Upload
safsdf
View
216
Download
0
Embed Size (px)
Citation preview
7/25/2019 Questions for Practice
1/13
Questions for Practice
1. A four digit number is such
that it has the following
properties(i) It is a perfect square(ii) The rst two digits are
equal(iii) The last two digits are
equal
Find all such numbers.
7/25/2019 Questions for Practice
2/13
2.There are n! nec"laces such that rst nec"lace
contains # beads$ second contains % beads
and so on&&& the ith nec"lace contains I beadsmore than the number of beads in (i&1)th
nec"lace . Find total no. of beads in all n
nec"laces.
7/25/2019 Questions for Practice
3/13
'. alculate)41(mod52039
7/25/2019 Questions for Practice
4/13
7/25/2019 Questions for Practice
5/13
. To pro*e Fermat +o. F# is a
composite no. i.e to pro*e
,1-F#
7/25/2019 Questions for Practice
6/13
#. Find the no. of was /0,
can be resol*ed as the
product of two factors.
7/25/2019 Questions for Practice
7/13
,. Find +o. of was in which
''12 can be resol*ed into
two factors which are prime to
each other.
%. Find the sum of di*isors of
1#/
7/25/2019 Questions for Practice
8/13
/. Find the remainder when
1(2)is di*ided b 2.
7/25/2019 Questions for Practice
9/13
7/25/2019 Questions for Practice
10/13
. how that there is a natural
no. n such that n3 when
written in decimal
representation ends e4actl in1' 5eros.
7/25/2019 Questions for Practice
11/13
10. A67 is a cclic
quadrilateral $ 4$$5 are
distances from A to lines
67$6 and 7 resp.pro*e that
7/25/2019 Questions for Practice
12/13
z
Cd
y
BC
x
BD+=
11. If A67 is a cclic
quadrilateral then$A.8A6.697.7A:;67.
87A.A696.7:12. Two sides of a triangle are
,3cmand cm2 The medians
to these sides are
perpendicular to each other.
Find the third side.1'. A7$6$+ are coolinear.and the
7/25/2019 Questions for Practice
13/13
line through them is
perpendicular to the line
?oining the orthocenter @ and
circumcenter of triangle
A6 .