For how many integral values of x will |(x-1!)| + |(x-2!)| + |(x-3!)| + |(x-4!)| asuume a minimum value?

Since there is a modulus function, all the values except 1,2,3,4 will not give minimum values. So, for x = 1, 4 . Value = 9. for x = 2,3 . Value = 4. There for for values, x = 2,3. We have minimum value for the expression. Please correct me if I'm wrong.

Is there a general method to solve problems based on finding number of integral solutions, or do should we try out whatever works each time? For eg. What is the number of positive integral solutions for x^2 + 3y^2 = z^2

Hi There is no general method to solve such questions. Each question requires some rearrangement to make it easy to solve.In the given questio, we can write it asx^2 + y^2 + 2y^2 = z^2We can see that if x = y, then we have(x+y)^2 = z^2Thus, if x+y = z , we will have a solution.Hence we can have infinite solutions for the given problem.

No one but (she/her) ever made a perfect score on the test. Please explain the general rule regarding the proper use of pronouns in such cases.

When a noun or pronoun is used as the subject of a verb, it is said to be in the Nominative case. When a noun or pronoun is used as the object of a verb, it is said to be in the Objective or accusative case. Also, a noun which comes after a preposition is said to be in the accusative case. "she" is used when pronoun is the subject of a sentence and her is used when the pronoun is the object of the sentence. The correct answer will be "her" because it is coming after a preposition "but".

No one but "her" ever made a perfect score on the test is the correct usage. Shrishti's explanation is correct.

Maybe we're not as rich as (they/them), but I bet we're much happier. Please explain the general rule regarding the proper use of pronouns in such cases.

Hi,Here 'them' should be correct. The general rule is, wherever the object form is required use object form. Similarly, wherever the subject form is required, use the subject form of the pronoun.

how do i solve para jumbles

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how to od reading comphrehension

Hi Charan, Implementing the following strategy can help you increase your accuracy in Reading Comprehension: 1. Identify the theme of every paragraph while reading the RC for the first time. 2. Identify the specific questions. These are questions that pertain to a specific paragraph in the essay. These questions can be answered with greater accuracy. 3. For the 'generic questions', try to eliminate the least likely options. As a general strategy, choose the RC whose topic is familiar to you. Try to answer at least three of the four questions in the RC. You can practise RC questions at the following link: https://cracku.in/cat/quotient

sir my 10th inter and grad. aggregates are 69.83, 77.5, 62.86 and 13 months jobs experience with in and out........can i get into IIMs with good cat percentile

Hi Karthik, You can't change your past grades. Focus rather on improving your CAT score as it is in your hands. A good tool to analyse where you stand with respect to your peers is the CAT percentile predictor. Do check it out here: https://cracku.in/percentile-predictor

If x and y are even integers ,then the number of solutions of x^2 - Y^2 = 7389746232 is

Didn't understand can u please elaborate a little bit more

Hi Gaurav,The prime factorization of the number is 2^3 X 3 X 11 X 1879 X 14897=> (x+y)(x-y) must be equal to this.Since both are even, both x+y and x-y must be even. So, we will assign 2 2s to each of them. So we haveSo, the number of factors of the remaining number will be 2 X 2 X 2 X 2 X 2So, number of pairs of x+y and x-y available are 16.Each of this pair will give unique values of x and y. Thus, 16 is the correct answer.