What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at least one head is _______.

Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with constant $$'C'$$ is

The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on two equal sub intervals each of length $$1,$$ equals to