List of top Questions asked in CAT

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4), and (−2, 8), respectively. Then, the coordinates of the vertex D are
The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
For natural numbers x,y, and z, if xy+yz=19 and yz+xz=51, then the minimum possible value of xyz is
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
Ankita buys 4kg cashews, 14kg peanuts, and 6kg almonds when the cost of 7kg cashews is the same as that of 30kg peanuts or 9kg almonds. She mixes all three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent buying almonds is
The largest real value of a for which the equation\( |x+a|+|x−1|=2\) has an infinite number of solutions for x is
A donation box can receive only cheques of ₹100,₹250 and ₹500. On one good day,the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained,is
If \(c=\frac{16x}{y}+\frac{49y}{x} \)for some non-zero real numbers x and y,then c cannot take the value
If \((3+2\sqrt2)\) is a root of the equation ax2 + bx + c = 0 and \((4+2\sqrt3)\) is a root of the equation ay2 + my + n = 0,where a,b,c,m and n are integers, then the value of \((\frac{b}{m}+\frac{c−2b}{n})\) is
Consider six distinct natural numbers such that the average of the two smallest numbers is 14 and the average of the two largest numbers is 28. Then,the maximum possible value of the average of these six numbers is
Two ships are approaching a port along straight routes at constant speeds. Initially,the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km,the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance,in km,between the other ship and the port will be
In an examination,the average marks of students in sections A and B are 32 and 60,respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer,then the difference between the maximum and minimum possible number of students in section A is
If\(\left(\frac{\sqrt{7}}{5}\right)^{3x - y} = \frac{875}{2401}\) and \(\left(\frac{4a}{b}\right)^{6x - y}\)\(=\left(\frac{2a}{b}\right)^{y - 6x}\), for all non-zero real values of a and b,then the value of x+y is
The average of all 3-digit terms in the arithmetic progression 38,55,72,...,is
Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3:5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is
Let \(A\) be the largest positive integer that divides all the numbers of form \(3^k+4^k+5^k\), and \(B\) be the largest positive integer that divides all the numbers of the form \(4^k+3(4^k)+4^{k+2}\), where k is any positive integer. Then \((A+B)\) equals
In a village, the ratio of number of males to females is 5:4. The ratio of number of literate males to literate females is 2:3. The ratio of the number of illiterate males to illiterate females is 4:3. If 3600 males in the village are literate, then the total number of females in the village is
Amal buys 110kg of syrup and 120kg of juice, syrup being 20% less costly than juice, per kg. He sells 10kg of syrup at 10% profit and 20kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
A trapezium ABCD has side AD parallel to BC, ∠BAD=90∘, BC=3 cm, and AD=8 cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is
For natural numbers x,y, and z, if xy+yz=19 and yz+xz=51, then the minimum possible value of xyz is
For any real number x, let [x] be the largest integer less than or equal to x. If \(\sum_{n=1}^N \left[ \frac{1}{5} + \frac{n}{25} \right] = 25\) then N is
Working alone,the times taken by Anu,Tanu and Manu to complete any job are in the ratio \(5:8:10\). They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However,Anu and Tanu work together for the first 6 days,working 6 hours 40 minutes per day. Then,the number of hours that Manu will take to complete the remaining job working alone is
Mr.Pinto invests one-fifth of his capital at \(6\%\),one-third at \(10\%\) and the remaining at \(1\%\),each rate being simple interest per annum.Then,the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
Regular polygons A and B have number of sides in the ratio \(1:2\) and interior angles in the ratio \(3:4\).Then the number of sides of B equals