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January 23rd, 2013, 02:06 PM
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Join Date: Mar 2012

I want to appear for Indian institute of technology JEE so can you provide me question paper with solution in PDF format.

Here I am providing the solved question paper for IIT JEE.

Q.Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p (0) is
Ans:- [9]
Since least degree hence p(x) is cubic.
Let p (x) = ax3+ bx2+ cx + d
p (1) = 6 = a + b + c + d …… (1)
p (3) = 2 = 27a + 9b + 3c + d …… (2)
p'(x) = 3ax2+ 2bx + cp'(1) = 0 = 3a + 2b + c …… (3)
p’(3) = 0 = 27a + 6b + c …… (4)
(4) (3) 24a + 4b = 0 b = 6a …… (5)
(2) (1) 4 = 26a + 8b + 2c
From (5)
-4 = 26a 48a + 2c
4 22a
c 11a 2
2
…… (6)
From (3)
3a + 2b + c = 0
3 (a) + 2 ( 6a) + (11a 2) = 0
3a - 12a + 11a 2 = 0
2a = 2 a = 1
c = f (0) = 11a 2 = 11 - 2 = 9

For the complete solved question paper click on the attachment.
Attached Files
File Type: pdf IIT JEE Solved question paper.pdf (1.89 MB, 128 views)

Last edited by Anuj Bhola; October 17th, 2019 at 12:25 PM.
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