Consider a sequence of numbers $\style{font-family:'Times New Roman'}{a_1,a_2,\;a_3,......,\;a_n}$ where $a_n=\frac1n-\frac1{n+2}$ for each integer $\style{font-family:'Times New Roman'}{n>0}$. What is the sum of the first 50 terms?
$ \underset{n\;times}{\underbrace{a+a+a+...+a}=a^2b} $ and $ \underset{m\;times}{\underbrace{b+b+b+...+b}=ab^2} $ , where $a$, $b$, $n$ and $m$ are natural numbers. What is the value of $ \left(\underbrace{m+m+m+...+m}_{n\;times}\right) $ $ \left(\underbrace{n+n+n+...+n}_{m\;times}\right) $?
For non-negative integers, a, b, c, what would be the value of a+b+c if log a + log b + log c = 0?
Given that $\frac{\log\;P}{y-z}=\frac{\log{\displaystyle\;}{\displaystyle Q}}{z-x}=\frac{\log{\displaystyle\;}{\displaystyle R}}{x-y}=10$ for $\style{font-family:'Times New Roman'}{x\neq y\neq z,}$ what is the value of the product PQR?
Consider the following sentences:
All benches are beds. No bed is a bulbs are lamps.
Which of the following can be inferred?
I. some beds are lamps.
ii. some lamps are beds.
If the radius of a right circular cone is increased by 50%, its volume increases by
The following sequnce of numbers is arranged in increasing order: 1,x ,x, x, y, y, 9, 16, 18. Given that the mean and median are equal, and also equal to twise the mode, the value of y is
Students applying for hostel rooms are allotted rooms in order of seniority. Students already stayning in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.
Given the data below, which room will Ajit stay in ?
The last digit of (2171)^{7} + (2172)^{9} + (2173)^{11} + (2174)^{13} is
Two machine M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R, S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects, Job Q on 3 objects, Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?
The bar graph below shows the output of five carpenters over one month , each of whom made different items of furniture : chairs, tables, and beds.
Consider the following statements.
i. The number of beds made by carpenter C2 is exactly the same as the number of tables made by carpenter C3.
ii.The total number of chairs made by all carpenter is less than the total number of tables
Which one of the following is true?
Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.
Proposition : If a card has an even value on one side, then its opposite face is red.
The cards which MUST be turend over to verify the above propositon are
What is the value of x when $ \style{font-family:'Times New Roman'}{\begin{array}{l}81\times\left(\frac{16}{25}\right)^{x+2}\div\left(\frac35\right)^{2x+4}=144\\\end{array}}$?
Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is
A map shows the elevations of Darjeeling, Gangtok, Kalimpong, Peeling, and Siliguri. Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok.
Which of the following statements can be inferred from the paragraph above?
i. Peeling is at a higher elevation than Kalimpong.
ii. Kalimpong is at a lower elevation than Darjeeling.
iii. Kalimpong is at a higher elevation than Siliguri.
iv. Siliguri is at a lower elevation than Gangtok.
P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?
Budhan covers a distance of 19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walk the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is
The points in the graph below represent the halts of a lift for durations of 1 minute, over a period of 1 hour.
Which of the following statements are correct?
i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period
ii. The elevator stays on the fourth floor for the longest duration over the one hour period
Which product contributes the greatest fraction to the revenue of the company in that year?
If $ \mathrm f\left(x\right)=2x^7+3x-5 $, which of the following is a factor of $\mathrm{f}\left(x\right)$ ?
In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.
Choose the most appropriate set of words from the options given below to complete the following sentence.
_________ ___________ is a will, _________ is a way.
$(x\%\mathrm{of}y)+(y\%\mathrm{of}x)$ is equivalent to .
The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:
A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?
Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
If ROAD is written as URDG, then SWAN should be written as:
A function f(x) is linear and has a value of 29 at x = –2 and 39 at x = 3. Find its value at x = 5.
The exports and imports(in crores of Rs.) of a country from the year 2000 to 2007 are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest ?
Choose the most appropriate equation for the function drawn as a thick line, in the plot below.
The head of a newly formed government desires to appoint five of the six selected members P,Q,R,S,T, and U to portfolios of Home, Power, Defense, Telecom, and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power or Telecom, then she must get the other one. T insists on a portfolio if P gets one. Which is the valid distribution of portfolios ?
Mr. Vivek walks 6 meters North-east, then turns and walks 6 meters South-east, both at 60 degrees to east. He further moves 2 meters South and 4 meters West. What is the straight distance in metres between the point he started from and the point he finally reached?
Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is the probability that the third card is a king?
The given question is followed by two statements; select the most appropriate option that solves the question Capacity of a solution tank A is 70% of the capacity of tank B. How many gallons of solution are in tank A and tank B? Statements: (I) Tank A is 80% full and tank B is 40% full (II) Tank A if full contains 14,000 gallons of solution.
How many four digit numbers can be formed with the 10 digits 0,1,2,….9 if no number can start with 0 and if repetitions are not allowed?
Read the following table giving sales data of five types of batteries for years 2006 to 2012:
Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
84
2008
96
105
135
2009
150
2010
2011
60
165
45
120
2012
115
85
160
100
145
Out of the following which type of battery achieved highest growth between the years 2006 and 2012?
There are 16 teachers who can teach Thermodynamics (TD), 11 who can teach Electrical Sciences (ES), and 5 who can teach both TD and Engineering Mechanics (EM). There are a total of 40 teachers. 6 cannot teach any of the three subjects, i.e. EM, ES or TD. 6 can teach only ES. 4 can teach all three subjects, i.e. EM, ES and TD. 4 can teach ES and TD. How many can teach both ES and EM but not TD?
If y = 5x^{2} + 3, then the tangent at x = 0, y = 3
A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?
Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct?
The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?
One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?
The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)
In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ____ years.
The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate?
The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram?
X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?
10% of the population in a town is HIV^{+}. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV^{+} individuals 95% of the time, and HIV^{−} individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _______
A number is as much greater than 75 as it is smaller than 117. The number is:
X and Y are two positive real numbers such that $2X+Y\le 6andX+2Y\le 8$. For which of the following values of ( X ,Y) the function f( X ,Y)=3X+ 6Y will give maximum value?
If $\left|4X-7\right|=5$ then the values of $2\left|X\right|-\left|-X\right|$ is:
Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011.
In 2011, which of the following two categories have registered increase by same percentage?
A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level.
Abhishek is elder to Savar. Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements?
The cost function for a product in a firm is given by 5q^{2}, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x - 0.1x^{2} where y is the height of the arch in meters. The maximum possible height of the arch is
Given the sequence of terms, AD CG FK JP, the next term is
Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged
An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
If Log(P)=(1/2) Log(Q)=(1/3) Log (R), then which of the following option is TRUE?
P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:
A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?
A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to them equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?
25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
If 137 + 276 = 435 how much is 731 + 672?
5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?
Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1^{st} January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
In what order were they born (oldest first)?