Two different prime numbers between
4 and 18 are chosen. When their sum is
subtracted from their product then a
number x is obtained which is a
multiple of 17. Find the sum of digits of
number x.
Prove that the radius of a circle
passing through the midpoints
of the sides of a triangle ABC is
half the radius of a circle circum-
scribed about the triangle.
Let A and B is 3×3 matrix of equal number
where A=symmetric matrix
....B=skew symmetric matrix
and the relation... (A+B)(A−B)=(A−B)(A+B)
then..the value of.. ... k
(AB)^T =(−1)^k (AB)
(a) −1 (c) 2
(b) 1 (d) 3
Given in an isosceles triangle a
lateral side b and the base angle α.
Compute the distance from the
centre of the inscribed circle to the
centre of the circumscribed circle.
Carol was given three numbers and
was asked to add the largest of the
three to the product of the other two.
Instead, she multiplied the largest with
the sum of the other two, but still got
the right answer. What is the sum of
the three numbers?
A matrix has N rows and 2k−1
columns. Each column is filled with
M ones and N−M zeros.
A given row j is “cool” if and only if
Σ_(i=1) ^(2k−1) a_(ji) ≥ k. Find the minimum and
the maximum number of cool rows
for given N, k and M.
Let Akbar and Birbal together have n
marbles, where n > 0.
Akbar says to Birbal, “If I give you some
marbles then you will have twice as
many marbles as I will have.” Birbal
says to Akbar, “If I give you some
marbles then you will have thrice as
many marbles as I will have.”
What is the minimum possible value of
n for which the above statements are
true?
In the arrangement shown, the wedge
is smooth and has a mass M. The sphere
has a mass m. The system is released
from rest from the position shown.
There is no friction anywhere. Find the
contact force between the wall and the
sphere.
Blocks P and R starts from rest and
moves to the right with acceleration
a_P = 12t m/s^2 and a_R = 3 m/s^2 . Here t
is in seconds. The time when block Q
again comes to rest is
Prove that two straight lines with
complex slopes μ_1 and μ_2 are parallel
and perpendicular according as μ_1 = μ_2
and μ_1 + μ_2 = 0. Hence if the straight
lines α^ z + αz^ + c = 0 and β^ z + βz^ + k = 0
are parallel and perpendicular according
as α^ β − αβ^ = 0 and α^ β + αβ^ = 0.