List of top Questions asked in CAT- 2012

Feminism is not simply a movement to ensure that women will have equal rights with men \underline{but that a commitment for eradicating the ideology of domination} that permeates Indian culture at various levels.
Consider a sequence \( S \) whose \( n \)th term \( T_n \) is defined as \( T_n = 1 + \frac{3}{n} \), where \( n = 1, 2, \ldots \). Find the product of all the consecutive terms of \( S \) starting from the 4th term to the 60th term.

A train travels 360 km at a uniform speed. If the speed is increased by 5 km/h, the journey takes 1 hour less. Find the original speed. 
 

A number is divisible by 3 and 5. What is the smallest such number greater than 100? 
 

What is the value of $\sin 30^\circ + \cos 60^\circ$? 
 

What is the value of $2^{100} \mod 5$? 
 

A car \( A \) starts from a point \( P \) towards another point \( Q \). Another car \( B \) starts (also from \( P \)) 1 hour after the first car \( A \), and overtakes it after covering 30% of the distance \( PQ \). After that, the cars continue. On reaching \( Q \), car \( B \) reverses and meets car \( A \), after covering \( 2\frac{1}{3} \) of the distance \( QP \). Find the time taken by car \( B \) to cover the distance \( PQ \) (in hours).
When asked for his taxi number, the driver replied, “If you divide the number of my taxi by 2, 3, 4, 5, 6 each time you will find a remainder of one. But if you divide it by 11, the remainder is zero.” What is the taxi number?
A vessel has a milk solution in which milk and water are in the ratio 4:1. By addition of water to it, milk solution with milk and water in the ratio 4:3 was formed. On replacing 14 L of this solution with pure milk, the ratio of milk and water changed to 5:3. What is the volume of the water added?

What is the remainder when $7^{100}$ is divided by 8? 
 

Arrange the sentences to form a coherent paragraph:
A. It also fosters innovation.
B. Education empowers individuals.
C. It enables critical thinking.
D. Society benefits from educated citizens.
Find the incorrect usage of the word “TIME”.
Choose the correct word: The policy had a ___ effect on growth.
The company's ___ approach led to success.

What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$? 
 

In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).

A man invests Rs. 5000 at 6% simple interest per annum. How much interest will he earn in 3 years? 
 

What is the sum of digits of $2^{10}$? 
 

The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?
If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

What is the probability that a leap year has 53 Sundays? 
 

\( A, B, C \) can independently do a work in 15, 20, and 30 days respectively. They work together for some time after which \( C \) leaves. A total of ₹18000 is paid for the work and \( B \) gets ₹6000 more than \( C \). For how many days did \( A \) work?

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

Which sentence is grammatically incorrect?