Vijayarekha October 2017

1 st October 2017
TALENT
ACADEMY VIJAYAREKHA Volume V Issue No. 10 PSC a’-c-]-co£m amknI
ASn-ÿm\ KWnXw
{XntImWw
Ü
Ü
Ü
A
B
C
aq∂p-h-i-ßfpw aq∂p-tIm-Wp-Ifpw
D≈ G‰hpw sNdnb kwhrX
cq]w
hnI¿Ww hc-bv°m≥ Ign-bmØ
GI _lp-`pPw
Hcp {XntIm-W-Ønse aq∂p-tIm-
Wp-I-fpsS Af-hp-I-fpsS XpI
F√m-bnt∏mgpw 180 0 Bbn-cn-°pw.
1. Hcp {XntIm-W-Øns‚ tImWp-Iƒ
4 : 5: 3 F∂ Awi-_-‘-Øn-emWv
Fn¬ sNdnb tIm¨ F{X?
(a) 75 0 (b) 60 0
(c) 45 0 (d) 90 0
Ans: (c) 45 0
sNdnb tImWns‚ Afhv
Ü
3
= 180 0 × 4 + 5 + 3
= 180 0 × 12
3
= 45 0
Hcp {XntIm-W-Ønse sNdnb hiß-fpsS
Af-hp-I-fpsS XpI aq∂masØ
hi-tØ-°mƒ IqSp-X-em-bncn-°pw.
2. Xmsg ]d-bp-∂-h-bn¬ GXmWv
Hcp {XntIm-W-Øns‚ hi-ß-fm-
Ip∂ Af-hp-Iƒ
(a) 3, 6, 3 (b) 5, 12, 8
(c) 2, 1, 4 (d) 7, 6, 15
Ans: (b) 5, 12, 8
5 + 8 = 13
13 > 12
Ü
Ü
Ü
k a - ` p P { X n t I m W w
(Equilateral Triangle)
aq∂ph-i-ßfpw aq∂p tImWp-
Ifpw Xpeyamb {XntIm-Ww.
Hmtcm tImWp-I-fp-tSbpw Af-hp-
Iƒ 60 0 Bbn-cn°pw
A
B
a
h
a
a
Hcp hiw a Bbm¬,
Np‰-fhv
hnkvXo¿Æw =
Db-cw, h =
= 3a
C
3a
2
4
3a
2
3. Hcp ka-`pP {XntIm-W-Øns‚
Hcp hi-Øns‚ \ofw 6 sk.ao
Bbm¬ hnkvXo¿Æw F{X?
Ü
Ü
(a) 9 3 cm 2 (b) 6 3 cm 2
(c) 3 3 cm 2 (d) 12 3 cm 2
Ans: (a) 9 3 cm 2
hnkvXo¿Æw =
Xpey-h-i-߃ a bpw ]mZw b bpw
Bbm¬ A
B
a =
h
b
=
=
= a
3a
2
4
3 × 6
4
C
2
3 ×36
4
= 9 3 cm 2
ka-]m¿iz
{XntImWw
(Isosceles Triangle)
c≠v hi-ßfpw ]mZ-tIm-Wp-
IfpsS Af-hp-Ifpw Xpeyamb
{XntImWw
ka-]m¿iz-{Xn-tIm-W-Øns‚ hi߃
1 : 1 : 2 F∂ A\p-]m-X-
Øn-em-bn-cn-°pw.
Np‰-fhv
= 2a + b
b
hnkvXo¿Æw =
2 2
4 4a −b
1
Db-cw, h =
2 2
2 4a −b
4. Hcp ka-]m¿iz a´{XntIm-W-
Øns‚ Xpey-amb hi-ß-fn¬
H∂v 12cm Bbm¬ Xpey-a-√mØ
hi-Øns‚ \of-sa{X?
(a) 10 2 cm (b) 6 2 cm
(c) 12 2 cm (d) 5 2 cm
Ans: (c) 12 2 cm
Xpey-h-i-w = 12
Xpeya√mØ -h-i-w = 12 2
-(h-i߃ XΩn-ep≈ Awi-
_‘w = 1 : 1 : 2 )
= 12 : 12 : 12 2
5. Hcp ka-]m¿iz {XntIm-W-Øns‚
Np‰-fhv 20cm Dw Xpey-a-√mØ
hi-Øns‚ \ofw 6cm Dw
Bbm¬ Xpey-amb hi-ß-fpsS
\of-sa{X?
