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IIT JEE 2009 Mathematics Paper2 Code 1 Solutions

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.

              graph

        (D)    ∫ dy/(y+1) = ∫ dx

                => f(x) = 2ex - 1

                => f(ln2) = 3

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