List of top Questions asked in CAT- 2012

Find the incorrect usage of the word “STOP”.

Find the incorrect usage of the word “SOMBRE”.

Jurisprudence is the theory and philosophy of law. Students of jurisprudence aim to understand the fundamental nature of law and to analyse its purpose, structure, and application. Jurisprudential scholars (sometimes confusingly referred to as “jurists”) hope to obtain a deeper understanding of the law, the kind of power that it exercises and its role in human societies.

Letters of the word “ATTRACT” are written on cards and kept on a table. Manish lifts three cards at a time, writes all possible combinations of the three letters on a piece of paper, and then replaces the cards. He is to strike out all the words which look the same when seen in a mirror. How many words is he left with?

A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?

RD Laing developed a broad range of thought on interpersonal psychology. This deals with interactions between people, which he considered important, for an ethical action always occurs between one person and another. In books such as The Politics of Experience he dealt with issues concerning how we should relate to persons labelled by the psychiatric establishment as “schizophrenic”. ,

In the figure, \( OABC \) is a parallelogram. The area of the parallelogram is 21. Coordinates are: \( O = (0,0) \), \( A = (7,0) \), and point \( C \) lies on line \( x = 3 \). Find coordinates of \( B \).

If \( ax^2 + bx + c = 0 \) and \( 2a, b, 2c \) are in arithmetic progression, then which of the following are the roots of the equation?

If \( (a^2 + b^2), (b^2 + c^2) \) and \( (a^2 + c^2) \) are in geometric progression, which of the following holds true?

If \( x \) is a real number and \( \lfloor x \rfloor \) is the greatest integer \( \leq x \), then \[ 3\lfloor x \rfloor + 2 - \lfloor x \rfloor = 0 \] Will the above equation have any real root?

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \[ x^2 - 10x + 15 = 0, \] then find the quadratic equation whose roots are \( \left( \alpha + \frac{\alpha}{\beta} \right) \) and \( \left( \beta + \frac{\beta}{\alpha} \right) \).

A rectangle is drawn such that none of its sides has length greater than ‘\( a \)’. All lengths less than ‘\( a \)’ are equally likely. The chance that the rectangle has its diagonal greater than ‘\( a \)’ (in terms of %) is:

\( p \) is a prime and \( m \) is a positive integer. How many solutions exist for the equation \[ p^5 - p = (m^2 + m + 6)(p - 1)? \]

A certain number written in a certain base is 144. Which of the following is always true?

What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?

If the roots of the equation \[ (a^2 + b^2)x^2 + 2(b^2 + c^2)x + (b^2 + c^2) = 0 \] are real, which of the following must hold true?

Let \( P = \{2, 3, 4, \ldots, 100\} \) and \( Q = \{101, 102, 103, \ldots, 200\} \). How many elements of \( Q \) are there such that they do not have any element of \( P \) as a factor?

Find the remainder when \( 2^{1040} \) is divided by 131.