What is remainder when a number '$$x$$' is divided by 9?
I) The remainder left when '$$x$$' divided by 3 is zero.
II) The sum of the digits in '$$x$$' is 3
AP ICET 2021 Question Paper Shift-1 (17th Sep)
In the following questions, a question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions.
What is the distance between the points 'A' and 'B' ?
I) The velocity of the stream is 2Km/hr and the speed of the boat in still water is 15Km/hr.
II) The boat takes 30 hours to travel down stream from point 'A' to point 'B' and coming back to point 'C' which is in the midway between 'A' and 'B'
What is the present age of Anil?
I) Five years ago, Anil 's age was twice that of his son's age?
II) Five years hence, the ratio of the ages of Anil and his son will be 12 : 7
What is that two digit number?
I) The sum of the two digits of that number is 12
II) The difference between the two digits of that number is 6
What is the profit earned on selling the article '$$x$$'?
I) The article '$$x$$' is sold for Rs. 5100 after giving a discount of 15%.
II) If the article '$$x$$' is sold for the marked price, the profit could be 20%.
A, B, C, D, E and F are sitting around a circle facing its centre. Who is sitting at the immediate right of B?
I) 'A' is facing 'D'. Only 'C' is between 'A' and 'B'. 'F' is between 'E' and 'A'.
II) 'F' is sitting on the immediate left to 'E'. Only 'D' is between 'B' and 'E'. 'C' is not adjacent to F.
Among six persons A, B, C, D, E, F who is the tallest ?
I) 'C' is taller than only two persons. 'B' is taller than 'A' and 'E' is taller than only 'F'.
II) A' is shorter than only two persons. 'E' is taller than 'F' but shorter than 'C'. 'C' is shorter than 'A' and 'B' is shorter than 'D'.
What is the rate of interest 'R'?
I) The compound interest on Rs.3 500 in 2 years at the rate 'R' is equal to the simple interest in 4 years on Rs.1855
II) In 7 years, Rs. 2.300 at rate the 'R' becomes Rs. 4232 by simple interest.
What is Nitin's rank from the top, in a class of 40 students?
I) There are 10 students between Nitin and Naveen.
II) Naveen is twentieth from the top.
How many toys were sold on Monday?
I) It was 10% more than the number of toys sold on the previous day
II) On Sunday every third visitor to the shop bought a toy and there were 1500 visitors on Sunday
What was his average speed?
I) He travelled the last $$\frac{1}{4}$$ of the distance at 6 Kmph.
II) He travelled the first $$\frac{1}{4}$$ of the distance at 5 Kmph.
What is the arithmetic rnean of the real numbers p, q, r, s ?
I) p + q + s =25 + p
II) 5(r + s + p) = 17-5q
What percent of 45 is '$$x$$' ?
I) '$$x$$' is 40 percent of 135
II) 9 percent of '$$x$$' is less than 5
PQRS is a square with sides of length 6 and point 'A' is on the side QR. What is the area of the triangle PAQ?
I) $$AP > 6$$
II) 'A' is in the midpoint of QR.
What is the age of 'P' ?
I) 'P' is older than 'Q'
II) The age of 'Q' is 20 years
Is the integer 'n' divisible by 35?
I) 'n' is divisible by 14
II) 'n' is divisible by 15
What is the cost price of a chair?
I) If a discount of 25% were given, the selling price would have been less by Rs. 50.
II) Two successive discount of 5% each were given.
Ganesh and Gopal each caught some fish in a fish tank. Who caught more fish?
I) After Gopal stopped fishing, Ganesh continued fishing for another 15 minutes.
II) Ganesh caught $$\frac{2}{3}$$ times as many fish as Gopal caught.
What is the sum of the two positive integers?
I) One of the integer is 17.
II) The LCM of the integers is 51.
What is the $$3^{rd}$$ number of eight consecutive integers?
I) Their product is divisible by 720
II) The sum of all the eight integers is 84
Note :
In each of the following questions (from 21 to 30), a sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled by the correct answer from the four given options to complete the sequence without breaking the pattern.
