In a group of six women there are four dancers, four vocal musicians, one actress and three violinists. Girija and Vanaja are among the violinists while Jalaja and Shailaja do not know how to play on the violin. Shailaja and Tanuja are among the dancers. Jalaja, Vanaja, Shailaja and Tanuja are all vocal musicians and two of them are also violinists. If Pooja is an actress, who among the following is certainly a dancer and a violinist?

Let's break down the information step-by-step:

1. Violinists: Girija and Vanaja are violinists (Statement 1). Jalaja and Shailaja do not play the violin (Statement 2). This means we have Girija, Vanaja as violinists, and Jalaja, Shailaja as non-violinists.
2. Dancers: Shailaja and Tanuja are dancers (Statement 3).
3. Vocal Musicians & Violinists: Jalaja, Vanaja, Shailaja, and Tanuja are all vocal musicians (Statement 4). Two of these four are also violinists (Statement 5).
   • We know Vanaja is a violinist (from Statement 1).
   • We know Jalaja and Shailaja are NOT violinists (from Statement 2).
   • Therefore, among these four (Jalaja, Vanaja, Shailaja, Tanuja), the two violinists must be Vanaja and Tanuja. This confirms Tanuja is a violinist.
4. Actress: Pooja is an actress (Statement 6).

Now let's check the options to find who is certainly a dancer and a violinist:

• A) Jalaja: Is not a violinist (from Statement 2). So, cannot be a dancer and a violinist.
• B) Pooja: Is an actress. We have no information about her being a dancer or a violinist.
• C) Shailaja: Is a dancer (from Statement 3), but is not a violinist (from Statement 2). So, cannot be a dancer and a violinist.
• D) Tanuja:
  • She is a dancer (from Statement 3).
  • She is a violinist (deduced in step 3 above).
  • Therefore, Tanuja is certainly a dancer and a violinist.

The final answer is D) Tanuja.