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MATRIX MATCH TYPE
10. Match the statements/expressions in Column I with the values given in Column II.
Column I
Column II
(A)
The number of solutions of the equation xesinx - cosx = 0 in the interval (0, Π)
(p)
1
(B)
Value(s) of k for which the planes kx + 4y + z = 0, 4x + 5y + 2z = 0 and 2x + 2y + z = 0 intersect in a straight line
(q)
2
(C)
Value(s) of k for which |x-1| + |x-2| + |x+1| + |x+ 2| = 4k has integer solution(s)
(r)
3
(D)
If y' = y + 1 and y(0) = 1 then value (s) of y(ln2)
(s)
4
(t)
5
Sol. (A --> p); (B --> q, s); (C --> q, r, s, t); (D --> r)
(A) f'(x) > 0, for all x belongs to (0, p/2)
F(0) < 0 and f(p/2) > 0
So one solution
(B) Let (a, b, c) is direction ratio of the intersected line, then
ak + 4b + c = 0
4a + kb + 2c = 0
a/(8-k) = b/(4-2k) = c/(k2-16)
We must have 2 (8 - k) + 2 (4 - 2k) + (k2 - 16) = 0
=> k = 2, 4.
(C) Let f(x) = |x+2| + |x+1| + |x-1| + |x-2|
=> k can take value 2, 3, 4, 5.
(D) ∫ dy/(y+1) = ∫ dx
=> f(x) = 2ex - 1
=> f(ln2) = 3
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IIT JEE 2009 Mathematics Paper2 Code 1 Solutions...