In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

Let both $p$ and $k$ be prime numbers such that $\left(p^2+k\right)$ is also a prime number less than 30 . What is the number of possible values of $k$ ?

In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

Let PQR be a 3-digit number, PPT be a 3-digit number and $\mathbf{P S}$ be a 2-digit number, where $\mathbf{P}, \mathbf{Q}, \mathbf{R}, \mathbf{S}, \mathbf{T}$ are distinct non-zero digits. Further, $\mathrm{PQR}-\mathrm{PS}=\mathrm{PPT}$. If $Q=3$ and $T<6$, then what is the number of possible values of $(\mathbf{R}, \mathbf{S})$ ?

If there is inequality in the pattern of population growth, there is greater inequality in food production and utilisation. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only $16 \%$ of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

What is the maximum value of $n$ such that $7 \times 343 \times 385 \times 1000 \times 2401 \times 77777$ is divisible by $35^{\mathrm{n}}$ ?

If there is inequality in the pattern of population growth, there is greater inequality in food production and utilisation. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only $16 \%$ of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

If $N^2=12345678987654321$, then how many digits does the number N have?