Match of the column.
Column-I | Column-II |
(i) log10 5.log10 20 + (log10 2)2 = | [A] 4 |
(ii) Least value of x satisfying |2x| – |x – 4| = x + 4 is | [B] -4 |
(iii) If cos–1 x = sin–1 , for all x ∈ (–1, 1), then k is equal to | [C] 1 |
(iv) If f: [0, 2] → [2, 0] is bijective function defined by f(x) = ax2 + bx + c, where a, b, c are non-zero real numbers then f(2) is equal to | [D] 0 |
Text Solution
Verified by Experts(i) [C]; (ii) [B]; (iii) [A]; (iv) [D]; (ii) (i)
Ans.
(i) [C]
(ii) [B]
(iii) [A]
(iv) [D]
Sol. (i) log 10 5. log 10 20 + (log 10 2) 2 = (1 – log 10 2) (1 + log 10 2) + (log 10 2)
2 = 1
(ii) (i) If x < 0 the equation becomes
–2x + x – 4 = x + 4 i.e. x = – 4
(ii) If 0 ≤ x < 4, the equation becomes
2x + x – 4 = x + 4 i.e. x = 4 (No Solution)
(iii) If x ≥ 4, the equation becomes
2x – x + 4 = x + 4 i.e. x ≥ 4 (are solution)
Least value of x satisfying the equation is – 4.
(iii) Let cos –1 x = θ θ = 
sin –1 
= 
k = 4
(iv) Since f(x) is bijection
f(0) = 0 or 2 but f(0) = 0
c = 0 (which is not true)
f(0) = 2
∴ f (2) = 0
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