The maximum value of \( f(x) = (x - 1)^2 (x + 1)^3 \) is equal to \[ \frac{2^p 3^q}{3125} \,\, \text{then the ordered pair of} (p, q) \text{ will be} \]
If \[ \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k}, \] \(\text{then }\) [\(\mathbf{a}\) \(\mathbf{b}\) \(\mathbf{c}\)] \(\text{ depends on:}\)
Find a number from the given options which best completes the series: 39, 416, 525, \(\dots\), 749, 864
Statement: No table is a chair. Not a single chair is a stand. Every stand is a statue.
Conclusion: 1. Some statues which are stands are tables as well. 2. Some statues are not chairs.
Consider the circuit shown below and find the minimum number of NAND gates required to design it.
Consider the following minterm expression for \( F \): \[ F(P, Q, R, S) = \Sigma(0, 2, 5, 7, 8, 10, 13, 15) \] \(\text{The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is}\)
If \( n_1 \) and \( n_2 \) are the number of real valued solutions of \( x = |\sin^{-1} x| \) \(\text{and}\) \( x = \sin(x) \text{ respectively, then the value of} \, n_2 - n_1 \text{ is:}\)
