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Information Report

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ww
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5) and (2, –4) respectively.(
i
) Find the co-ordinates of the fourth vertex.(
ii
) Slope of line
AB
.(
iii
) Midpoint of
AB
.(
b
) he su! of t o nu!#ers is $ and the su! of their s%uares is 4&. a'in one nu!#er as
x
. fro! an e%uation in
x
and solve it to find the nu!#ers.
ACBE
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Saumen
du mukherjee /math /sample paper
SECTION — A
Note:
tte!pt all the %uestions fro! Section and any four %uestions fro! Section *.he intended !ar's for %uestions or parts of %uestions are iven in #rac'et + .
Attempt all Questions from this Section
[Marks 40]1.
(
a
) he difference #et een the co!pound interest paya#le half-yearly and si!ple intereston the sa!e su! of !oney lent out at & for a year is /s. &5. Find the su! of !oneylent out 0(
b
) Find the re!ainder hen 4
x
1 4
x
– 2
x
1 &3 is divided #y 2
x
– .
2
(
c
) ithout usin triono!etrically ta#le, 6valuate tan5cot 22cos 45cot tan 2
°°−− °°°
(
d
) he !id-point of the line se!ent 7oinin (2
x
, 4) and (–2,
y
) is (&, 2
x
1 &), Find thevalues of
x
and
y
+, , 2, 2
2.
(
a
) he !ean of &, , 5, , 4 and 4 is !. he nu!#ers , 2, 4, 2, , and
p
have !ean! – & and !edian
q
. Find
p
and
q
.(
b
) he area enclosed #y the circu!ferences of t o concentric circles is 43.5 c! . 8f the
2
circu!ference of the inner circle is 99 c!. :alculate the radius of the outer circle.(
c
) Mr. ;aul invests /s. &4, $5 in /s. & shares of a co!pany payin &4 dividend. 8f his annual inco!e fro! these shares is /s. &3&, find the !ar'et value of eachshare.+, 4,
3.
(
a
)
ABCD
is a parallelora! hose vertices
A
,
B
and
C
have the co-ordinates (–, 2), (&,
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12
8:S6 < – M=6M8:S
(
c
)hat should #e the !ini!u! !onthly deposit in a /.>. account for &2 years to et/s. 9, 39 on !aturity after &2 years at an interest rate of $.5 S.8. p.a. 0+, , 4
4.
(
a
) :onstruct a %uadrilateral
ABCD
such that
AB
? 9.2 c!,
BC
? 4 c!,
AD
? 2 c!,
BD
?9. c! and the point
C
is at e%uidistant fro!
B
and
D
.(
b
) 8n the iven fiure, chord
AE
and
BC
intersect each other at point
D
. 8f
CDE
∠
? $@,
AB
? 5 c!,
BD
? 4 c! and
CD
? $ c!, find
AE
.(
c
) 8n the iven fiure,
QPSRPT
∠ ∠
and.
PRQPTS
∠ ∠
(
i
) ;rove thatA.
PQRPST
∆∆
(
ii
) 8f
PT
B
ST
? B 4, Find
QR
B
PR
.+, 4,
QPSRT
SECTION-B
+
Anser any four questions from this section
.+4 Mar's
5.
(
a
) Solve the ine%uation B – 2&&2,
xxR
≤+_∑
(
b
) Fro! the piece of card#oard in the shape of rapeCiu! *:> and
ABDC
and
BCD
∠
? $@, a %uarter
B!EC
is re!oved. Diven
AB
?
BC
? .5 c! and
DE
? 2 c!.:alculate the area of the re!ainin piece ofthe card#oard.
ABCE!
(
c
) 8f

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