BCE : EGK :: KMQ : ________
$$1000 : 512 :: .............. : 343$$
10 : 99 :: 9 : _______
AFR : ZEQ :: EMG : _____
8 : 81 :: 9 : _____
LOSE : OSVI : : GAIN : _______
HARD : DONZ : : SOFT : _________
78 : 225 :: 69 : __________
54 : 96 :: 63 : ________
34 : 1849 :: 23 :_____________
Pick the odd thing out in the following.
Note: The following question follows a definite pattern. Observe the same and fill in the blank with suitable answer.
39, 155, 399, 1463, __________
ABS, CD25, EF61, GH113 , _______
24, 120, 336, 1320 , ________
6, 15, 35, 77, 143, _______
CW, EU, GS, KO, ________
(8,24), (48,120), (168,288), (360,528), _________
3D5, 5F7, 7 I 11, 11L13, _________
6, 35, 143, 323, _________
ACE, CFI, EIM, GLQ, ________
E, H, L, R, __________
Note:
The following table shows the number (in thousands) of toys of types P, Q, R, S and K manufactured by company during the years 2016 to 2020. Study the table carefully and answer questions 46 to 48
What was the approximate percentage of increase in the manufacture of type 'S' toys from 2016 to 2020?
The type of toy which recorded continuous growth in the manufacture during the given period is
The approximate percentage of increase in the manufacture of all toys from 2016 to 2020
Note:
The Pie charts given below represent allocations given to various items by two families 'A' and 'B'. Study these charts carefully and answer questions.
what is the approximate percentage of allocation by the family 'A' on recreation
The ratio of the allocations by the family 'B' on travel to that on other items is
What is the ratio of the allocation on travel to that on recreation by the family 'A'
What is the percentage of allocation made by the family 'B' on Food?
What is the ratio of allocation on food to that on travel by the family 'B'
Note:
120 students of a class participated in 3 events A, B, and C as follows: $$9x$$ students participated in event 'A'. $$11x$$ students in 'B'. $$12x$$ students in 'C'. $$2x$$ students in both 'A' and 'B'. $$3x$$ students in both 'B' and 'C', $$4x$$ students in both 'C' and 'A' and '$$x$$' students in all the 3 events. The number of students who participated in the event 'C' alone is 24. Based on this information answer questions.
The number of students who did not participate in any of the 3 events 'A', 'B', and 'C' is
The number of students who participated either in the event 'A' or in the event 'C' but not in the event 'B'. is
Note:
Each of the questions from 56 to 60 has different coding pattern. Identify the pattern and answer questions
In a code the word 'PERSON' is coded as 214 and the word 'MASTER' is coded as 164, then in the same code the word 'BENGAL' is coded as.
In a certain code the word 'PRINCE' is coded as 'DFJOQS' and the word 'MASTER' is coded as 'FSTUNB' then in the same code the word 'SOCIAL' is coded as.
In a certain code the word 'MANGO' is coded as 'JDKJL'. then in the same code the word 'GRAPE' is coded as.
In a certain code, the word 'BRAIN' is coded as 'PKCTD', then in the same code the word 'HEART' is coded as
In a certain code the word 'TEACHER' is coded as 'VULGOUX' then in the same code 'STUDENT' is coded as,
Note:
Each of the questions has different coding pattern. Identify the pattern and answer questions.
