Under what article of the Constitution of India can the President take over the administration of a state in case its constitutional machinery breaks down?

Statements:  Q = R; S ≥ T; P ≤ Q;  R > V; R > S; T ≥ U

Conclusions:

(i) R > U                       

Statement: D < M < P = V = E ≥ T > Z

Conclusion: I. P > Z II. D > E

Statements: B & C, C # D, D @ E, E % F

Conclusions: I.    C & F                     II. E # B

Statements: P < Q = S ≥ U; V ≤ P ≥ N > I

Conclusions: I. U < V II. Q > I

Statements: M % C & G @ T $ D; W % M # P 

Statements: P < L = O; N = M ≤ J ≤ K; M ≤ L

Conclusions:

I. K ≥ O

II. N ≤ L

III. O ≥ N

Statements:

A < C <  F;  G > H = F < K < L

Conclusions:

I).  G > K

II). K ≥ G

Statements: M $ K; K & N, N % R, R @ W

Conclusions:     

I. W & K