Question
if a2 + b2 +
c2Â =Â 2(4a -5b -9c)-122 , then a-b-c = ?Solution
a2 + b2 + c2 = 2(4a -5b -9c)-122 So a2 + b2 + c2 -2×4a +2 ×5b + 2×9c +122 = 0 a2 -2×4a +16 + b2 +2 ×5b+25 +c2 +2×9c+81 = 0 So (a-4)2 +(b+5)2+(c+9)2 = 0 As we know that if x2 + y2 +z2 = 0 then x=y=z = 0 So here a-4 = 0 so a =4; b +5 = 0 so b = -5 And c+9 =0 so c = -9 So now a-b-c = 4-(-5)-(-9) = 4+5+9 = 18
Statements:  E = F < G < H; I ≥ J = H; K > I
Conclusions:
I. E > J
II. K = J
III. F < K
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
Statements: P > R; Q > S = W < T ≥ V; R > U = Q
Conclusions:
I. Q < P
II. T > R
III. U > V
Statements:
T % W % B $ I @ L
Conclusions:
I. B * T
II. L © B
III. L * T
Statements: M ≤ N = O ≤ P; P = Q ≤ U; R > N = U
Conclusions:
I. R > O
II. U ≥ M
Statements: A > B ≥ C ≤ D; E ≥ F ≥ G = A
Conclusion:
I. E > D
II. D ≥ E
Statements: Y < X ≥ B < V; A < L ≤ K; R ≤ F ≤ O < X; V ≤ K
Conclusions:
I. R < K
II. A < B
III. Y < F
Statements : B ≤ I; E = D; H > F; C ≤ H; I = D; A ≤ B; H < E
Conclusions:
(i) I > F (ii) B ≤ H (iii) A ≤ E (iv) E...
Statements: U & K # X % I % W; T # M $ W; T @ N @ S
Conclusions:
I. X @ M
II. K $ S
III. N # I
Statement: A < B; D ≤ C = B; I > C; E ≥ B
Conclusion:
I. I > E
II. E ≥ I