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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.

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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.

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'. alculate)41(mod52039

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. To pro*e Fermat +o. F# is a

composite no. i.e to pro*e

,1-F#

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#. Find the no. of was /0,

can be resol*ed as the

product of two factors.

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,. 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#/

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/. Find the remainder when

1(2)is di*ided b 2.

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. how that there is a natural

no. n such that n3 when

written in decimal

representation ends e4actl in1' 5eros.

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10. A67 is a cclic

quadrilateral $ 4$$5 are

distances from A to lines

67$6 and 7 resp.pro*e that

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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

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line through them is

perpendicular to the line

?oining the orthocenter @ and

circumcenter of triangle

A6 .