Recent questions tagged cat2013

1
Functions $g$ and $h$ are defined on $n$ constants, $a_0,a_1,a_2,a_3,\dots a_{n−1}$, as follows: $\begin{array} g(a_p,a_q) & =a_{\mid p−q\mid}, \text{if } \mid p-q \mid \leq (n-4) \text{ and } \\ &=a_{n−\mid p−q\mid}, \text{if } \mid p-q\mid>(n-4) \end{array}$ ... $p+q$ is divided by $n$. If $n=10$, find the value of $g(g(a_2,a_8),g(a_1,a_7))$, $a_9$ $a_7$ $a_2$ $a_0$
2
Functions $g$ and $h$ are defined on n constants, $a_0,a_1,a_2,a_3,...a_{n−1}$, as follows: $g(a_p,a_q)=a\mid p−q\mid$ ,if $\mid p-q \mid\leq(n-4) =a_n−\mid p−q\mid$,if $\mid p-q\mid>(n-4) h (a_p,a_q)=a_k$, where $k$ is the remainder when $p+q$ is divided by $n$. If $h(a_k,a_m)=a_m$ for all $m$, where $1\leq m < n$ and $0 \leq k < n$, and $m$ is a natural number, find $k$. $0$ $1$ $n-1$ $n-2$
3
There are five cards lying on a table in one row. Five numbers from among $1$ to $100$ have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by $4$ ... that order. How many sequences can be written down on the sixth card? $2^23^3$ $4(3)^4$ $4^23^3$ $4^23^4$
4
Summary of the estimate of memory space occupied by the information worldwide, stored in various storage media, in the year $2000$ In the above graph, for any media of information storage, the figures in the brackets denote the amount of memory space occupied by the information stored worldwide in that ... $10,170\:TB$ $6,780 \: TB$ $1,703,170\:TB$ $\text{None of these}$
5
Summary of the estimate of memory space occupied by the information worldwide, stored in various storage media, in the year $2000$ In the above graph, for any media of information storage, the figures in the brackets denote the amount of memory space occupied by the information stored worldwide ... unit memory space occupied is the same for all the media mentioned. $37.5\%$ $45\%$ $57\%$ $54\%$
6
Let $P,Q,S,R,T,U$ and $V$ represent the seven distinct digits from $0$ to $6$, not necessarily in that order. If $PQ$ and $RS$ are both two-digit numbers adding up to the three-digit number $TUV$, find the value of $V$. $3$ $6$ $5$ $\text{Cannot be determined}$
7
In a bag there are total of $150$ coins in three denominations $₹1,₹2$ and $₹5$ with at least one coin of each denomination being present in the bag. The total value of the Re.$1$ coins is at least $50\%$ of the total value of the coins in the bag. If there are $23\:₹5$ coins in ... least $3\%$ of the total value of the coins in the bag, find the number of $₹2$ coins in the bag. $2$ $3$ $4$ $1$
8
Summary of the estimate of memory space occupied by the information worldwide, stored in various storage media, in the year $2000$ In the above graph, for any media of information storage, the figures in the brackets denote the amount of memory space occupied by the information stored worldwide ... stored in any single media within that category(approximately)? $68.75\%$ $62.5\%$ $96\%$ $98.3\%$
9
Summary of the estimate of memory space occupied by the information worldwide, stored in various storage media, in the year $2000$ In the above graph, for any media of information storage, the figures in the brackets denote the amount of memory space occupied by the information ... the following years is the earliest by which there will be a shortage of memory space? $2002$ $2003$ $2004$ $2005$
10
Consider the following two curves in the XY plane: $\\y=2x^3+3x^2+4\: \text{and} \\y=3x^2-2x+8$ Which of the following statements is true for $-3≤x≤2$? The two curves intersect thrice The two curves intersect twice The two curves intersect once The two curves do not intersect
11
Two cars P and Q start from two points A and B towards each other simultaneously. They meet for the first time $40$ km from B. After meeting they exchange their speeds as well as directions and proceed to their respective starting points. On reaching their starting points, they turn back with the ... at a point $20$ km from A. Find the distance between A and B. $130$ km $100$ km $120$ km $110$ km
12
Sujith looked at the six-digit number on his CAT admit card and said "If I multiply the first two digits with three, I get all ones. If I multiply the next two digits with six, I get all twos. If I multiply the last two digits $9$, I get all threes”. What is the sum of the digits of the number on Sujith's admit card? $30$ $33$ $60$ $45$
