If \(A = \{1, 2, 3, 4, 5, 6\}\), then the number of subsets of \(A\) which contain at least two elements is:
The total number of subsets of A is \(2^6 = 64\). The number of subsets with at least two elements is equal to the total number of subsets minus the number of subsets with zero elements (the empty set) and the number of subsets with one element.
Number of subsets with zero elements = 1 (the empty set)
Number of subsets with one element = 6 (one for each element)
Number of subsets with at least two elements = \(64 - 1 - 6 = 57\)
The total number of subsets of $ A $ is:
$$ 2^{|A|} = 2^6 = 64. $$
The number of subsets with 0 elements is:
$$ \binom{6}{0} = 1 \quad \text{(the empty set)}. $$
The number of subsets with 1 element is:
$$ \binom{6}{1} = 6. $$
Thus, the number of subsets with at least two elements is:
$$ 64 - 1 - 6 = 57. $$
A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit. He applied a resistance of \( 520 \, \Omega \) in \( R \). When \( K_1 \) is closed and \( K_2 \) is open, the deflection observed in the galvanometer is 20 div. When \( K_1 \) is also closed and a resistance of \( 90 \, \Omega \) is removed in \( S \), the deflection becomes 13 div. The resistance of galvanometer is nearly: