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Inequality                                                                                          179

                                         Answer with Solution




                                                  Concept Applicator


            1.   (c) N = P ≤ F ≥ L = K                           Solution for 11 to 15
                Hence F ≥ K. Which means either                  1.  (b) A ≥ B = C < D ≤ E
                I (F = K) or  II (F > K) follows                      I. D > A is not true, II. E > C is true.
            2.  (a) Z > T < M < J                                2.  (e) Split them as L > U ...(i)
                Which means T < J. Hence I follows.                   Combining (i) and (ii),
                But Z and J can’t be compared. Hence II does not      We get L > U > Z or L > Z
                follow.                                               Hence I follows.
            3.  (e) C ≥ G ≥ Q = Z ≥ R                                 Combining (ii) and (iv) we get K ≤ U < R or K < R
                Hence G ≥ Z and I follows.                            Hence II follows.
                Also C ≥ R and II follows.                       13.  (a) Y < J = P ≥ R > I
            4.  (d) A > B < C < D > E > F                             I. J > I is true, II. Y < R is not true.
                E and C can’t be compared. Hence II does not follow.   14.  (d) V ≥ K > M = N > S
                Z and J can’t be compared. Hence I does not follow.      K > T
                Consequently II does not follow either.
                                                                      I. T < N is not true, II. V = S is true.
            5.  (e) L > K > M ≥ N > O                            15.  (a) Split them as F ≤ X ...(i) X < A ...(ii)
                Hence O < M and I follows.
                                                                      R < X ...(ii) and X ≤ E ...(iv)
                Also O < K and II follows.                            Combining (i) and (iv) we get
            6.  (b)
            7.  (d)                                                   F ≤ X ≤ F or F ≤ E.
            8.  (e)                                                   Hence I follow.
            9.  (a)                                                   From (i) and (iii) R and F can’t be compared. Hence
                                                                      II does not follow.
            10.  (c)



                                                    Concept Builder

            Solution for 1 to 7                                  4.  (d) W ≤ D ...(i) D ≥ B ...(ii) B > H ...(iii)
            1.  (c) M < J ...(i) J ≤ R ...(ii) R = K ...(iii          H and D can’t be compared from (ii) and (iii)
                From (ii) and (iii) J≤ K or K ≥ J, ...(iv)            Hence I does not follows
                Hence either I (K = J) or II (K > J) follow           Nor can W and B he be compared From (i) and (ii).
            2.  (e) N ≥ T ...(i) T = H ...(ii) N < W ...(iii)         Hence II does not follows
                Combining these we get W > N ≥ T = H             5.  (b) F = T ...(i) T ≥ M ...(ii) M ≤ R ...(iii)
                Hence W > T and I follows.                            From (i) and (ii) F ≥ M ...(iv)
                Also H ≤ N and II follows
            3.  (a) F < R ...(i) R ≤ V ...(ii) V ≥ T ...(iii)         Hence M ≤ F and II follows
                From (i) and (ii) F < V... (iv)                       But R and F can’t be compared From (iii) and (iv)
                Hence F > V and I follows                             Hence I does not follow
                But F and T can’t be compared From (iii) and (iv)  6.  (a) H ≥ N ...(i) N > R ...(ii) R < J ...(iii)
                Hence II does not follow
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