If 'PROFIT' is coded as 'RTQHKV', then in the same code 'EIGHT' is coded as
If 'FAVOUR' is coded as 'ROUVAF' and 'PAPER' is coded as 'REPAP', then in the same code 'CERTAIN' is coded as,
If 'RANGER' is coded as 'ARGNRE', then in the same code 'CHAIRS' is coded as
If 'ROAD' is coded as 'GDRU', then in the same code. 'BEAT', is coded as
If 'SWEET' is coded as 'QUCCR', then in the same code, 'MEALS' is coded as
For the following questions answer them individually
If $$9^{th}$$ February 2012 was Thursday, the day of February 19, 2016 was
The time between 2 and 3 O'clock at which the minute hand and the hour hand in a clock are in the same straight line but in opposite directions, is
A clock is set right at 8.00 am on 1-1-2018. The clock gains 15 min in 24 hours. The time(nearly) on the clock when the actual time is 10.00 am on 04-01-2018 is
X' is the father of 'Y' and 'Z' is the son of 'W'. 'R' is the brother of 'X' and 'Y' is the sister of 'Z'. Then 'W' is related to 'R' as
'Y' to 'Z' is $$\frac{4}{5}$$ th of the maximum speed allowed. A car departs from the station. 'Y' at 2.00 pm and arrived the station 'Z' at 7.30 pm. A train departs from station 'Y' at 2.00 pm and arrived the station 'Z' at 10.00 pm. By how much the car's speed is more than the maximum allowed speed of the train, if the car was stopped 30 minutes for lunch break?
Anil started from his house for school 't' minutes later then his normal time and travelled with $$\frac{4}{3}$$ of the usual speed to arrive at the school 't' minutes early. Next day if he started 't' minutes earlier than the previous day and travelled with $$\frac{8}{11}$$ of his usual speed, then he would have reached his school
In a group of boys sitting in a row, Ramesh is $$8^{th}$$ from the left and Mohan is $$11^{th}$$ from the right. If Ramesh is fourteenth from the left when they interchange their places, then the position of Mohan now from the right is
In a code language if $$‘+’$$ means $$‘x’, ‘x’$$ means $$‘-’, ‘-’$$ means $$‘\div’$$ and $$‘\div’$$ means $$‘+’$$, then $$2 \div 4 + 8 - 16 \times 32 \div 64 \times 128 \div 256 =$$
If 3 * 1 = 20, 6 * 1 = 50 and 2 * 6 = - 40 then 5 * 8 =
If B stands for $$‘>’, ‘C’$$ stands for $$‘≮’ , ‘D’$$ stands for $$‘=’, ‘E’$$ stands for $$‘≯’ , ‘F’$$ stands for $$‘<’$$ and $$‘x' , ‘y’$$ and $$‘z’$$ are real numbers, then (4$$x$$ F 5y) and (5y E 3z) $$\Rightarrow$$
Choose the correct meaning of the word given:
discordant
Entreat
Implore.
Disclose
For the following questions answer them individually
Fill in the blank by choosing the correct meaning of the word given:
To corner a market means to _____________ a market.
Choose the correct meaning of the word given:
momentous
That which is sure to happen
Judicious
Axiomatic
Paragon
A collector of ancient relics
To deviate from focus
A remedy to counter the evil effects of poison
Latent
For the following questions answer them individually
Fill in the blank by choosing the correct meaning of the word given:
The outgoing CEO was very friendly with the press and it really _____ him even for what he did not achieve.
Choose the appropriate answer:
D.C.F. stands for
The contingency theory stresses on the importance of
ISDN stands for
A sentence used to check transmission by a terminal
Surge price in services such as airlines or aggregate cab services are generally restored due to
'kbps' stands for
A blue collar job is one which involves working
"To be on the same page" means
A financial instrument that contains a written agreement to repay the amount at an agreed time is
Which of the below is not an indirect tax?
Usually our purchasing power increases because of
A method used by fraudsters to capture customer's personal or account information of credit card is called
A senior official appointed by RBI to handle and redress complaints against deficiency in certain banking services is known as
In business parlance. 'Merchandise' means
'Overheads' in accounts of a business organization refer to
Fill in the blank by choosing the appropriate answer:
Lack of civic sense is the root cause _____ all the problems of sanitation.
In ancient India, Indian merchants had been engaged in overseas business _______ centuries.
Applications for the post should be received ________ April 25th.
He is a man who always stands ______ his words.
She ___________ working at the college as soon as she gets her US visa.