13
$a,b$ and $c$ are the lengths of the triangle $ABC$ and $d,e$ and $f$ are the lengths of the sides of the triangle $DEF$. If the following equations hold true: $a(a+b+c)=d^2\\b(a+b+c)=e^2\\c(a+b+c)=f^2$ then which of the following is always true of triangle $DEF$? It is an acute-angled triangle It is an right-angled triangle It is an obtuse-angled triangle None of the above
14
In a triangle $PQR$, $PQ=12$ cm and $PR=9$ cm and $\angle Q+\angle R=120^{\circ}$. If the angle bisector of $\angle P$ meets $QR$ at $M$, find the length of $PM$ $\dfrac{28\sqrt5}{9}$ cm $\dfrac{42\sqrt5}{11}$ cm $\dfrac{36\sqrt3}{7}$ cm $4\sqrt3$
15
The following is the table of points drawn at the end of all matches in a six-nation Hockey tournament, in which each country played with every other country exactly once. The table gives the positions of the countries in terms of their respective total points scored(i.e. ... $0$ $1$ $2$ Cannot be determined
16
The following is the table of points drawn at the end of all matches in a six-nation Hockey tournament, in which each country played with every other country exactly once. The table gives the positions of the countries in terms of their respective total points ... Which of the following matches was a draw? India vs South Korea Spain vs Netherlands Netherlands vs South Korea Spain vs South Korea
17
The following is the table of points drawn at the end of all matches in a six-nation Hockey tournament, in which each country played with every other country exactly once. The table gives the positions of the countries in terms of their respective total points scored(i.e., in ... $5$ $6$ $7$ Cannot be determined
18
A cuboidal aquarium, of base dimensions $100\:cm \times 80\:cm$ and height $60\:cm$, is filled with water to its brim. The aquarium is now tilted along one of the $80\:cm$ edges and the water begin to spill. The tilting is continued till the water surface touches a ... . Now the box is returned to its original position. By how many centimeters has the height of water reduced? $50$ $40$ $20$ $10$
19
Some persons are standing at distinct points on a circle, all facing towards the center. Each possible pair of persons who are not adjacent sing a three-minute song, one pair after another. If the total time taken by all the pairs to finish singing is $1$ hour, find the number of persons standing on the circle $5$ $7$ $9$ $8$
20
In a triangle $PQR$, $PQ=12$ cm and $PR=9$ cm and $\angle Q+\angle R=120^{\circ}$. Find the length of QR $\dfrac{15}{\sqrt2}$ cm $3\sqrt13$ cm $5\sqrt5$ cm $5\sqrt17$ cm
21
The following is the table of points drawn at the end of all matches in a six-nation Hockey tournament, in which each country played with every other country exactly once. The table gives the positions of the countries in terms of their respective total points scored(i.e., in the ... $5$ $4$ $3$ $2$
22
Outside a sweet shop, its name "Madhu Sweet House" is displayed using blinking lights. Each word flashes at a regular interval and remains lit for $1$ second. After remaining lit for $1$ second, "Madhu" remains unlit for $3 \dfrac{1}{2}$ seconds, "Sweet" remains ... words flash together and the next time the last two words flash together $45$ seconds $22.5$ seconds $112$ seconds $6.75$ seconds
23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0$, $g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$
24
A television company manufactures two models of televisions-A and B. Each unit of model A requires four hours to manufacture and each unit of model B requires two hours to manufacture. The total time available in a month to manufacture these two models is $1600$ hours. The profits ... maximize the profit. $200$ model as As and $600$ model Bs $800$ model as As $800$ model Bs None of the above
25
The age of a son, who is more than two years old, is equal to the units digit of the age of his father. After ten years, the age of the father will be thrice the age of the son. What is the sum of the present ages of the son and the father? $30$ years $36$ years $40$ years Cannot be determined
26
Given that $-3<x \leq – \dfrac{1}{2}$ and $\dfrac{1}{2} < y \leq 7$, which of the following statements is true? $\text{max}(x+y)(x-y)] – \text{min}[(x+y)(x-y)]=57 \dfrac{1}{2}$ $\text{max}[(x+y)^2]=169/4$ $\text{min}[(x-y)^2]=1$ All of the above
