Match the statements/expressions given in Column - I with the values given in Column – II
Column - I Column - II
cos 
, (q) 
where [y] denotes the largest integer less than or equal to y
vectors 
, 
and 
and 
where 
and 
are unit (s) 
vectors satisfying 
(t) π
Text Solution
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→ (q, s), → (p, r, s, t), → (t), → (r)
Sol. 2 sin 2 θ + sin 2 2 θ = 2
⇒ sin 2 2 θ = 2 cos 2 θ ⇒ 4sin 2 θ cos 2 θ = 2cos 2 θ
⇒ cos 2 θ = 0 or sin 2 θ = 
⇒ cos θ = 0 or sin θ = 
⇒ θ = 
or 
⇒ f(x) = 
cos 
possible points of discontinuity of 
are 
= n , n 
I
⇒ x = 
⇒ x = 
, 
, 
, π
f (x) = 0 cos 0 = 0
f(x) = 1 cos 0 = 1
∴ discontinuous at x = 
. Similarly discontinuous at x = 
, 
, π
V = 
= π cubic units
+ 
+ 
= 
⇒ 
+ 
= – 
⇒ 
= 
⇒ a 2 + b 2 + 2 
. 
= 3c 2
⇒ 2 + 2 cos θ = 3
⇒ cos θ = 
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