GATE Civil 2021 Set 1 | GA Question: 9

Question

A function, $\lambda$, is defined by

$\lambda \left ( p,q \right )=\left\{\begin{matrix} \left ( p-q \right )^{2}, & \text{if} \:p\geq q, \\ p+q, &\text{if} \: p< q.\end{matrix}\right.$

The value of the expression $\dfrac{\lambda \left ( -\left (- 3+2 \right ),\left ( -2+3 \right ) \right )}{\left ( -\left ( -2+1 \right ) \right )}$ is:

• A. $-1$
• B. $0$
• C. $\frac{16}{3}$
• D. $16$

Answer 1

The value of the expression $\dfrac{\lambda \left ( -\left (- 3+2 \right ),\left ( -2+3 \right ) \right )}{\left ( -\left ( -2+1 \right ) \right )} =  \dfrac{\lambda(-(-1),1)}{-(-1)} = \dfrac{\lambda(1,1)}{1} = \dfrac{(1-1)^{2}}{1} = \dfrac{0}{1} = 0.$

So, the correct answer is $(B).$