# Recent questions tagged cat2011

1 vote
1
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if$n$is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined
2
Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding $\text{GCD}.$ If $90$ of the numbers written by Vishal were prime, how many numbers did Vaibhav write? $6$ $8$ $10$ Cannot be determined
3
On a plate in the shape of an equilateral triangle $\text{ABC}$ with area $16\sqrt 3\;\text{sq cm}$, a rod $\text{GD}$, of height $8\:\text{cm}$, is fixed vertically at the centre of the triangle. $\text{G}$ ... the area of the triangle $\text{CGD}\:\text{(in sq cm)}$. $3 \sqrt {19}$ $4 \sqrt {19}$ $12 \sqrt {3}$ None of these
4
Mohan is a carpenter who specialises in making chairs. For every assignment he undertakes, he charges his commision and cost. His commission is fixed and equals $₹560$ per assignment while the cost equals $₹2n^2$ where, $n$ is the total number of chairs he makes. If for a certain assignment the ... respectively. $13\:\text{and}\:19$ $13\:\text{and}\:20$ $14\:\text{and}\:19$ $14\:\text{and}\:20$
5
Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible? $2475$ $4950$ $9900$ $1000$
6
The values of the numbers $2^{2004}\:\text{and}\:5^{2004}$ are written one after another. How many digits are there in all? $4008$ $2003$ $2004$ None of these
7
In the figure alongside, $\text{O}$ is the centre of the circle and $\text{AC}$ is the diameter. The line $\text{FEG}$ is tangent to the circle at $\text{E}$. If $\angle \text{GEC}= 52^{\circ}$, find the value of $\angle e+\angle c.$ $154^{\circ}$ $156^{\circ}$ $166^{\circ}$ $180^{\circ}$
8
Auto fare in Bombay is $₹\:2.40$ for the first $1\:\text{km}$,$₹\:2.00$ per km for the next $4\:\text{km}$ and $1.20$ for each additional km thereafter. Find the fare in rupees for $k\:\text{km}(k\geq5)$. $2.4k+1.2(2k-3)$ $10.4+1.2(k-5)$ $2.4+2(k-3)+1.2(k-5)$ $10.4+1.2(k-4)$
9
One morning, Govind Lal the owner of the local petrol bunk, was adulterating the petrol with kerosene. He had two identical tanks- the first was full of pure petrol while the second was empty. First he transferred an arbitrary amount of petrol from the first tank into the second and then replaced the petrol removed ... of $25$% ? $42\frac{6}{7}\%$ $66\frac{2}{3}\%$ $83\frac{1}{3}\%$ $100\%$
10
One morning, Govind Lal the owner of the local petrol bunk, was adulterating the petrol with kerosene. He had two identical tanks- the first was full of pure petrol while the second was empty. First he transferred an arbitrary amount of petrol from the first tank into the second and then ... following can be the concentration of petrol in the second tank? $50\%$ $60\%$ $66\frac{2}{3}\%$ $80\%$
11
In the figure alongside, $\triangle \text{ABC}$ is equilateral with area $\text{S. M}$ is the mid-point of $\text{BC and P}$ is a point on $\text{AM}$ extended such that $\text{MP = BM}$. If the semi-circle on $\text{AP intersects CB}$ extended at $\text{Q}$ ... is true? $\text{T} = \sqrt{2}\; \text{S}$ $\text{T = S}$ $T = \sqrt{3}\; \text{S}$ $\text{T = 2S}$
1 vote
12
Let $\text{S}_n$ denote the sum of the squares of the first $n$ odd natural numbers. If $\text{S}_n=533n,$ find the value of $n$. $18$ $20$ $24$ $30$
13
There are two water drums in my house whose volumes are in the ratio $1: 5$. Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by the time I return from my college, i.e., at $1: 30$ pm, the smaller drum would just be full. ... , when was the smaller drum full? $1 : 18\;\text{pm}$ $1 : 28\;\text{pm}$ $1 : 26\;\text{pm}$ Cannot be determined
14
Two cars $\text{A}$ and $\text{B}$ start from two points $\text{P}$ and $\text{Q}$ respectively towards each other simultaneously. After travelling some distance, at a point $\text{R}$, car $\text{A}$ develops engine trouble. It continues to travel at $\text{2/3 rd}$ of its usual speed to meet car ... $\text{A}$ and $\text{B}$. $4:1$ $2:1$ $3:1$ $3:2$
15
$\text{A}$ is standing $5$ m East and $4$ m North of a point $\text{P}$ while $\text{B}$ is standing $15$ m East and $24$ m North of $\text{P. A}$ walks at a speed of $1.4$ m/s while $\text{B}$ walks at a speed of $2.1$ ... , then which of the following is true of the distance of closest approach $d_1\text{'}$ between them? $d_1>5$ m $d_1<5$ m $d_1=5$ m Cannot be determined
16
$\text{A}$ is standing $5$ m East and $4$ m North of a point $\text{P}$ while $\text{B}$ is standing $15$ m East and $24$ m North of $\text{P. A}$ walks at a speed of $1.4$ m/s while $\text{B}$ walks at a speed of $2.1$ m/s. If $\text{A}$ ... walking towards each other and finally meet at a point $\text{Q,}$ then find the distance $\text{PQ}.$ $13$ m $12\sqrt 3$ m $15$ m $13\sqrt 2$ m
17
Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$
18
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these
19
Rekha drew a circle of radius $2\;\text{cm}$ on a graph paper of grid $1\;\text{cm}\times1\;\text{cm}$. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained ... than the correct value, In the above question what is the minimum possible value of $d?$ $4.56$ $5.56$ $6.56$ $3.56$
20
Rekha drew a circle of radius $2\;\text{cm}$ on a graph paper of grid $1\;\text{cm}\times1\;\text{cm}$. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was $d\:\text{sq cm}$. less than the correct value, then find the maximum possible value of $d?$ $6.28$ $7.28$ $7.56$ $8.56$
21
Study the following table and answer the questions that follow. Disbursement of Loans by Various Banks from $1982$ to $1986$ (In $₹$ ... the average disbursement of loans record the highest percentage increase over that of the previous year? $1984$ $1986$ $1985$ $1983$
22
Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.
