Column I Column II (A) In a triangle \triangleXYZ, let a,b\text{and}c be the length of the sides opposite to the angles X,Y\text{and}Z, respectively. If 2(a^2-b^2)=c^2 \text{and} \lambda=\frac{\sin(X-Y)}{\sin Z} ,then possible values of n for which \cos(n\pi\lambda)=0 is (are) (P) 1 (B) In a triangle\triangleXYZ,let a,b\text{and}c be the length of the sides opposite to the anglesX,Y\text{and}Z,respectively.If 1+cos2X-2cos2Y=2sinX,sinY,then possible value(s) of a/b is (are) (Q) 2 (C) In \mathbb{R}^3,let \sqrt3i^{∧}+j^{∧},i^{∧}+\sqrt3j^{∧} \text{and} \betai^{∧}+(1- \beta)j^{∧} be the position vectors of X, Y \text{and} Z with respect of the origin, respectively. If the distance of Z from the bisector of the acute angle of \overrightarrow{OX} \text{with} \overrightarrow{OY}\text{is}3/\sqrt2. then the possible value(s)of |β| is (are) (R) 3 (D) Suppose that F(\alpha) denotes the area of the region bounded by x=0,x-2,y^2=4x\text{and}y=|\alphax-1|=|\alphax-2|+\alphax,\text{where} \alpha∊{0,1}.Then the value(s) of F(\alpha)+8/3\sqrt2.where \alpha=0 and \alpha=1 is (are) (S) 5 (T) 6 [JEE Adv 2015 P1]

Correct Answer is : (A) → (P, R, S), (B) → (P), (C) → (P, Q), (D) → (S, T)

(A) → (P, R, S), (B) → (P), (C) → (P, Q), (D) → (S, T)

(A) → (P, S, T), (B) → (P), (C) → (P, Q), (D) → (S, T)

(A) → (P, Q, S), (B) → (P), (C) → (P, Q), (D) → (S, T)

(A) → (P, R, S), (B) → (Q), (C) → (P, Q), (D) → (S, T)

Properties of Triangle

Section: Mathematics

Question : 8 of 15

Marks: +1, -0

Column I

Column II

(A)

In a triangle △XYZ, let a,b‌and‌c be the length of the sides opposite to the angles X,Y‌and‌Z, respectively. If 2(a2−b2)=c2and‌λ=

sin(X−Y)

sinZ

,then possible values of n for which cos(nπλ)=0 is (are)

(P)

(B)

In a triangle△XYZ,let a,b‌and‌c be the length of the sides opposite to the anglesX,Y‌and‌Z,respectively.If 1+cos2X−2cos2Y=2sinX,sinY,then possible value(s) of

is (are)

(Q)

(C)

In ℝ3,let √3

∧

+√3

∧

‌and‌β

∧

+(1−β)

∧

be the position vectors of X,YandZ with respect of the origin, respectively. If the distance of Z from the bisector of the acute angle of

→

‌with‌

→

‌is‌

√2

. then the possible value(s)of |β| is (are)

(R)

(D)

Suppose that F(α) denotes the area of the region bounded by x=0,x−2,y2=4x‌and‌y=|αx−1|=|αx−2|+αx,whereα∊0,1.Then the value(s) of F(α)+

√2.where α=0 and α=1 is (are)

(S)

(T)

[JEE Adv 2015 P1]

(A) → (P, R, S), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, S, T), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, Q, S), (B) → (P), (C) → (P, Q), (D) → (S, T)
(A) → (P, R, S), (B) → (Q), (C) → (P, Q), (D) → (S, T)

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