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tomato subjective

Graphing inequality (Tomato subjective 90)

Problem: Draw the region of points \({\displaystyle{(x,y)}}\) in the plane, which satisfy \({\displaystyle{|y| {\le} |x| {\le} 1}}\). Solution: \({\displaystyle{|y| {\le} …

Rational Function Inequality (Tomato subjective 77)

problem: For \({x > 0}\), show that \({\displaystyle{\frac{x^n – 1}{x – 1}}{\ge}{n{x^{\frac{n – 1}{2}}}}}\), where \({n}\) is a positive integer. …

Perpendiculars from Center (Tomato subjective 107)

Problem : If a, b and c are the lengths of the sides of a triangle ABC and  if \( …

Sum of polynomials (Tomato subjective 173)

Problem : Let be polynomials in , each having all integer coefficients, such that . Assume that is not the …

Round robin tournament (Tomato subjective 172)

Problem : Suppose there are teams playing a round robin tournament; that is, each team plays against all the other …

Arrangement of Similar Items (TOMATO Subjective 49)

Problem: \(x\) red balls, \(y\) black balls,\(z\) white balls are to be arranged in a row. Suppose that any two balls …

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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