This might be one option.
set.seed(234078)
df <- data.frame(q1.banana = sample(0:1, 10, replace = TRUE),
q1.apple = sample(0:1, 10, replace = TRUE),
q1.melon = sample(0:1, 10, replace = TRUE))
library(reshape2)
# Melt the data
df1 <- melt(df)
df1$value <- as.numeric(df1$value)
library(plyr)
# Now use ddply to sum the values
ddply(df1,.(variable),summarize,Freq=sum(value))
variable Freq
1 q1.banana 3
2 q1.apple 4
3 q1.melon 5
Another option
> colSums(df)
q1.banana q1.apple q1.melon
3 4 5