It was raining ________ by the time we finished the game.
I ___________ never seen such a movie before.
The manager wanted to bring _____________ a real change in the company.
Choose the appropriate answer:
The streets were flooded when the pipeline bursted.
1 2 3 4
identify the error
He broke a antique and expensive vase.
1 2 3 4
identify the error
It is not very warm today
Put a question tag.
For the following questions answer them individually
Fill in the blank by choosing the appropriate answer:
We are committed _________ learning grammar.
Choose the appropriate answer:
Change the sentence into passive voice 'Read the story carefully’.
The teacher said. “Have you done your homework?”
Change into indirect speech.
Fill in the blank by choosing the appropriate answer:
I prefer sleeping under a roof ______ sleeping outdoors
Let us _________ our differences and work for our nation
Much of what he says ______ untrue.
The meaning of 'a herculean task' is ___________.
My little sister is afraid ________ dogs.
I _____ your company ____ his.
Read the passage below and choose the correct answer for questions 126-130
The sun is the most direct source of energy. It powers the flow of wind and water cycle and sustains life. Plants use this energy to synthesize carbohydrates from simple substances like carbon dioxide and water. All the food is derived from the process of photosynthesis. In fact, energy by which all animals including human beings live is generated by the oxidation of the food produced by the plants. The sun contains in its core hydrogen nuclei moving at very great speeds. Whenever these nuclei collide and fuse to form a nucleus of heavier element it results in nuclear reactions. These reactions generate tremendous amount of energy. It is this energy that power sun.
The sum emits lights of different wavelengths. If sunlight is passed through a prism each of these wavelengths is refracted by a different amount. Violet has the shortest wavelength and red has the longest. The wavelength of green is midway between that of violet and red. Light with wavelength shorter than that of violet is called ultraviolet light. Light with wavelength longer than that of red light is called infrared light. About one third of the light from the sun is infrared. We know that nuclear reactions that go on in the interior of the sun liberate a large amount of energy. Nuclei of deuterium, which is the heavier isotope of hydrogen, collide in the sun's interior to produce helium. The energy liberated in these reaction fires the sun, which, in turn, emits lights of different wavelengths. Of these wavelengths, it is the infrared wavelengths that heat up the earth. The reaction in which the hydrogen in the sun is converted into helium is called a fusion reaction.
Light with wave length shorter than that of violet is called
How are carbohydrates synthesized?
What is fusion reaction?
What is the main idea of the first paragraph?
What is deuterium?
Read the passage below and choose the correct answer for questions 131-135
"A little learning is a dangerous thing" - when Alexander Pope wrote this famous line he had in mind contemporary poetasters, versifiers, and critics who made themselves ridiculous on account of their shallow and superficial knowledge. But what was said about these people has a ring of universal truth. In every walk of life, be it arts or literature, science or politics, engineering or economics, law or administration, incomplete and superficial knowledge always leads to dangerous consequences. An ill-educated teacher will misguide the students. An incompetent surgeon would play with the lives of his patients. An ill-trained solider will become a danger to his comrades rather than his enemies. A lawyer without a thorough knowledge of law would min his clients, similarly, an inefficient engineer will build bridges which may fall under the weigl1t of the vehicles on it. Therefore, we cannot rely on persons who are not proficient in their subject. Such persons are a danger to themselves and to others also. They never realize their short comings and hence make no progress. A man of little learning is more prone to be conceited than a really learned person, for the latter regards himself as a mere child gathering pebbles on the shores of the ocean of knowledge.
What is the meaning of the word ridiculous?
What is not a walk of life?
What leads to dangerous consequences?
Who will misguide?
Who is a mere child gathering pebbles on the shore of the ocean of knowledge?
