List of top Questions asked in CAT- 2014

The ratio of the ages of A and B is 3:4. Five years hence, the ratio will be 4:5. What is the present age of A?
On a certain day, the sum of the date and the square root of the month gives the square of the month. Find the date.
The sum of the squares of three consecutive integers is 110. What is the smallest integer?
If $a^2 + b^2 = 25$ and $ab = 12$, what is $(a + b)^2$?
If $2x + 3y = 15$ and $x - y = 1$, what is the value of $x + y$?
The lengths of the sides of a right-angled triangle are in geometric progression. What is the ratio of the sines of its acute angles?
What is the value of $2^{10}$?
If $\sin \theta + \cos \theta = \sqrt{2}$, what is $\sin \theta \cos \theta$?
Lal divides his garden into several identical squares and places posts at all the corners of all the squares. He then plants one tree per square. If a rectangular garden uses 36 posts in all, find the maximum number of trees that he could have planted.
A series in which any term is equal to the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and determine the series. It is known that the difference of the squares of the ninth and eighth terms of a Fibonacci series is $840$. Find the 12th term of that series.
A car travels 240 km in 4 hours. What is its speed in km/h?
A sum of Rs. 2000 is invested at 10% per annum compound interest. What is the amount after 2 years?
The sum of the first $n$ terms of an arithmetic progression is $3n^2 + 2n$. What is the 10th term?
A shopkeeper marks an article 20% above cost price and offers a 10% discount. If the cost price is Rs. 500, what is the profit?
Harry Potter bought a triangular piece of land of area $150\ \text{m}^2$. Harry measured two sides of the plot and found the largest side to be $50\ \text{m}$ and another side to be $10\ \text{m}$. Find the exact length of the third side.
A is a non-empty set having $n$ elements. P and Q are two subsets of A such that $P \subseteq Q$. Find the number of ways of choosing the subsets P and Q.
In any society that values liberty and regards it as a right, punishment will be viewed very seriously, to be __________ only if a very good justification for it is __________.
Our Constitution is so simple and __________ that it is always possible to meet extraordinary needs by changes in emphasis and arrangement without loss of essential __________.
Three persons A, B, and C start running simultaneously on three concentric circular tracks from three collinear points P, Q, and R respectively, which are collinear with the centre and on the same side of the centre. The speeds of A, B, and C are $5\ \text{m/s$, $9\ \text{m/s}$, and $8\ \text{m/s}$ respectively. The lengths of the tracks are:} A: $400\ \text{m}$, B: $600\ \text{m}$, C: $800\ \text{m}$.
A and B run clockwise, and C runs anti-clockwise. Find the first time after they start when A, B, and C are collinear with the centre and on the same side of the centre.
If $f_{1}(x) = \frac{2}{2+x}$ and $f_{n}(x) = \frac{1}{1+f_{n-1}(x)}$, where $n>1$, then find the approximate value of $f_{50}(1)$.
If the roots of the equation $x^2 - 6x + k = 0$ are real and their product is 8, what is the value of $k$?
If $3x = 4y = 12z$, what is the ratio $x:y:z$?
The numbers $1, 2, \dots, n$ are written in natural order. Numbers in odd places are struck off to form a new sequence. This process is continued until only one number is left. If $n = 1997$, find the last remaining number.
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
Using the same Venn diagram, how many students study exactly two subjects?