List of top Mathematics Questions asked in GATE Chemical Engineering

A probability distribution function is given as:

\[ p(x) = \begin{cases} \dfrac{1}{a}, & x \in (0, a) \\ 0, & \text{otherwise} \end{cases} \]

Where \( a \) is a positive constant. For a function \( f(x) = x^2 \), the expectation of \( f(x) \) is:

A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is
Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors \(\hat{i}, \hat{j}\), and \(\hat{k}\). Let vector \(\mathbf{a} = \sqrt{2}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}\), and vector \(\mathbf{b} = \frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j} - \hat{k}\). The inner product of these vectors (\(\mathbf{a} \cdot \mathbf{b}\)) is: