Bootcamp week-1 list related problems. Test cases are here : https://gist.github.com/tamizhgeek/6e09fbb4d6e448bea213

ListUtils.scala

package assignments

object ListUtils {
  def findLast(list : List[Int]) :Int = {
    list match {
      case a :: Nil => a
      case a :: b => findLast(b)
    }
  }

  def lenCustom(list: List[Int]) : Int = {
    list match {
      case (Nil) => 0
      case (a :: Nil) => 1
      case (a :: b) => 1 + lenCustom(b)
    }
  }

  def penultimate(list: List[Int]) : Int = {
    list match {
      case (a :: b :: Nil)  =>  a
      case (a :: b) => penultimate(b)
    }
  }

  def reverse(list: List[Int]) : List[Int] =  {
    def collect(list: List[Int], newList : List[Int]) : List[Int] = {
      list match {
        case (Nil) => newList
        case a :: b => collect(b, a :: newList)
      }
    }
    collect(list, List())
  }

  def removeDuplicates(list : List[Int]) : List[Int] = {
    list match {
      case Nil => Nil
      case a :: Nil => a :: Nil
      case (a1 :: a2 :: b) => {
        if(a1 == a2)
          removeDuplicates(a1 :: b)
        else
          a1 :: removeDuplicates( a2 :: b)
      }
    }
  }

  def drop(interval : Int, list : List[Int]) : List[Int] = {
    def collect(currentIdx : Int, newList : List[Int]) : List[Int] = {
      if(lenCustom(list) == currentIdx) return newList

      if(((currentIdx + 1) % interval) == 0) collect(currentIdx + 1, newList)
      else collect(currentIdx + 1, newList :+ list.apply(currentIdx))
    }
    collect(0, List())
  }

  def slice(start : Int, end : Int, list : List[Int]) : List[Int] = {
    def collect(currentIdx : Int, newList : List[Int]) : List[Int] = {
      currentIdx match {
        case a if(a < start) => collect(a + 1, newList)
        case a if(a >= start && a < end) => collect(a + 1, newList :+ list.apply(a))
        case a => newList
      }
    }
    collect(0, List())
  }
}

Line 34, 47, 60 - Using Any invalidates any type checks that compiler can give you. We refrain from using Any unless totally required. If the intentions were to support all types of list, it is better to use generics (we'll cover it soon in the forth coming sessions).
Line 50 - Could we've used a simple if-else for this? Pattern matching seems a bit of an overkill here.
Line 51, 54, 63-65: Would throw a compiler warning since the type are erased when converting to byte code. We can avoid the ': Int' part safely since currentIdx is of type Int.

Ashwanth - Nailed. Pattern matching can be deceptive. You need to be clear when to use it and when to use if-else. And, secondly help the Type checker by not giving Any :)
L#51, 54 cases can be converted to Case 0 => do_something and Case _ => do_something_else

Incorporated the comment changes. But i have a lot of questions. Will come and bug either of you to get more clarity.