Remove rows with the same value across all columns

Here is an option with rowSums; the logic is to check if there is any value in the row that is different (NA doesn't count) from one of the columns that you are interested in:

df[rowSums(df[-1] != df[[2]], na.rm = TRUE) != 0,]

#  cars test1 test2 test3 test4 test5 test6 test7
#1 Car1     0     0     1     2     0     1     3
#3 Car3     3     2     5     2     1     1     2
#5 Car5     4     0     2     2     0     1     0
#7 Car7     1     2     6     1     1     3     1
#8 Car8     3     5     7     1     3     4     1

keep <- apply(df[2:8], 1, function(x) length(unique(x[!is.na(x)])) != 1)
df[keep, ]

  cars test1 test2 test3 test4 test5 test6 test7
1 Car1     0     0     1     2     0     1     3
3 Car3     3     2     5     2     1     1     2
5 Car5     4     0     2     2     0     1     0
7 Car7     1     2     6     1     1     3     1
8 Car8     3     5     7     1     3     4     1