23
Study the following table and answer the questions that follow. Disbursement of Loans by Various Banks from $1982$ to $1986$ (In $₹$ ... years. Which of the banks qualify as on the year $1986?$ $\text{A}$ $\text{B}$ $\text{C}$ None of these
24
Study the following table and answer the questions that follow. Disbursement of Loans by Various Banks from $1982$ to $1986$ (In $₹$ ... for that year the lowest? $\text{C}, 1986$ $\text{B}, 1984$ $\text{C}, 1985$ $\text{A}, 1985$
25
Each of the following pie charts gives the percentage split up of the total time spent by a certain student towards preparation of CAT $2005$ The number of areas of study for which the critical analysis was done at friends’ place alone is at most $2$ $3$ $5$ $6$
26
Each of the following pie charts gives the percentage split up of the total time spent by a certain student towards preparation of CAT $2005$ If atleast $5\%$ of the time spent on each area of study was spent on solved examples of that area, then the time spent on solved examples in any area of study, ... spent on that area of study, is at most. $21\frac{1}{6}\%$ $30\%$ $38\frac{1}{3}\%$ $55\%$
27
When Munna Bhai joined the university of South Ghatkopar for his M.S., Mr. Irani, his professor, asked him to prove his calibre in a test conducted for the entire class. The class comprised of exactly $10$ students. The test contain exactly $10$ multiple choice ... $10$ questions- I through X. Who are the jigris of Chinky? Niran and Rahul Rahul and Sastry Sastry and Lucky Cannot be determined
28
When Munna Bhai joined the university of South Ghatkopar for his M.S., Mr. Irani, his professor, asked him to prove his calibre in a test conducted for the entire class. The class comprised of exactly $10$ students. The test contain exactly $10$ multiple choice type ... the $10$ questions- I through X. Who among the following is not the jigri of any of the ten students? Jassi Praveen Lucky Rahul
29
When Munna Bhai joined the university of South Ghatkopar for his M.S., Mr. Irani, his professor, asked him to prove his calibre in a test conducted for the entire class. The class comprised of exactly $10$ students. The test contain exactly $10$ multiple choice type ... for the $10$ questions- I through X. Munna is the jigri of Sastry and Ritesh Niran and Praveen Lucky and Rahul Jassi an Lucky
30
Each of the following pie charts gives the percentage split up of the total time spent by a certain student towards preparation of CAT $2005$ At the most what percentage of total time was spent on test taken in VA and LA? $10\%$ $20\%$ $66\frac{2}{3}\%$ $100\%$
31
Sentences given in the question, when properly sequenced form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical oder of sentences from among the four given choices to construct a coherent paragraph. Paucity of serious thought is no surprise in the government, but ... policy only? SC/ST's deserve them more. $\text{ABCD}$ $\text{CDBA}$ $\text{DABC}$ $\text{ACBD}$
32
Given below are sentences, each using the question word different ways. Identify the sentence which uses the question word in a grammatically incorrect manner. Happen Accept it, mistakes will happen It happened on a system that worked I promise nothing will happen to you If so happens I’m going your way
33
In the following question, four different sentences are given. Choose the option that contains the grammatically incorrect sentence/s. He is feeling that this relocation is nothing but the kick upstairs. Consensus is now emerging at our state and national levels. A more and more rigorous circle is ... unlikely to escape. It happened up on a system that worked. I, IV I, II, III I, III, IV I, III
34
The question given below consists of a sentence which is divided into four parts, numbered (A) through (D). Only one part in the sentence is not acceptable in standard written English. Identify that part in the sentences which contains the error. Her acceptance of speech Was well received Eliciting thunderous applause At several points
35
Each question consists of sentences, which have one or two blanks, each blank indicating that something has been omitted. Below each sentence are four numbered words or sets of words labelled (A) through (D). Choose the set of words that, when ... not compare things explicitly, but suggests, a likeness between them. sarcastic...unfair blatant...overt metaphorical...implied sanguine...inherent
36
In the given question, all the sentences except one sentence,when properly sequenced form a coherent paragraph. Each sentence is labeled with a letter. Choose the sentence which does not form a part of the paragraph from among the four given choices. The revolution called Human Relations is quieter ... into hired hands subject to the orders of managers. $\text{A}$ $\text{B}$ $\text{C}$ $\text{D}$
37
Sentences given in the question, when properly sequenced form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the four given choices to construct a coherent paragraph. Overcoming the handicap of crushing poverty, he has had a ... controversy even found its way to the court. $\text{ACDB}$ $\text{BDAC}$ $\text{ACBD}$ $\text{BACD}$