Column IColumn 2Column 3(I)cos(sin−1(sin5π6))=(i)1(P)f(x)=3x3−13x

1.	Column IColumn 2Column 3(I)cos(sin−1(sin5π6))=(i)1(P)f(x)=3x3−13x2+14x−2 hasthree roots α,β,γ, then value of\|sin(tan−1α+tan−1β+tan−1γ)\|=(II)cos(cos−1(−sin7π6))=(ii)1√2(Q)(√3cosec20∘−sec20∘)8=(III)∣∣cos{tan−1(tan15π4)}∣∣=(iii)12(R)4√2(sin12∘)(sin48∘)(sin54∘)=(IV)sin((cos−1{1√2(cos9π10−sin9π10)}+7π20)−1×π2)(iv)√32(S)If the angles A, B and C of atriangle are in an arithmetic progressionand if a,b and c denote the lengths ofsides opposite to A,B and C respectively,then the value of the expression12(acsin2C+casin2A)is Which of the following options is only INCORRECT combination?
Answer» $\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & c o s (s i n^{- 1} (s i n \frac{5 π}{6})) = & (i) & 1 & (P) & f (x) = 3 x^{3} - 13 x^{2} + 14 x - 2 h a s t h r e e r o o t s α, β, γ, t h e n v a l u e o f \| s i n (t a n^{- 1} α + t a n^{- 1} β + t a n^{- 1} γ) \| = (I I) & c o s (c o s^{- 1} (- s i n \frac{7 π}{6})) = & (i i) & \frac{1}{\sqrt{2}} & (Q) & \frac{(\sqrt{3} c o s e c 20^{\circ} - s e c 20^{\circ})}{8} = (I I I) & ∣ ∣ c o s {t a n^{- 1} (t a n \frac{15 π}{4})} ∣ ∣ = & (i i i) & \frac{1}{2} & (R) & 4 \sqrt{2} (s i n 12^{\circ}) (s i n 48^{\circ}) (s i n 54^{\circ}) = (I V) & s i n ({(c o s^{- 1} {\frac{1}{\sqrt{2}} (c o s \frac{9 π}{10} - s i n \frac{9 π}{10})} + \frac{7 π}{20})}^{- 1} \times π^{2}) & (i v) & \frac{\sqrt{3}}{2} & (S) & I f t h e a n g l e s A, B a n d C o f a t r i a n g l e a r e i n a n a r i t h m e t i c p r o g r e s s i o n a n d i f a, b a n d c d e n o t e t h e l e n g t h s o f s i d e s o p p o s i t e t o A, B a n d C r e s p e c t i v e l y, t h e n t h e v a l u e o f t h e e x p r e s s i o n \frac{1}{2} (\frac{a}{c} s i n 2 C + \frac{c}{a} s i n 2 A) i s \end{matrix}$ Which of the following options is only INCORRECT combination?

Column IColumn 2Column 3(I)cos(sin−1(sin5π6))=(i)1(P)f(x)=3x3−13x2+14x−2 hasthree roots α,β,γ, then value of|sin(tan−1α+tan−1β+tan−1γ)|=(II)cos(cos−1(−sin7π6))=(ii)1√2(Q)(√3cosec20∘−sec20∘)8=(III)∣∣cos{tan−1(tan15π4)}∣∣=(iii)12(R)4√2(sin12∘)(sin48∘)(sin54∘)=(IV)sin((cos−1{1√2(cos9π10−sin9π10)}+7π20)−1×π2)(iv)√32(S)If the angles A, B and C of atriangle are in an arithmetic progressionand if a,b and c denote the lengths ofsides opposite to A,B and C respectively,then the value of the expression12(acsin2C+casin2A)is Which of the following options is only INCORRECT combination?

Answer»

$\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & c o s (s i n^{- 1} (s i n \frac{5 π}{6})) = & (i) & 1 & (P) & f (x) = 3 x^{3} - 13 x^{2} + 14 x - 2 h a s t h r e e r o o t s α, β, γ, t h e n v a l u e o f | s i n (t a n^{- 1} α + t a n^{- 1} β + t a n^{- 1} γ) | = (I I) & c o s (c o s^{- 1} (- s i n \frac{7 π}{6})) = & (i i) & \frac{1}{\sqrt{2}} & (Q) & \frac{(\sqrt{3} c o s e c 20^{\circ} - s e c 20^{\circ})}{8} = (I I I) & ∣ ∣ c o s {t a n^{- 1} (t a n \frac{15 π}{4})} ∣ ∣ = & (i i i) & \frac{1}{2} & (R) & 4 \sqrt{2} (s i n 12^{\circ}) (s i n 48^{\circ}) (s i n 54^{\circ}) = (I V) & s i n ({(c o s^{- 1} {\frac{1}{\sqrt{2}} (c o s \frac{9 π}{10} - s i n \frac{9 π}{10})} + \frac{7 π}{20})}^{- 1} \times π^{2}) & (i v) & \frac{\sqrt{3}}{2} & (S) & I f t h e a n g l e s A, B a n d C o f a t r i a n g l e a r e i n a n a r i t h m e t i c p r o g r e s s i o n a n d i f a, b a n d c d e n o t e t h e l e n g t h s o f s i d e s o p p o s i t e t o A, B a n d C r e s p e c t i v e l y, t h e n t h e v a l u e o f t h e e x p r e s s i o n \frac{1}{2} (\frac{a}{c} s i n 2 C + \frac{c}{a} s i n 2 A) i s \end{matrix}$

Which of the following options is only INCORRECT combination?

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