Column Matching-begin array - c - c - hlineColumn I - Column II Wlinealigned A - - In a triangle XY Z- let a - b and c be the - lengths of the sides opposite to the angles - text X - Y- and Z- respectively- If 2 a 2- b 2- c 2- and -sin X-Y-sin Z- then possible values lend aligned -text P 111Weginaligned-text angles X- Y and Z- respectively- If -text1-cos 2 X-2 cos 2 Y-2 sin X sin Y- then - possible values of a-b is are e n d aligned - text Q 2 111

When α=0 Area bounded by the curves =2× 3 ∫_0^2 2√(x) dx =6 8√(2)3 When α=1 nbsp; Required area = ar(OABC) ar(OAED) ar( BCD) =6 8√(2)3 12× 2× 1 =5 8√(2)3 ...

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Standard XII

Mathematics

Transpose of a Matrix

Column Matchi...

Question

Column Matching:

$Column (I)Column (II)(A) In a triangle △XYZ, let a,b and c be thelengths of the sides opposite to the anglesX,Y and Z, respectively. If 2(a2−b2=c2and λ=sin(X−Y)sinZ, then possible valuesof n for which cos(nπλ)=0 is (are)(P) 1(B) In a triangle △XYZ, let a,b and c bethe lengths of the sides opposite to theangles X,Y and Z, respectively. If1+cos2X−2cos2Y=2sinXsinY, thenpossible value(s) of ab is (are)(Q) 2(C) In R2, let √3^i+^j,^i+√3^j and β^i+(1−β)^jbe the position vectors of X,Y and Z withrespect to the origin O, respectively. If thedistance of Z from the bisector of the acuteangle of −−→OX with −−→OY is 3√2, then possiblevalue(s) of |β| is (are) (R) 3(D) Suppose that F(α) denotes the area of the region bounded by x=0,x=2,y2=4xand y=|αx−1|+|αx−2|+αx, whereα∈{0,1}. Then the value(s) of F(α)+83√2,when α=0 and α=1, is (are)(S) 5(T) 6$
Option $(D)$ matches with which of the elements of right hand column?

P

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Solution

The correct options are
D $S$
E $T$
When $α = 0$

Area bounded by the curves $= 2 \times 3 - \int_{0}^{2} 2 \sqrt{x} d x = 6 - \frac{8 \sqrt{2}}{3}$

When $α = 1$

Required area
$= ar (O A B C) - ar (O A E D) - ar (△ B C D)$
$= 6 - \frac{8 \sqrt{2}}{3} - \frac{1}{2} \times 2 \times 1 = 5 - \frac{8 \sqrt{2}}{3}$

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Similar questions

Q. Column Matching:

Column (I)Column (II)(A) In a triangle △XYZ, let a,b and c be thelengths of the sides opposite to the anglesX,Y and Z, respectively. If 2(a2−b2=c2and λ=sin(X−Y)sinZ, then possible valuesof n for which cos(nπλ)=0 is (are)(P) 1(B) In a triangle △XYZ, let a,b and c bethe lengths of the sides opposite to theangles X,Y and Z, respectively. If1+cos2X−2cos2Y=2sinXsinY, thenpossible value(s) of ab is (are)(Q) 2(C) In R2, let √3^i+^j,^i+√3^j and β^i+(1−β)^jbe the position vectors of X,Y and Z withrespect to the origin O, respectively. If thedistance of Z from the bisector of the acuteangle of −−→OX with −−→OY is 3√2, then possiblevalue(s) of |β| is (are) (R) 3(D) Suppose that F(α) denotes the area of the region bounded by x=0,x=2,y2=4xand y=|αx−1|+|αx−2|+αx, whereα∈{0,1}. Then the value(s) of F(α)+83√2,when α=0 and α=1, is (are)(S) 5(T) 6

Option

(D)

matches with which of the elements of right hand column?

