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# tomato subjective

### Integer Roots (Tomato Subjective 175)

Problem:- Let $$\text{P(x)}=x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\dots+a_{1}x+a_{0}$$ be a polynomial with integer coefficients,such that,$$\text{P(0) and P(1)}$$  are odd integers.Show that (a)$$\text{P(x)}$$ does not have …

### The Gifts Distribution (TOMATO Subjective 48)

Problem: Find the different number of ways $$5$$ different gifts can be presented to $$3$$ children so that each child receives at least …

### Dictionary Ranking (TOMATO Subjective 50)

Problem: All the permutation of the letters $$a,b,c,d,e$$ are written down and arranged in alphabetical order as in dictionary. Thus the arrangement …

### Number of Onto Functions (TOMATO Subjective 46)

Problem: A function $$f$$ from set $$A$$ into set $$B$$ is a rule which assigns each element $$x$$ in $$A$$, a unique (one and only one) …

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