Question

(5.346)³+(3.654)³/[(5.346)²+(3.654)²-5.346×3.654]​

Answer 1

Step-by-step explanation:

2sin2θ−1

,14,3

4−2sin2θ

form the first three terms of an A.P. Its fifth term is equal to-

Hard

Solution

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Correct option is D)

Since the numbers are in A.P.

∴28=3

2sin2θ−1 +3

4−2sin2θ

⇒28= 39

sin2θ +9

sin2θ81

Let x=9

sin2θ

Hence, x

2−84x+243=0

⇒(x−81)(x−3)=0∴x=81 or 3

∴x=9

sin2θ

=81,3 or 9

2,91/2

∴sin2θ=2 or 1/2

Since sin2θ cannot be greater than 1 so we choose sin2θ=

21

Hence the terms in A.P. are

30

,14,27 i.e. 1, 14, 27.

∴T5=a+4d=1+4×13=53

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Answer 2

Step-by-step explanation:

2sin2θ−1

,14,3

4−2sin2θ

form the first three terms of an A.P. Its fifth term is equal to-

28=3

2sin2θ−1 +3

4−2sin2θ

⇒28= 39

sin2θ +9

sin2θ81

Let x=9

sin2θ

Hence, x

2−84x+243=0

(x−81)(x−3)=0∴x=81 or 3

∴x=9

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