Match the following
Column-I | Column-II |
(i) Let & If the point of intersection of the lines & is P. then λ2(OP) (where O is the origin) is | [A] 0 |
(ii) If and and is equal to, then x + y + z is equal to | [B] 5 |
(iii) The number of values of x for which the angle between the vectors + (x3 – 1)& is obtuse | [C] 7 |
(iv) Let P1 = 2x – y + z = 7 & P2 = x + y + z = 2. If P be a point that lies on P1, P2 and XOY-plane be the point that lies on P1, P2 and YOZ-plane & R be the point that lies on P1, P2 & XOZ plane then [Area of ΔPQR] is(where [⋅ ] denotes greatest integer function) | [D] 11 |
Text Solution
Verified by Experts(i) [D]; (ii) [C]; (iii) [A]; (iv) [A]
Ans.
(i) [D]
(ii) [C]
(iii) [A]
(iv) [A]
Sol.
(i) 
Solving two lines λ = μ = 1
∴ 
∴ λ 2 (OP) = 11
(ii) 
∴ x + y + z = 7
(iii) 
< 0
∴ x
9 (x 3 – 1) + x (x 3 –1) + 1 < 0
x 12 + x 4 – x 9 – x + 1 < 0
L.H.S. > 0 ∀ x ∈ R
(iv) obviously points P,Q and R are collinear points
∴ Area of Δ PQR = 0
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