Mathematics Test 9

Result

Mathematics Test 9

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

If x = 2 + 2^1/3 + 2^2/3, then the values of x³ – 6x² + 6x is-

A
-2

B
3

C
4

D
2

Solution

x = 2 + 2^1/3 + 2^2/3

(x – 2) = 2^1/3 + 2^2/3 …(1)

(x – 2)³ = (2^1/3 + 2^2/3)³

⇒ x³ – 8 – 6x (x – 2) = 2 + 4 + 3.2 (x – 2) from (1)

⇒ x³ – 6x² + 12 x – 8 = 6 + 6x – 12

⇒ x³ – 6x² + 6x = 8 – 6 = 2 Ans
Question 2
4 / -1

If fourth term of an HP is 3/5 and its 8^th term is 1/3, then its first term is-

A
2/3

B
3/2

C
1/4

D
None of these

Solution

From A.P.

a + 3d = 5/3

and a + 7d = 3

Solving we get d = 1/3, a = 2/3

Then first term of H.P. = 3/2