You Are On Multi Choice Question Bank SET 4386
219301. If $$f(x)=x^3-4x+p$$ , and f(0) and f(1) are of opposite signs, then which of the following is necessarily true[CAT 2004]
219302. Suppose n is an integer such that the sum of digits on n is 2, and $$10^{10} < n < 10^{11}$$. The number of different values of n is
219303. A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?[CAT 2004]
219305. N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?[CAT 2004]
219306. A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post then how far (in metres) is son standing form his father?
219308. Each family in a locality has at most two adults, and no family has fewer than 3 children.Considering all the families together, there are adults than boys, more boys than girls, and more girls than families.Then the minimum possible number of families in the locality is
219309. Let $$C$$ be a circle with centre $$P_0$$ and $$AB$$ be a diameter of $$C$$. Suppose $$P_1$$ is the mid point of the line segment $$P_0B$$,$$P_2$$ is the mid point of the line segment $$P_1B$$ and so on. Let $$C_1,C_2,C_3,...$$ be circles with diameters $$P_0P_1, P_1P_2, P_2P_3...$$ respectively. Suppose the circles $$C_1, C_2, C_3,...$$ are all shaded. The ratio of the area of the unshaded portion of $$C$$ to that of the original circle is
219310. Consider the sequence of numbers $$a_1, a_2, a_3$$....... to infinity where $$a_1 = 81.33$$ and $$a_2 = -19$$ and $$a_j = a_{j-1} - a_{j-2}$$ for $$j > 3$$. What is the sum of the first 6002 terms of this sequence?
219311. A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is $$\pi$$ r during the first 30 seconds, $$\pi$$ r/2 during next one minute, $$\pi$$ r/4 during next 2 minutes, $$\pi$$ r/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
219312. Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has
219313. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be?
219314. In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
219315. On a semicircle with diameter AD, chord BC is parallel to the diameter. Further; AD and BC are separated by 2cm, while AD has length 8. What is the length of BC?
219316. A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle? 
219317. 
In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If angle CBE = 65°, then what is the value of angle DEC?
219319. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is
219321. Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?
219322. In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts.Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?
219324.
Directions for the following four questions: Answer the questions on the basis of the information given below.The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves the space blank. The scanner output read as follows:
In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0) / 5 = 3.6. Some additional facts are also known about the students’ grades. These are(i) Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.(ii) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.(iii) Tara received the same grade in exactly three courses.What grade did Preeti obtain in Statistics?
219328.
Directions for the following four questions: Answer the questions on the basis of the information given below.
The data points in the figure below represent monthly income and expenditure data of individual members of the Ahuja family, the Bose family, the Coomar family, and the Dubey family.The X axis represents Expenditure and the Y axis represents the Income of the individual members.For these questions, savings is defined as Savings = Income - ExpenditureWhich family has the lowest average income?
219332.
Directions for the following four questions: Answer the questions on the basis of the information given below.
Prof. Singh has been tracking the number of visitors to his homepage? His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to.To which country does University 5 belong?
219335. Visitors from how many universities from UK visited Prof. Singh's homepage in the three days?
219340.
Directions for the following four questions: Answer the questions on the basis of the information given below.A study was conduced to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country.
Which of the following pairs of countries are most dissimilar?
219343. Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the odd one out?
219344.
Directions for the following four questions: Answer the questions on the basis of the information given below.
Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each games. In each diagram, the three outer triangles communicate the number of runs scored by the three top scores from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournaments; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.For how many Indian players is it possible to calculate the exact M-index?
219348.
Directions for the following four questions: Answer the questions on the basis of the information given below.Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation. The following five facts about the participants are given.(a) The number of labour experts in the camp was exactly half the number of experts in each of the three other categories.(b) Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.(c) None of the continents sent more than three experts in any category.(d) If there had been one less Australasian expert, then the Americas would have had twice as many experts as each of the other continents.(e) Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.Which of the following combinations is NOT possible?
219349. If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?
219350. Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?i. At least oneii. At most two
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