet the x-axis and y-axis in T and G respectively, then find the angle at which the tangent at P to the curve is inclined to the tangent at P to the circle through the points T, P, G.
. Let a and b are two unequal real numbers. Let M is an n×n matrix with all a’s above the diagonal and b’s below the diagonal and 
along the diagonal.
as N1, and it should be divisible by 7. Continue this process till you form N6. Find N and N6. How long you can go like this?
with real coefficients has both roots greater than 1, then show that the equation 
has at least two real roots.
is a function such that 
. Find the value of f(0).
