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Recent questions tagged rmo
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Show that 3^2008+4^2009 can be written as product of two positive integers each of which is larger than
asked
Apr 5, 2019
in
Mathematics
by
kratos
rmo
+1
vote
1
answer
Suppose in the plane 10 pairwise non-parallel lines intersect one another. What is the maximum possible number of polygons
asked
Apr 3, 2019
in
Mathematics
by
kratos
rmo
+3
votes
1
answer
If a, b, c are three real numbers such that | a – b | ≥ | c |, | b – c | ≥ | a |, |c-a|≥|b|,
asked
Apr 3, 2019
in
Mathematics
by
kratos
rmo
+2
votes
1
answer
In a quadrilateral ABCD, it is given that AB = AD = 13, BC = CD = 20, BD = 24. If r is the radius of the circle inscribable in the quadrilatera
asked
Apr 2, 2019
in
Mathematics
by
kratos
rmo
nsea
+3
votes
1
answer
Let f(x) = cos^2x + cos^22x + cos^23x. Number of values of x ∈[0,p] for which f(x) equals the smallest positive integer is
asked
Mar 30, 2019
in
Mathematics
by
kratos
isc
class-11
kvpy
icse
mathematical induction
rmo
class-12
basic algebra
+3
votes
1
answer
In a triangle ▲ ABC, ∠C = 3 ∠B = 2 ( ∠ A + ∠ B). Find the three angles.
asked
Mar 28, 2019
in
Mathematics
by
kratos
pythagoras theorem
cbse
ncert class 10 maths
class-10
triangles
rmo
+3
votes
1
answer
Find all fractions which can be written simultaneously in the forms (7k - 5)/(5k - 3) and (6I - 1)/(4I - 3), for some integers k,l.
asked
Mar 28, 2019
in
JEE
by
kratos
rmo
jee
jee mains
vector algebra
+1
vote
1
answer
Prove that there does not exist any positive integer n < 2310 such that n (2310 - n) is a multiple for 2310.
asked
Mar 28, 2019
in
Mathematics
by
kratos
rmo
+3
votes
1
answer
Let P(x) = x^2 + ax + b be a quadratic polynomial where a and b are real numbers.
asked
Mar 26, 2019
in
Mathematics
by
kratos
rmo
+2
votes
1
answer
Points D, E are taken on the side BC of a triangle ABC such that BD = DE = EC. If ∠BAD = x, ∠DAE = y, ∠EAC = z,
asked
Mar 24, 2019
in
JEE
by
kratos
properties of triangles
jee
class-9
triangles
jee mains
rmo
congruence and inequalities of triangles
+2
votes
1
answer
The wavelength of red colour is 7 x 10^-7 m and that of blue colour is 4 x 10^-7 m. Will the speed of both the colours be the same in
asked
Mar 23, 2019
in
Class 12
by
kratos
neet
spectrum
spectrum of light
class-10
icse
rmo
special senses
+3
votes
1
answer
Find all real numbers a such that 3 < a < 4 and a(a - 3{a}) is an integer.
asked
Mar 22, 2019
in
Mathematics
by
kratos
rmo
+3
votes
1
answer
Let T be the smallest positive integer which, when divided by 11, 13, 15 leaves remainders in the sets {7, 8, 9}, {1, 2, 3}, {4, 5, 6} respectively.
asked
Mar 20, 2019
in
Mathematics
by
kratos
rmo
+2
votes
1
answer
The length of each side of a convex quadrilateral ABCD is a positive integer. If the sum of the lengths of any three sides is divisible
asked
Mar 15, 2019
in
Mathematics
by
kratos
rmo
+1
vote
1
answer
Find the sum of the following series up to n terms: .6 +.66 +. 666 +…
asked
Mar 13, 2019
in
JEE
by
kratos
class-11
jee
jee mains
rmo
binomial theorem
sequences and series
+1
vote
1
answer
A positive integer k is said to be good if there exists a partition of {1, 2, 3, ..., 20} into disjoint proper subsets such that
asked
Mar 12, 2019
in
Mathematics
by
kratos
rmo
+1
vote
1
answer
Let AB be a chord of a circle with centre O. Let C be a point on the circle such that ∠ABC = 30° and O **** inside the triangle ABC.
asked
Mar 10, 2019
in
Mathematics
by
kratos
rmo
+1
vote
1
answer
Let f(x) = sin x/3 + cos 3x/10 for all real x. Find the least natural number n such that f(nπ + x) = f(x) for all real x.
asked
Mar 10, 2019
in
Mathematics
by
kratos
rmo
+3
votes
1
answer
Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively.
asked
Mar 7, 2019
in
Class 10
by
kratos
tangents
circles
intersecting chord
class-9
class-10
icse
rmo
+3
votes
1
answer
Integers a, b, c satisfy a + b – c = 1 and a^2 + b^2– c^2 = –1. What is the sum of all possible values of a^2 + b^2 + c^2?
asked
Mar 7, 2019
in
Mathematics
by
kratos
rmo
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