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())
  }
}

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.