List of top Questions asked in XAT- 2015

Six words are given below:
I. Cacophonic
II. Cacographic
III. Calamitous
IV. Catastrophic
V. Contraindicative
VI. Cataclysmic
Which of the above words have similar meanings?

Which of the following is not a term of ‘disapproval’?

Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, $A$ and $B$, can fill the empty cone in $8$ hours and $12$ hours, respectively. The outlet pipe $C$ (at the bottom) can empty a filled cone in $4$ hours. When the cone is completely filled with water, all three pipes are opened. Two of the pipes remain open for $20$ hours continuously and the third pipe remains open for a lesser time. As a result, the height of water comes down to $50%$. Which of the following options would be possible?

A person is standing at a distance of 1800 meters facing a giant clock at the top of a tower. At 5.00 p.m., he can see the tip of the minute hand of the clock at 30 degree elevation from his eye level. Immediately, the person starts walking towards the tower. At 5.10 p.m., the person noticed that the tip of the minute hand made an angle of 60 degrees with respect to his eye-level. Using three-dimensional vision, find the speed at which the person is walking. The length of the minute hand is \( \frac{200}{\sqrt{3}} \) meters (where \( \sqrt{3} = 1.732 \)).

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

Product $M$ is produced by mixing chemical $X$ and chemical $Y$ in the ratio $5:4$. Chemical $X$ is prepared by mixing two raw materials, $A$ and $B$, in the ratio $1:3$. Chemical $Y$ is prepared by mixing raw materials, $B$ and $C$, in the ratio $2:1$. Then the final mixture is prepared by mixing $864$ units of product $M$ with water. If the concentration of the raw material $B$ in the final mixture is $50%$, how much water had been added to product $M$?

A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?

In an examination, two types of questions are asked: one mark questions and two marks questions. For each wrong answer, of one mark question, the deduction is 1/4 of a mark and for each wrong answer, of two marks question, the deduction is 1/3 of a mark.
Moreover, 1/2 of a mark is deducted for unanswered question. The question paper has 10 one mark questions and 10 two marks questions. In the examination, students got all possible marks between 25 and 30 and every student had different marks. What would be the rank of a student, who scores a total of 27.5 marks?

What is the sum of the following series? $-64, -66, -68, \ldots, -100$

An ascending series of numbers satisfies the following conditions: i. When divided by 3, 4, 5 or 6, the numbers leave a remainder of 2.
ii. When divided by 11, the numbers leave no remainder. The 6th number in this series will be:

A three-digit number has digits in strictly descending order and is divisible by 10. By changing the places of the digits a new three-digit number is constructed in such a way that the new number is divisible by 10. The difference between the original number and the new number is divisible by 40. How many numbers will satisfy all these conditions?

If the last $6$ digits of $\,[M! - N!]$ are $999000$, which of the following options is {not possible for $M \times (M-N)$? Both $M$ and $N$ are positive integers with $M>N$. (Here $M!$ denotes $M$ factorial.)}

Find the equation of the graph shown below.

If \(f(x^{2}-1)=x^{4-7x^{2}+k_{1}\) and \(f(x^{3}-2)=x^{6}-9x^{3}+k_{2}\) then the value of \((k_{2}-k_{1})\) is}

If $a,b,c,d$ are four different positive integers selected from $1$ to $25$, then the highest possible value of \(\dfrac{(a+b)+(c+d){(a+b)+(c-d)}\) would be:}

For a positive integer $x$, define $f(x)$ such that $f(x+a) = f(ax)$, where $a$ is an integer and $f(1)=4$. If $f(1003)=k$, then the value of $k$ will be:

The figure below has been obtained by folding a rectangle. The total {visible area of the folded figure is $144\ \text{m}^2$. Had the rectangle not been folded, the current overlapping part would have been a {square}. What would have been the total area of the original (unfolded) rectangle?}

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7\(\frac{1}{2}\) ft, and cost of construction is Rs. 100 per sq.ft. Find the lowest possible cost to construct 50% of the total road.

In the diagram below, $CD = BF = 10$ units and $\angle CED = \angle BAF = 30^\circ$. What would be the area of $\triangle AED$?

Two diagonals of a parallelogram intersect each other at coordinates $(17.5,\,23.5)$. Two adjacent points of the parallelogram are $(5.5,\,7.5)$ and $(13.5,\,16)$. Find the lengths of the diagonals.

Devanand’s house is 50 km West of Pradeep’s house. On Sunday morning, at 10 a.m., they leave their respective houses. Under which of the following scenarios, the minimum distance between the two would be 40 km?
Scenario I: Devanand walks East at a constant speed of 3 km/h and Pradeep walks South at 4 km/h.
Scenario II: Devanand walks South at 3 km/h and Pradeep walks East at 4 km/h.
Scenario III: Devanand walks West at 4 km/h and Pradeep walks East at 3 km/h.

The parallel sides of a trapezoid ABCD are in the ratio of 4 : 5. ABCD is divided into an isosceles triangle ABP and a parallelogram PBCD (as shown below). ABCD has a perimeter equal to 1120 meters and PBCD has a perimeter equal to 1000 meters. Find $\sin \angle ABC$, given that $2 \angle DAB = \angle BCD$.

The centre of a circle inside a triangle is at a distance of 625 cm from each of the vertices of the triangle. If the diameter of the circle is 350 cm and the circle is touching only two sides of the triangle, find the area of the triangle.

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.
Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

Identify the correct sequence of words would most that aptly fit the blanks in the following passage.
It is ______ (i) ______ that the accused had ______ (ii) ______ ______ (iii) ______ from all criminal activities by adopting the ______ (iv) ______ of a sanyasi. However, despite repeated requests from the counsel for prosecution, the court has ______ (v) ______ a lie detector to ascertain the truth.