Q. Column Matching:

Column (I)Column (II)(A) In a triangle △XYZ, let a,b and c be thelengths of the sides opposite to the anglesX,Y and Z, respectively. If 2(a2−b2)=c2and λ=sin(X−Y)sinZ, then possible valuesof n for which cos(nπλ)=0 is (are)(P) 1(B) In a triangle △XYZ, let a,b and c bethe lengths of the sides opposite to theangles X,Y and Z, respectively. If1+cos2X−2cos2Y=2sinXsinY, thenpossible value(s) of ab is (are)(Q) 2(C) In R2, let √3^i+^j,^i+√3^j and β^i+(1−β)^jbe the position vectors of X,Y and Z withrespect to the origin O, respectively. If thedistance of Z from the bisector of the acuteangle of −−→OX with −−→OY is 3√2, then possiblevalue(s) of |β| is (are) (R) 3(D) Suppose that F(α) denotes the area of the region bounded by x=0,x=2,y2=4xand y=|αx−1|+|αx−2|+αx, whereα∈{0,1}. Then the value(s) of F(α)+83√2,when α=0 and α=1, is (are)(S) 5(T) 6

Option

(D)

matches with which of the elements of right hand column?

Q. Column Matching:

Column (I)Column (II)(A) In a triangle △XYZ, let a,b and c be thelengths of the sides opposite to the anglesX,Y and Z, respectively. If 2(a2−b2=c2and λ=sin(X−Y)sinZ, then possible valuesof n for which cos(nπλ)=0 is (are)(P) 1(B) In a triangle △XYZ, let a,b and c bethe lengths of the sides opposite to theangles X,Y and Z, respectively. If1+cos2X−2cos2Y=2sinXsinY, thenpossible value(s) of ab is (are)(Q) 2(C) In R2, let √3^i+^j,^i+√3^j and β^i+(1−β)^jbe the position vectors of X,Y and Z withrespect to the origin O, respectively. If thedistance of Z from the bisector of the acuteangle of −−→OX with −−→OY is 3√2, then possiblevalue(s) of |β| is (are) (R) 3(D) Suppose that F(α) denotes the area of the region bounded by x=0,x=2,y2=4xand y=|αx−1|+|αx−2|+αx, whereα∈{0,1}. Then the value(s) of F(α)+83√2,when α=0 and α=1, is (are)(S) 5(T) 6

Option

(D)

matches with which of the elements of right hand column?

Q. Which of the following option is correct?

\begin{matrix} List I & List II \begin{matrix} (A) The minimum value of the expression \frac{{sec}^{4} α}{{tan}^{2} β} + \frac{{sec}^{4} β}{{tan}^{2} α} \forall α, β \in (0, π / 2) is \end{matrix} & (1) 1 \begin{matrix} (B) If z_{1}, z_{2} are two non-zero complex numbers satisfying the equation ∣ ∣ ∣ \frac{z_{1} + z_{2}}{z_{1} - z_{2}} ∣ ∣ ∣ = 1, then the value of \frac{z_{1}}{z_{2}} + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (\frac{z_{1}}{z_{2}}) is \end{matrix} & (2) 2 \begin{matrix} (C) Number of integers in the range of function y = \frac{x^{2} + x + 3}{x^{2} + 2 x + 6}, x \in R is \end{matrix} & (3) 0 \begin{matrix} (D) If y = (3)^{(- 3)^{1 / (1 - x)}}, then lim x \to 1^{+} y is \end{matrix} & (4) 8 \end{matrix}

Q. Which of the following option is incorrect?

\begin{matrix} List I & List II \begin{matrix} (A) The minimum value of the expression \frac{{sec}^{4} α}{{tan}^{2} β} + \frac{{sec}^{4} β}{{tan}^{2} α} \forall α, β \in (0, π / 2) is \end{matrix} & (1) 1 \begin{matrix} (B) If z_{1}, z_{2} are two non-zero complex numbers satisfying the equation ∣ ∣ ∣ \frac{z_{1} + z_{2}}{z_{1} - z_{2}} ∣ ∣ ∣ = 1, then the value of \frac{z_{1}}{z_{2}} + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (\frac{z_{1}}{z_{2}}) is \end{matrix} & (2) 2 \begin{matrix} (C) Number of integers in the range of function y = \frac{x^{2} + x + 3}{x^{2} + 2 x + 6}, x \in R is \end{matrix} & (3) 0 \begin{matrix} (D) If y = (3)^{(- 3)^{1 / (1 - x)}}, then lim x \to 1^{+} y is \end{matrix} & (4) 8 \end{matrix}

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The correct options are D S E TWhen α=0 Area bounded by the curves =2×3−∫202√x dx=6−8√23 When α=1 Required area =ar(OABC)−ar(OAED)−ar(△BCD) =6−8√23−12×2×1=5−8√23