Ü
B
(a) 5cm (b) 7cm
(c) 6cm (d) 10cm
Ans:(b) 7cm
Np‰-fhv = 2a + b = 20
2a + 6 = 20
2a = 14
14
a = 2
= 7cm
OR
Np‰-fhv = 20cm
Xpeyamb c≠v h-i-ßfpsS XpI
= 20 - 6 = 14cm
Xpeyamb h-i-ßfpsS \ofw
14
= 2
= 7cm
h n j - a - ` p P { X n t I m W w
(Scalene Triangle)
aq∂p hi-ßfpw aq∂p tImWp-IfpsS
Af-hp-Ifpw hyXy-kvXamb
{XntIm-Ww.
hnj-a-`p-P-{Xn-tIm-W-Ønse hi߃
a, b, c F∂n-h Bbm¬
Np‰-fhv
= a + b + c
hnkvXo¿Æw = s(s− a)(s−b)(s−c)
;
A
a c a + b+
c
s =
2
C
b
6. Hcp hnj-a-`pP {XntIm-W-Øns‚
hi-ß-fpsS Af-hp-Iƒ 3cm,
4cm, 5cm F∂nh Bbm¬
hnkvXo¿Æw F{X?
(a) 4 cm 2 (b) 8 cm 2
Ü
Ü
(c) 12 cm 2 (d) 6 cm 2
Ans : (d) 6 cm 2
hnkvXo¿Æw =
=
=
s (s − a)(s −b)(s
− c)
6(6-3) (6-4) (6-5)
6 × 3×
2×
1
a = 3
b = 4
c = 5
a + b+
c
s =
2
= 3 + 4+
5
36
=
2
= 6 cm 2
=6
a ´ { X n t I m W w
(Right angled Triangle)
Hcp tImWns‚ Afhv 90 0 Bb
{XntImWw
a´-{Xn-tIm-W-Øns‚ henb hi-
Øns‚ (I¿Æw) h¿Kw sNdnb
c≠v hi-ß-fpsS (]m-Zw, ew_w)
h¿§-ß-fpsS XpIbv°v Xpey-am-bncn-°pw
(ss]-X-tKm-dkv kn≤m-¥w).
(]m-Zw) 2 + (ew-_w) 2 = (I¿Æw) 2
Ü
ew_w
A
B
]mZw
C
Hcp a´-{Xn-tIm-W-Øns‚
]mZw = b
ew_w = h
I¿Æw = k Bbm¬
Np‰-fhv = b + h + k
hnkvXo¿Æw = 2
1 bh
7. Hcp a´{XntIm-W-Øns‚ Hcp
tIm¨ 35 0 Bbm¬ a‰v tImWp-
Iƒ GsX√mw?
(a) 45 0 , 90 0 (b) 55 0 , 90 0
(c) 60 0 , 90 0 (d) 40 0 , 90 0
Ans: (b) 55 0 , 90 0
{XntIm-W-Ønse tImWp-I-fpsS
Af-hp-I-fpsS XpI = 180 0
a´{XntIm-W-w Bb-Xn-\m¬
Hcp tIm¨ = 90 0
3 -masØ tIm¨ = 180 - (90 + 35)
= 180 - 125 = 55 0
8. Hcp a´{XntIm-W-Øns‚ ]mZw
8cm Dw Dbcw 10cm Dw Bbm¬
hnkvXo¿Æw ImWpI
(a) 32 cm 2 (b) 80 cm 2
(c) 20 cm 2 (d) 40 cm 2
Ans : (d) 40 cm 2
hnkvXo¿Æw
I¿Æw
= 2
1 bh
= 2
1 × 8 × 10
= 40 cm 2
9. 12 ao‰-¿ \of-ap≈ Hcp kvXw`-
Øns‚ ASn-bn¬ \n∂v 5 ao‰¿
AI-se-bmbn \neØv Hcp Ip‰n
ASn-®n-cn-°p-∂p. kvXw`-Øns‚
apI-fn¬ \n∂v Ip‰n-bpsS apI-fntebv°v
Hcp Iºn -sI-´-W-sa-n¬
Iºn°v F{X ao‰¿ \ofw thWw?
(a) 17cm (b) 11cm
(c) 12cm (d) 13cm
Ans:(d) 13cm
Nn{XØn¬ AB kvXw`hpw BC
kvXw`-Øn¬ \n∂v Ip‰n-bn-tebv°p≈
AI-ehp-am-bm¬
AB 2 + BC 2 = AC 2 ,
AC= I¿Æw
AC 2 = (12) 2 + (5) 2
= 144 + 25 = 169
12 ao‰¿
A
AC = 169
B 5 ao‰¿ C
= 13cm
Hcp {Xn-tIm-W-Ønse aq∂p tImWp-
Ifpw 90 0 bn¬ Ipd-hm-bm¬ \yq\-{XntImWw
F∂pw 90 0 bn¬ IqSp-X-embm¬
_rlXv {XntImWw F∂pw
]dbp∂p.
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