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Old Exam Papers June 2012 (Set 2)

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(b) Find the point of inflexion of the following curve :<br />

2 2 3<br />

yca x h<br />

x<br />

fuEu oØ ds ufr&ifjorZu fcUnq Kkr dhft;s %<br />

5. (a) Show that :<br />

2 2 3<br />

yca x h<br />

x<br />

m n<br />

Bbm , ng<br />

m n<br />

bgbg <br />

<br />

iznf'kZr dhft;s %<br />

(b) Evaluate :<br />

b g<br />

m n<br />

Bbm , ng<br />

m n<br />

bgbg <br />

<br />

b g<br />

z 3 2<br />

b g<br />

0 1<br />

eku Kkr dhft;s %<br />

xy 1<br />

x y dxdy<br />

z 3 2<br />

b g<br />

0 1<br />

xy 1<br />

x y dxdy<br />

600 4 MT-02<br />

3. (a) Find the envelope of the circles drawn upon the<br />

central radii of the ellipse x<br />

a<br />

2<br />

2<br />

2<br />

y<br />

1 2 as diameters.<br />

b<br />

mu o`Ùkksa dk vUokyksi Kkr dhft;s tks nh?kZo`Ùk<br />

2 2<br />

x y<br />

1<br />

2 2 dh /kqzokUrj&js[kkvksa dks O;kl ekudj [khpsa<br />

a b<br />

x;s gSaA<br />

(b) Show that sin xb1 cos xg<br />

is a maximum at<br />

x <br />

3 .<br />

iznf'kZr dhft;s fd sin xb1 cos xg,<br />

x <br />

3 ij<br />

mfPp"B gSA<br />

4. (a) Find the asymptotes of the following curve :<br />

3 2 2 3 2 2<br />

y xy x y x x y 1 0<br />

fuEu oØ dh vuUrLif'kZ;k¡ Kkr dhft;s %<br />

3 2 2 3 2 2<br />

y xy x y x x y 1 0<br />

MT-02 3 PTO

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