IIT JEE maths solutions

7/30/2019 IIT JEE maths solutions

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5. (2)

Now,2 2x y

116 9

A = 4, b = 3

23 7C 1

44

So, foci = ae,0 7,0

Radius of new wide = 2 2

0 7 3 0

= 4.Centre = (0, 3)

Equation of wide = 2 2 2x 0 y 3 4

= 2 2x y 6y 9 16

=2 2

x y 6y 7 0

6. (3)2

Adj A A

2

1 3

1 3 3 4 1

2 4 4

7. (3)

p q ~ p ~ q p q ~ q ~ p p^ ~ q ^ ~ p ^ q p q ~ q ~ p

T T F F T T F T

T F F T F F F T

F T T F T T F T

F F T T T T F T

8. (3)

Mid-points are 0,1 , 1,1 and 1,0

Vertices are 0,0 , 2,0 , 0,2

radius of incentre : 2 2 x co-ordinate 2 2

9. (1)

3f x 2x 3x K

2f x 6x 3 0 for all x Hence, only one root is positive at max

10. (4) f x dx x

5 3 3x x dx Let t x

1

2

3

-1

-2

-3

1 2 3-4 -1-2-3 4

(0, 0)

(0, 2)

(2, 0)


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2dt 3x dx

So,

3 3

5 3 2x f x

x x dx 3x dx3

1

t f t dt3

After Inequation by parts,

1 t t dt ft t dt dt3

1

t t dt as f x dx a3

Putting t as 3x

3 3 3 21 x x x 3x dx3

3 3 2 31 x a x x dx c3

11. (3)

k 1 x 8y 4k

kx k 3 y 3k 1

For no solutionk 1 8

0k k 3

And atleast one of4k 8 k 1 4k

and 03k 1 k 3 k k 3

The only value of k which satisfies is k = 3.

No. of values = 1.

12. (3)

Tn is the number of triangle formed by joinly vertices of n sided polygon

So, nn 3T C n 1

n 1 3T C

n 1 n n

n 1 n 3 3 2T T C C C 10

x 5

13. (3)

Circle 2 21S x y 5 2

Equation of tangent 25

y mx tan2

.(1)

Parabola 22S y 4 5x

5y mx

m .(2)

(1)&(2) one some equation

25 5

1 m2 m

4 2m m 2

2 2m 1 m 2 0


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So, m 1 So, y x 5 y is a tangent

M 1 , satisfies the equation 4 2m 3m 2 0 Hence, S-I is True

S-II is True

14. (2)

Point of intersection (9, 3)

Area =3

Right left

0

X X .dy

3

2

0

2y 3 y .dy

= 9

15. (3)tan A cot A

1 cot A 1 tan A

2 2sin A cos A

cosA sin A cos A sin A cos A sin A

3 3sin A cos A

sin A cos A sin A cos A

2 2sin A cos A sin A cos A

sinAcosA

secA.cosecA 1

16. (1)3

6

cosxI dx

cos x sin x

3

6

2I dx3 6 6

I12

17. (2)

1 1 2x 1

1sec tan x tan tan x

1 x

1 12

1 1 2

x

2y x 3 0


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18. (4)

z

z

otg 2

19. (1)Self Explanatory

20. (3)

o30

x 3y 3

3, 0

1

y 0 x 33

x-axis

Hence, option (3) is correct

21. (4)S 0.7 0.77 0.777 ........(20terms)

7S 0.9 0.99 0.999 ....(20terms)9

7 2 37S 20 10 10 10 ... 20 terms9

20

1 1

1

10 1 107

S 209 1 10

20

7 1 1S 20 1

9 9 10

207 179 1081

Hence option (a) is correct

22. (4)4 5

5 54 5

1 2 1C C

3 3 3

5 5

10 1 11

3 3


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23. (4)

1 10

3 x 1x 1x

101 1

3 2x x

10 r r 1 1

10 3 2rC x x

10 r r 10 3 2

rC x

r 4 10

410.9.8.7

C 2104!

24. (4)

n A 2 n B 4

n A B 8 8 8 8 8

3 4 5 8C C C ..... C 219

25. (4)

AB BC CA 0

BC AB CA

AB CABM

2

Now, AM BM AB

AB CAAM 33

2

26. (2)

dyx

dx

2

2

xx 0

xy

xx 0

2

Slope

x x 0

x x 0

x 0 x 0 x 2 x 2 y 2 y 2

1P 2, 2 2P 2, 2

T : y 2 2 x 2 T : y 2 2 x 2 x intercept 1 x intercept 1

C

M

BA

5i 2 j 4k

3i 4k


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30. (2)

A B

CD

p

2 2p q

N

p

q

p

tanq

p

tanAn

p

tanAN

tan tan R

1 tan tan AN

ptan

q tan p pq

p q p tan AN1 tanq

p p tan qq AN q

q tan p

2 2p tan pq q tan pq

q tan p

2 2p q sinp sin qsin

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IIT JEE maths solutions