Match the column.
Column –IColumn –II(i) Range of the function f(x) = is [m, M] then m + M is eq…

Question

Match the column.
Column –IColumn –II(i) Range of the function f(x) =    is [m, M] then m + M is equal to[A] 1(ii) If , n ∈ N,         then maximum value of n is equal to[B] 0(iii) A line through (0, 0, 0) and perpendicular to plane is = =  then a + b+ c may be[C] 3(iv) Two lines whose equation areL1 :  andL2 :  lie in the same plane.    If L1 intersects a plane x + y + z = 15 at P, then distance of P from (3, 4, 3) is[D] 5

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [B]; (ii) [D]; (iii) [A]; (iv) [C]. Ans.
(i) [B]
(ii) [D]
(iii) [A]
(iv) [C]
Sol. (i) Let f(t) = 
 ≤ f(t) ≤ 3 ∀ t ∈ R
log 3  ≤ log 3  ≤ log 3 3
–1 ≤ f(x) ≤ 1 ∴ m + M = 0
(ii) cot –1  > 
⇒  <  ⇒ n < 
⇒ n max = 5
(iii) (k + 1) 2 e (k+1)x – 4(k + 1) e (k+1)x + 4e (k+1)x = 0
⇒ (k + 1) 2 – 4(k + 1) + 4 = 0
⇒ k + 1 = 2 ⇒ k = 1
(iv) Lines L 1 and L 2 are coplanar if
 =  ⇒ λ = 4
Let L 1 :  =  =  = t
∴ Any point on it is P(2t + 3, 3t + 2, 4t + 1)
It lies on the plane x + y + z = 15
⇒ 9t + 6 = 15 ⇒ t = 1
∴ distance of P(5, 5, 5) from (3, 4, 3) = 3

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Column –I	Column –II
(i) Range of the function f(x) = is [m, M] then m + M is equal to	[A] 1
(ii) If , n ∈ N, then maximum value of n is equal to	[B] 0
(iii) A line through (0, 0, 0) and perpendicular to plane is = = then a + b+ c may be	[C] 3
(iv) Two lines whose equation are L1 : and L2 : lie in the same plane. If L1 intersects a plane x + y + z = 15 at P, then distance of P from (3, 4, 3) is	[D] 5

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