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1 Maths 2013 March(or)
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U N I T I I
S o l v e : (x2
y 2 ) d x + 2 JU dy = 0
(x2
y 2 ) d x + 2 Jqy o fy = o ; b i o @o h m
So l v e : (1 + y 2 ) d x - (t a n
'y X ) d y
(l + y 2 ) d x = (t a n
'y X ) d y ; b i n e o b M
S o l v ed x
2+ y - c o s e c x b y t h e m e t h o d o f v a r i a t i o n o f p a r a m e t e r s
+ y - c o s e C X : in b c p m m o 8 j & 5 ge CP SCP i n e o - f t ) m
So l v e (x2 D Z
x D + 2 ) y - x l o g x
(x2 D 2
x D + 2 ) y - x l o g x i3 o @o h M
F i n d t h e e q u a t i o n o f t h e p l a n e t h r o u g h t h e p o i n t s (2,
2,
1) , (9,
3,
6 ) a n d
p e r p e n cl i c u l a r t o t h e p l a n e 2 x + 6 y + 6 z = 9
(2,
2,
1) , (9,
3,
6 ) B o m b o {0 0 G ° g s m 2 x + 6 y + 6 z - 9 6 u ° n g o o e) o r r ° b o & 6 u m
c m s b b h 6 ¬ a m ; in n ; Su m
F i n d t h e l e n g t h a n d e q u a t i o n t o t h e l i n e o f S D Be t w e e n t h e l i n e s
X 3= =
)=
X 3=
3 1
y 8.
Z 3=
)=
x + 3 y + 7.
Z 6
3 2 43 o (S D ) h q s egeb h ¢f J ° el : D c mb
F i n d t h e l i m i t i n g p o i n t s o f t h e c o a x i a l s y s t e m o f s p h e r e s
x2
+ y 2
+ z2 Bx + 2 y 2 z + 3 2 = 0 ×
2 + y
2 + z
2 7x + z + 5 3 - 0
: 5 h 6 ¬ a" en h l y ° a o 3 bbn RS h (5e3 m q egb @eDo ei »b o ; in h r ; in m
T u r n O v e r
1
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Fi ncl t h e v e r t e x o f t h e c o n e xz 2 y
: + : 3z
2 { x y + 5 y z 6 z x + Bx 19 y 2 z 2 0 - 0
Tz 2 v
2 + 3 z
z, l × y + 5 y z 6 z x + Bx 19 7 2 z 2 0 = 0 b h 6 ¬ a m ; M a o s o b h : i : L)
gh p ; h b n
U N I T I V
S h o w t h a t t h e s e m i v e r t i c a l a n g l e o f a r i g h t c i r c u l a r c o n e h a v i n g t h r e e m i r t u a l ly
p e r p e n d i c u l a r g e n e r a t o r s i 8 T a n1
5 6 -b t io 0 0 8 ) o n ° b o & m eb a : S aeJu ge f lb o a o o u 2 5 » ei o w b % 6 t a h :
iu
2 : 3
S h o w t h a t t h e e q u a t i o n o f t h e r i g h t c i r c u l a r c y l i n d e r w h o s e a x i s i s t h e l i n e
X a=
V P.
z z a n d w h o s e r a d i u s i s r i s
m n
X a ) 2 + j P) 2
+ (z r ) 2 r2 (1 2
+ l n 2
+ n 2 ) = U(x a ) + m (7 P) + n (z r ) ] 2
e9 $ -y P
_
Z m Hm$i gm , c: t ut ? He ) oou5i j ch : g 5 b h 6 e a mm n
X a ) 2 + (J P ) 2
+ (z r ) 2 r2
e9:
2 5 I f f i , 72 a r e t h e r a d i i o f t w o o r t h o g o n a l s p h e r e s t h e n s h o w t h a t t h e r a d i u s o f t he
c i r c l e o f t h e i r i n t e r s e c t i o n i 8
o d f b F 6q?e o u sia 0 g en 5 6 ) m f i ,
72 ¬ \ ) EPD o o eoaDe5 ; SM 3 ; b g ) o i s 5%a J$i 0 gm
2 6 JPi n d t h e e q u a t i o n o f t h e c o n e w h o s e v e r t e x i s (1,
1,
O) a n d w h o s e g u i d i n g c u r v e i s
b h 6 e a " - -5 ) f i ° ; b m
13 104