Read the passage below and choose the correct answer for questions 136-140
As long as 340 BC, the Greek philosopher Aristotle in his book 'On the Heavens', was able to put forward two good statements for believing that the earth was a round sphere rather than a flat plate. First he realised that eclipses of the moon were caused by the earth coming between the sun and the moon. The earth's shadow on the moon was always round, which would be true only if the earth was spherical. If the earth had been a flat disc, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a time when the sun was directly under the centre of the disc. Second, the Greeks knew from their travels that the North star appeared lower in the sky when viewed in the South than it did in the more northerly regions (since the North star lies over the North pole), it appears to be directly above an observer at the North pole, but to someone looking from the equator, it appears to lie just at the horizon, From the difference in the apparent position of the North star in Egypt and Greece, Aristotle estimated the distance around the earth was 400,000 stadia.
Aristotle belonged to which country?
What does put forward mean?
The Greeks found that the North star appeared lower in the sky ____________
The North star appears to be directly above an observer ________
The meaning of the word elongated is
Read the passage below and choose the correct answer for questions.
The Hyperloop is a proposed mode of passenger and freight transportation, first used to describe an open source vactrain design released by a joint team from Tesla and SpaceX. Hyperloop is described as a sealed tube or system of tubes with low air pressure through which a pod may travel substantially free of air resistance or friction. The Hyperloop could potentially convey people or objects at airline or hypersonic speeds while being energy efficient compared with existing high-speed rail systems. This, if implemented, may reduce travel times compared to train and airplane travel over distances of under approximately 1,500 kilometers (930 miles).
Elon Musk first publicly mentioned the Hyperloop in 2012, His initial concept incorporated reduced-pressure tubes in which pressurized capsules ride on air bearings driven by linear induction motors and axial compressors. The Hyperloop Alpha concept was first published in August 2013, proposing, and examining a route running from the Los Angeles region to the San Francisco Bay Area, roughly following the Interstate 5 corridor. The Hyperloop Genesis paper conceived of a hyperloop system that would propel passengers along the 350-mile (560 km) route at a speed of 760 mph (1,200 km/h), allowing for a travel time of 35 minutes, which is considerably faster than current rail or air travel times. Preliminary cost estimates for this LA-SF suggested route were included in the white paper - US$6 billion for a passenger-only version, and US$7.5 billion for a somewhat larger-diameter version transporting passengers and vehicles. However, transportation analysts expressed doubts that the system could be constructed on that budget, including some predictions that the Hyperloop would be several billion dollars over budget once construction, development and operation costs are taken into consideration.
The Hyperloop concept has been explicitly "open-sourced" by Musk and SpaceX, and others have been encouraged to take the ideas and further develop them. To that end, a few companies have been formed, and several interdisciplinary student-led teams are working to advance the technology. SpaceX built an approximately 1-kilometer-long (0.62 mi) subscale track for its pod design competition at its headquarters in Hawthorne, California. TUM Hyperloop set the world record of 463 km/h (288 mph) in July 2019 during the Hyperloop pod competition at SpaceX. Virgin Hyperloop conducted the first human trial in November 2020 at its test site in Ls Vegas.
Which of the following is not true about Hyperloop?
The Hyperloop Alpha concept proposed
Choose the in-correct sentence.
''open-soured" implies that
What did Virgin Hyperloop do in November 2020?
