In each of the following questions predict the results first and then use the Lisp interpreter to check your answers:1. Write down the results of typing the following expressions in Lisp. (one line at a time).(list 'big 'cat 'sat)(cons 'the (list 'big 'cat 'sat))(list 'all (list 'good 'people) 'should (list 'go 'ahead))(cdr (car (cdr '(a (b c) d(cdadr '(a (b c) d))2. What will be the value of the last expression in each case?a. (setq a '(u v w)) (set (car (cdr a)) 'b) (cons v a)b. (setq A 'A) (setq B 'A) (list A B 'B)3. What will be the result of each of the following sets of s-expressions typed in Lisp environment?a. (defun double (x) (* 2 x)) (double 2.3)b. (defun times-square (x y) (* x y y)) (times-square 4 3)c. (defun TIMES-CUBE (X Y) (* X Y Y Y)) (defun CUBE-TIMES (X Y) (TIMES-CUBE Y X)) (CUBE-TIMES 3 2)Using an editor you may type the above functions in separate files with "lsp" or ".lisp" extension (you may use the editor which comes with Allegro Lisp - under file menu choose new option; write the code; save the program under the name double. lsp). And then load the program into the Allegro Lisp environment for execution (under file menu choose load option; write the name of the program double. lsp ). After loading the program you may execute any functions within that file using the listener window; CL-USER 1> (double 5) ;running the function double 104. Evaluate each of the following s-expressions:a. (atom '3)b. (floatp '(A B))c. (listp '(A B))d. (not (null 'nil))e. (not (atom '(A B)))f. (eq 'a 'a)g. (eq '(A B) (list 'A 'B))h. (eq 3 3.0)i. (equal 3 3.0)j. (eq 2.3 (+ 1.1 1.2))k. (and (atom '3) (listp '(A B)))5. Write two different s-expressions to access symbol C for each of the following lists. a. (A B C D E)b. ((A B C) (D E F))c. ((A B) (C D) (E F))d. (A (B C D) E F)6. Write a function DOT-PRODUCT that takes two lists, each list has three numbers (elements), and produces the dot product of the vectors that they represent. For example, -> (DOT-PRODUCT '(1.2 2.0 -0.2) '(0.0 2.3 5.0)) -> 3.6 The answer for this question can be found in file DOT-PRODUCT. LSP in the same directory. The key for designing a lisp function is using recursion.7. Write a function COUNT-NUMBER that counts the number of numbers that occur in a list. It should work like this: -> (COUNT-NUMBER '(A 2.3 B 5 4.53 C F)) -> 3 Hint: To determine whether s-expression is a number or not, use numberp function. The following examples show how numberp works:-> (numberp 5)-> T-> (numberp 5.5)-> T-> (numberp T)-> nil-> (numberp ‘(A B))-> nil8. Write a function NEW-LIST that takes a number as its argument and constructs a list of that length containing all Ts. For example,-> (new-lit 5)-> (T T T T T)9. The Lisp function LENGTH counts the number of elements in the top level of a list. Write a function ALL-LENGTH of one argument that counts the number of atoms that occur in a list at all levels. Thus, the following lists will have the following ALL-LENGTHs. (A B C) => 3 ((A (B C) D (E F)) => 6 (NIL NIL (NIL NIL) NIL ) => 5Turn in your responses to these questions 6-9 in one single Lisp program file (.lsp or .lisp file)