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.

If $4 \leq x \leq 8$ and $2 \leq y \leq 7$, then what is the ratio of maximum value of $(x+y)$ to minimum value of $(x-y)$ ?

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.

There are $n$ sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1 . What is the value of $n$ ?

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 $(\mathbf{R}, \mathbf{S})$ ?