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Algebra

Blazing goIITian

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10 Feb 2008 12:07:42 IST

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"TARGET IIT - JEE 2008 || CHALLENGING PROBLEMS FROM MATHS"

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HI FRIENDS,

I WOULD TRY MY BEST TO GET THE BEST MATHS QUESTIONS THAT ARE OF THE SAME STANDARD AS THAT OF THE PRESENT IIT-JEE LEVEL AND WE SHALL HAVE RELATED DISCUSSIONS ON THEM.

HEY FRIENDS,

PLEASE GIVE YOUR ANSWER WITH FULL SOLUTION SO THAT EVERY VIEWER UNDERSTANDS IT WELL........

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Comments (9)

Avinash Bhat

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10 Feb 2008 12:14:59 IST

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QN.1 Type : Only one of the options is correct.

A sequence A₁, A ₂, A₃ ............. , A_n of real numbers is such that :

A₁   = 0
| A₂ | = | A₁ + 1 |
| A₃ |   =   | A₂ + 1 |
.
.
.
| A_n |   = | A_n-1 + 1 |

Then the Arithmetic Mean of all these numbers cannot be less than:

(a) - 7 / 2
(b) - 5 / 2
(c) - 3 / 2
(d) - 1 / 2

Avinash Bhat

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10 Feb 2008 12:34:17 IST

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QN.2 Type : Match the following.

(A) I_n = ₀

^/4 tanⁿx dx (P) I₁ , I₂ , I₃ ........... are in A.P.

(B) I_n = ₀

^/2 cos (nx) cosⁿx dx (Q) I₁ , I₂ , I₃ ........... are in G.P.

(C) I_n = ₀

sin (2nx) / sin x dx (R) I₁ , I₂ , I₃ ........... are in H.P.

(D) I_n = ₀

( sin (nx) / sin x )² dx (S) I₁ + I₃ , I₂ + I₄ , I₃ + I₅ ........... are in H.P.

Avinash Bhat

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14 Feb 2008 18:16:21 IST

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No one ????

Hari Shankar

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14 Feb 2008 18:53:48 IST

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1st one's -1/2. i will give the soln only if no one gets it.

rockey

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15 Feb 2008 00:57:32 IST

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1. -1/2

Sonal

Cool goIITian

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15 Feb 2008 16:36:13 IST

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HEY CUMMON GIVE THE SOLUTIONS NOW....

Avinash Bhat

Blazing goIITian

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18 Feb 2008 19:54:05 IST

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The answer is correct for QN.1............

But, no one has got the full solution ???

What about question 2 ? Is it that difficult ?

Hari Shankar

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18 Feb 2008 20:02:36 IST

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Bhattre!

We have |a₂| = |a₁+1| => (a₂)² = (a₁)²+2a₁+1

|a₃| = |a₂+1| => (a₃)² = (a₂)²+2a₂+1

|a_n| = |a_n-1+1| => (a_n)² = (a_n-1)²+2a_n-1+1

|a_n+1| = |a_n+1| => (a_n+1)² = (a_n)²+2a_n+1

Adding up the equations and noticing that each (a_i)² gets subtracted in the subsequent equation, we get

(a_n+1)²= 2(a₁+a₂+...+a_n)+n>0

Hence (a₁+a₂+...+a_n)/n>-1/2

This means the AM of the terms from 1 to n is greater than -1/2.

abhishek sinha

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21 Jan 2012 23:18:38 IST

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2. (A)-(S)(B)-(Q)(C)-(P)(D)-(R)

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