For the following questions answer them individually
If $$m \neq 0, n^{2} \neq 1$$ and $$2^{m^{a^{2}}} = (2^{m})^{n^{2}}$$ then 'm' in terms of 'n' is
If $$2^{x} = 4^{y} = 16^{z}$$ and $$xyz = 1728$$, then $$5x + 3y + 2z =$$
In a mixture of 48 litres of milk and water the ratio of milk and water is 5 : 3. If 2 more litres of water is added to this mixture, then the ratio of milk to water in this new mixture is
A bag with 200 coins consists of 10 rupee, 5 rupee and 2 rupee coins whose values are in the ratio 10 : 15 : 8. Then number of 5 rupees coins in the bag is
If Rs. 19,200 is divided between 'P', 'Q' and 'R' in such that for every rupee that 'P' has, 'Q' has 20 paise, and for every rupee that 'Q' has, 'R' has 40 paise, then the share of 'R' in rupees is
$$\sqrt{\sqrt{49} + \sqrt{16} + 5}=$$
$$\sqrt[3]{10^{2}\sqrt{625}}$$
If $$x = \sqrt{9} + \sqrt{25}$$ and $$y = \sqrt{121} + \sqrt{4}$$, then
The number of zeros required to write the integers 1 to 200 (both inclusive) is
The least 5 digit number that leaves the remainder 17 when divisible by 18, 24, 30 is
A person spent $$\frac{2}{9}$$th of his salary on house rent, $$\frac{2}{5}$$th of the remaining amount on food, $$\frac{2}{3}$$rd of the remaining amount on miscellaneous and rest he saved. If the amount spent on miscellaneous is Rs.13,300, then the amount he spent on house rent, in rupees is
If $$x$$ : y : z = 3 : 4: 5, then $$\frac{x}{yz}:\frac{y}{zx}:\frac{z}{xy}$$
$$16\left[ 42 -\left\{35 - ( 17 - \overline{4- 7}) - 5\right\} - 2\right] =$$
The ascending order of the fractions
$$\frac{97}{103},\frac{99}{105},\frac{101}{108},\frac{103}{110}$$ is
If $$33\frac{3}{5}%$$ of $$29\frac{3}{4}$$ of $$'x'$$ is 357, then $$x =$$
In an election between two candidates, one got 68% of votes and won by a difference of 3240 votes. If there are no invalid votes, then the total number of votes polled is
A man lost $$12\frac{1}{2}$$% of his money in a business. After spending 70% of the remaining money, if he is left with Rs. 210, then the amount of money (in Rs.) he invested in that business is
By selling two articles for a sum of Rs 17,700 a dealer makes a profit of 15% on the first article and a loss of 15% on the second. On the whole if he gets a net loss of Rs. 300, then the cost price of the first article (in rupees) is
Two successive profits of 10% and 5% are equal to a single profit of
A trader marks his goods at 25% above his cost price and allows a discount of 12.5%. Then the percentage of profit he makes is
Four persons 'P', 'Q', 'R', and 'S' entered into a partnership. 'P' subscribed $$\frac{1}{3}$$ of the capital for 4 months. 'Q' subscribed $$\frac{1}{4}$$ of the capital for 6 months. 'R' subscribed $$\frac{1}{6}$$ of the capital for 8 months and 'S' the rest for 3 months. Then the share of 'S' out of a total profit of Rs. 1,18.000 at the end of the year (in Rs.) is
'P' and 'Q' entered into a partnership with Rs. 20,00,000 and Rs 40,00,000 respectively. After four months, they invested Rs. 1,00,000 each in it. If the annual profit is Rs. 18,40,000, the difference between the shares of profits of 'P' and 'Q' (is Rs.) is
'P' , 'Q' and 'R' started a business. The capital of 'P' is four-fifth of the capitals of 'Q' and 'R' together and the capital of 'Q' is one third of the capital of 'P' and 'R' together. Then the share (in Rs.) of R in their earned profit of Rs. 1,08,000 is
Two pipes 'P' and 'Q' can respectively fill a cistern in 48 minutes and 60 minutes respectively. Both the pipes are opened for 20 minutes and then the pipe 'Q' is turned off. Then the time ,(in minutes) it takes further to fill the cistern is
Two pipes can separately fill a cistern in 12 minutes and 16 minutes respectively and a waste pipe can drain it at 20 gallons per minutes, If all the three pipes are opened simultaneously the cistern is filled in 24 minutes. Then the capacity of the cistern, in gallons, is
