CAT 2023 Question Paper (Available): Download CAT Question Paper with Solutions PDF

Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals

How many boxes have at least one sack containing 9 coins?

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4 ) the following sentence would best fit.
Sentence: This philosophical cut at one's core beliefs, values, and way of life is difficult enough.
Paragraph: The experience of reading philosophy is often disquieting. When reading philosophy, the values around which one has heretofore organised one's life may come to look provincial, flatly wrong, or even evil. __(1)_. When beliefs previously held as truths are rendered implausible, new beliefs, values, and ways of living may be required. _ (2) . What's worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed. Sometimes philosophical writing is even strictly critical in that it does not even attempt to provide an alternative after tearing down a cultural or conceptual citadel. (3). The reader of philosophy must be prepared for the possibility of this experience. While reading philosophy can help one clarify one's values, and even make one self-conscious for the first time of the fact that there are good reasons for believing what one believes, it can also generate un-remediated doubt that is difficult to live with.

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4 ) the following sentence would best fit.
Sentence: This philosophical cut at one's core beliefs, values, and way of life is difficult enough.
Paragraph: The experience of reading philosophy is often disquieting. When reading philosophy, the values around which one has heretofore organised one's life may come to look provincial, flatly wrong, or even evil. __(1)_. When beliefs previously held as truths are rendered implausible, new beliefs, values, and ways of living may be required. _ (2) . What's worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed. Sometimes philosophical writing is even strictly critical in that it does not even attempt to provide an alternative after tearing down a cultural or conceptual citadel. (3). The reader of philosophy must be prepared for the possibility of this experience. While reading philosophy can help one clarify one's values, and even make one self-conscious for the first time of the fact that there are good reasons for believing what one believes, it can also generate unremediated doubt that is difficult to live with.

Let \(a, b, m\) and \(n\) be natural numbers such that \(a >1\) and \(b >1\) . If \(a^m+b^n = 144^{145}\) , then the largest possible value of \(n − m\) is