27
Each side of a polygon is either parallel to the $x$-axis or parallel to the $y$-axis. A corner of the polygon is known as convex if the corresponding internal angle is $90^\circ$ and as concave if the corresponding internal angle is $270^\circ$. If the polygon has $26$ convex corners, the number of its concave corners is $18$ $22$ $26$ $24$
28
The density of a liquid is defined as the weight per unit volume of the liquid. The densities of two liquids A and B are in the ratio $2:1$. The liquid B evaporates at a rate (in kg/hr) which is twice as fast compared to that of liquid A, which evaporates at a rate of ... is $1.04$ times that of the original mixture. Assume that there is no chemical reaction between the liquids $2.5$ $3$ $3.5$ $4$
29
Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III
30
The line $L$ passing through the points $(1,1)$ and $(2,0)$ meets the $y$-axis at $A$. The line through the point $\bigg(\dfrac{1}{2},0 \bigg)$ and perpendicular to $L$ meets the $y$-axis at $B$ and $L$ at $C$. Find area of the triangle $ABC$ $\dfrac{25}{16} \\$ $\dfrac{16}{9} \\$ $\dfrac{32}{19} \\$ $\dfrac{40}{23}$
31
The following question presents four statements, of which three, when placed in appropriate order, would form a contextually complete paragraph. Pick the statements that is not part of the context But as access to other texts is enjoyed more widely, some of the dominance ... form or another are used and as long as they are issued or approved by the state, they will remain a political issue.
32
Psychotherapeutic processes deal with psychological problems, ranging From mild ones like a depressed mood, to more subtle ones like interpretation of dreams to more controversial problems like dissociative identity disorder. Denied emotions (not admitting or voicing one's emotions ... of the mind are grounded in the unconscious, while the other considered them to be triggered by the conscious.
33
Psychotherapeutic processes deal with psychological problems, ranging From mild ones like a depressed mood, to more subtle ones like interpretation of dreams to more controversial problems like dissociative identity disorder. Denied emotions (not admitting or voicing one's emotions to the ... open interaction can positively influence a psychotherapeutic decision. I,III,IV,V I,IV,V I,II,IV II,IV,V
34
Psychotherapeutic processes deal with psychological problems, ranging From mild ones like a depressed mood, to more subtle ones like interpretation of dreams to more controversial problems like dissociative identity disorder. Denied emotions (not admitting or voicing one ... thoughts. It is very difficult to gauge emotional honesty. Dreams often, are indicative of emotions that remain unexpressed.
35
Psychotherapeutic processes deal with psychological problems, ranging From mild ones like a depressed mood, to more subtle ones like interpretation of dreams to more controversial problems like dissociative identity disorder. Denied emotions (not ... psychotherapists when pursuing their objectives. the inability to understand the unconscious can divert psychotherapists from their objectives.
36
Each of nine persons. P, Q, R, S, T, U, V, W and X, lives in a different flat in an apartment building, which has six floors (excluding the ground floor, which is used only for parking) and three flats on each floor. The three flats on each floor are in a row ... cannot be true? W lives on the third floor. Q lives on the third floor. R lives on the second floor. P lives on the second floor.
37
Each of nine persons. P, Q, R, S, T, U, V, W and X, lives in a different flat in an apartment building, which has six floors (excluding the ground floor, which is used only for parking) and three flats on each floor. The three flats on each floor are in a row and ... is living on the same floor as X. Q is living on the second floor. P is living on the third floor. W is living alone on his floor.
Each of nine persons. P, Q, R, S, T, U, V, W and X, lives in a different flat in an apartment building, which has six floors (excluding the ground floor, which is used only for parking) and three flats on each floor. The three flats on each floor are in a row and no ... X lives. If Q lives on the third floor, then how many combinations of persons could live on the second floor? $8$ $6$ $5$ $7$