Two persons 'A' and 'B' together can finish a piece of work in 16 days while 'B' and 'C' together can complete the same work in 20 days. If 'A' , 'B' , 'C' work together, the same work is completed in 12 days, then the number of days required for 'A' alone to complete the work is
If 'P' and 'Q' can do a piece of work in 18 days, 'Q' and 'R' can do it in 24 days, 'P' and 'R' can do it in 36 days, then the time (in days) needed by 'P' alone to finish that work, is
A window is in the shape of a rectangle surmounted by a semicircle on the length side of the rectangle. If the dimensions of the sides of the rectangle. If are 16 cm and 6 cm, then the area of the that window, in square centimetres, is
If the perimeter and diagonal of a rectangle are 18 m and 5 m respectively, then the area of that rectangle (in sq. meter) is
If a metallic solid sphere of diameter 6 cm is drawn into a uniform wire of diameter 4 mm, then the length (in meters)of the wire so drawn is
Three circles of radius 8 cm each are touching each other externally. Then the area (in sq. cm) inside the triangle formed by joining their centres that is covered by the 3 circles is
If the angle of a sector of a circle of radius 21 cm is $$75^{\circ}$$, then the perimeter of that sector approximately (in cms)
The floor area of a conical shaped tent is 154 sq.m and its vertical height is 24m. If each square meter of canvas costs Rs. 15.50, the approximate cost of the canvas needed for the tent (in Rs) is
$$15_{(10)} = ............... _{(2)}$$
For a,b ∈$$Z^{+}$$, define a*b as the remainder obtained when $$a^{2}b$$ is divided by 23. Then 7*13 =
The contra positive of $$p \rightarrow(q \rightarrow r)$$ is equivalent to
If $$f(x) = \frac{x+1}{x-1}$$ for $$x \neq 1$$, then $$f o (f o f)(x) =$$
The equation of the straight line passing through the point (2 , -3) and making equal intercepts on the coordinate axes, is
$$\frac{1}{\sin 10^{\circ}} - \frac{\sqrt{3}}{\cos 10^{\circ}} =$$
When $$ax^{2} + bx + 2$$ is divided by $$x-1$$ and $$x+2$$ if the remainders are 6 and 0 respectively, then the quadratic equation formed with 'a' and 'b' as its roots is
If the system of equations $$cx+3y = c-3$$ and $$12x+cy =c$$ has infinitely many solutions, then the value of 'c' is
The sum of all the odd integers between 2 and 100 is
If in a geometric progression, the difference between $$5^{th}$$ term and $$4^{th}$$ term is 576 and the difference between its $$2^{nd}$$ term and first term is 9, then the $$6^{th}$$ term of that progression is
$$A = \begin{bmatrix}2 & 2 & 1 \\ 1 & 2 & 2 \\ 2 & 1 & 2 \end{bmatrix} \Rightarrow (Adj A)^{-1} =$$
The incenter of the triangle formed by the points (2 , 3) , (-2 ,-5) and (-4 , 6) is
If the arithmetic mean of $$x_{1}, x_{2},.... x_{n}$$ is 51 , then the arithmetic mean of $$7x_{1}- 21, 7x_{2}- 21, 7x_{3}-21....7x_{n}- 21$$ is
The median of 12, 14, 10, 16, 8, 6, 18, 15, 11 is
The mode of 42, 36, 44, 38, 36, 40, 45, 36 is
If the median of some numbers is 16.8 and their arithmetic mean is 18.4, then their mode is
The mean deviation of 1, 2, 3, 4, 2 about their arithmetic mean is
The standard deviation of four consecutive positive integers is
The arithmetic mean of the 10 numbers is 6, but it was later observed that one of the numbers was misread as 9. After correcting the wrong entry, if their mean was 7, then actual value of that wrong entry is
If a problem in probability is given to 3 students 'P', 'Q' and 'R' whose chances of solving it are $$\frac{1}{3},\frac{3}{4}$$ and $$\frac{1}{2}$$ respectively, then the probability that the problem will be solved is
The probability that a student 'A' succeeds in a test is 0.85 and the probability that 'B' succeeds in the same test is 0.75. Then the probability that exactly one of them succeeds in that test is
'A' and 'B' are two sets such that n(A) = 4 and n(B) = 2. If a relation from A to B is selected at random, then the probability that their relation is not a function is
