What is the value of $$x + y + z$$?
(I) $$3x - y + 2z$$
(II) $$x + 5y+ 2z = 10$$
TS ICET 2022 Question Paper Shift-2 (28th July)
In the following questions numbered 1 to 20, 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.
If $$x, y$$ are positive integers, is $$\sqrt{x^{2} + y^{2}}$$ an integer?
(I) $$x : y = 1 : 2$$.
(II) $$x + y$$ is multiple of 7.
Is the positive integer n divisible by 462?
(I) 715 divides n.
(II) 210 is a factor of n.
What is height of the cylinder?
(I) Volume of the cylinder is $$48cm^{3}$$.
(II) The lateral surface area of the cylinder- is $$28cm^{2}$$.
If $$x$$ and y are integers then is z an even integer?
(I) $$z = (x + y)^{2}$$.
(II) $$Z = 2x + 4y$$.
If a, b, c are integers, is a < b ?
(I) $$a^{2} + b^{2} + c^{2} = 0$$.
(II) b < a + c.
What is the cost of erecting a fence around a rectangular field?
(I) The area of the field is 24000 square meters.
(II) The cost of fencing Rs.150 per meter.
If m, n are positive integers greater than 4, then what is the value of m+n?
(I) mn = 48.
(II) m > n.
What is the common ratio of the Geometric Progression?
(I) The sum of the first four terms is 80.
(II) The first and fourth terms are 2 and 54 respectively.
What is the positive integral value of $$x$$?
(I) $$57 < 7x + 1 < 71$$.
(II) $$25 < x 2 < 81$$.
What is the selling price of the sofa?
(I) The marked price of the sofa is Rs.7500.
(II) The profit the merchant gets by selling the sofa is Rs.900.
What is the present age of the person A?
(I) Today is A's birthday.
(II) After one year he will be twice as old as he was ten years ago.
What is the area of the circle?
(I) The circle circumscribes a square of area 49 $$cm^{2}$$
(II) The circle is inscribed in a triangle of area 48$$cm^{2}$$.
How many marks did he get in Mathematics?
(I) The average of his marks in Mathematics, Physics and Chemistry is 79.
(II) The average of his marks in Mathematics and Chemistry is 72.
Is $$f(x)$$ an even function?
(I) $$f(x) = g(x) + g(- x), x \epsilon ℝ$$
(II) $$g(x) = \cos x, x \epsilon ℝ$$
How many people are there in the queue between two persons A and B?
(I) A is the $$15^{th}$$ from the end of the line.
(II) B is in the centre of the line and there are 10 more ahead of him.
In a Carrom Board game of doubles played by four players A, B, C and D, who is sitting opposite to A?
(I) B is sitting opposite to D.
(II) C is sitting facing North.
In a queue of 20 people waiting at the counter what is the position of A from the end of the line?
(I) B is the fifth person in front of A from A.
(II) B is eighteenth person from the end of the line.
Will it be Friday tomorrow?
(I) Day before yesterday is Tuesday.
(II) Sunday is a holiday.
Four boys A, B, C, D sit around a round table side by side facing the centre of the table. Then who sits to the left of B?
(I) B and C face each other and A sits between Band C.
(II) D sits to the right of C and sits opposite to A.
In the questions 21 -30, each contains two pairs of groups ( of letters or letters and numbers). The pattern that appears in one pair should be followed by the other pair also. Observe the pattern carefully and fill in the blanks appropriately.
CAM : USE :: SAT : ____________
FIG : KNL :: SET : ________
DBCE : QOPR :: JLKI : _____________
SOME : _________ :: WHAT : CRYF
PCD : SGI :: BKS : _____________
LEG? : IBD4 :: SIX24 : ____________
LO12QT : PS2UX :: BE7FT : _____________
12Ⓠ22 :Ⓢ:: ___________ : 18Ⓦ28
ZY : 650 :: XW : __________
MAT : 200113 :: TOE : ___________
In questions numbered 31 to 35 pick the odd thing out.
7, 21, 43, 73, 111, 157, 213, 273
Hen, Crow, Pigeon, Eagle, Sparrow, Vulture, Parrot, Dove
Crow, Dog, Hen, Duck, Dove, Eagle, Peacock
30,120,180,270,480,750, 1080
Venus, Neptune, Uranus, Mercury, Titan, Earth, Jupiter
Note : Each of the questions from 36 to 45 follows a definite pattern, observe the same and fill in the blanks with suitable ones.
5, 10, 17, 26, _________ , 50, 65
2, 6, 12, 20, ________ , 42, 56, 72
$$(1 + \sqrt{2}), - 1, (- 1 + \sqrt{2}), (- 3 + 2\sqrt{2})$$, ________, $$(- 17 + 12\sqrt{2}), (- 41 + 29\sqrt{2})$$
$$\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, 1\frac{1}{6}, 1\frac{1}{2}$$, _________, $$2\frac{1}{6}$$
0, 6, 24, 60, _________ , 210,336
1, 1, 2, 6, 24, 120, 720, ___________
10, 30, 150, _________ , 11550, 150150
2, 4, 1, 5, 0, 6, -1, __________
6, 8, 5, 9, 4, 10, 3, ___________
$$1\frac{2}{3}, 1\frac{2}{11}, 1\frac{4}{19}$$, _________, $$1\frac{4}{43}$$.
The table gives the data of the sales (in crores of rupees) in one year of four companies I, II, III, and IV dealing with same type of electronic items in five major cities A, B, C, D and E. Based on the data answer the questions from 46 to 48.
Taking into consideration the total sales of all the companies in all the cities what is the precentage of sales of Company-I?
In all the cities put together which company recorded the maximum sales in that year?
Of all the companies put together what is percentage increase of sales of the products in the city E compared to the City A?
The following pie-chart shows the expenditure of a family. Based on this information answer the questions from 49 to 51.
How much (in rupees) the family can save if the total income is 72000 rupees?
The percentage of expenditure on food is
If the total income of the family is Rs.144000, then the amount (in rupees) spent by family on Rent and Education is
In a group of 100 persons, each reads at least one among three news papers T, E and H, 8 read a ll the three, 20 read both T and E, 18 read both E and Hand 14 read both T and H, 60 read E and 46 read T. Based on this data, answer the questions 52-55.
How many persons read only H?
How many persons read exactly two among the three E, T and H?
The ratio between the number of persons who read E and T is
The percentage of persons who read T is
In a certain code each consonant is coded as $$(n + 4) (mod 26)^{th}$$ consonant and each vowel is coded as the next vowel cyclically. The reverse process is used for decoding.
Based on this information answer the questions from 56 to 60.
OVAL is coded as
ICET is coded as
Which word is coded as ORANGE?
SECTION is coded as
Which word is coded as BULLET?
For the following questions answer them individually
If INPUT is coded as LQSXW then code for COMPUTER is
If PURCHASE is coded as 73429186 and ORDER is coded as 54064, the code for PROCEED is
If PRIVATE is coded as 1234567 and RISK is coded as 2398, then which of the following is coded as 962347?
If FAILURE is coded as KFNQZWJ, then the code for SUCCESS is
If NATION is coded as 467234 and GREEN is coded as 19554, then the code for INTEGRATION is
The calendar of the year that is identical with the calendrer of the year 2005 is
At what time between 4:00 and 4 : 30 will the hands of a clock be at right angle?
At what time between 9 o'clock and 10 o'clock will the hands of a clock be together?
Mrs. X meets a man at a party who is the brother of the sister of her husband. How is the man related to X?
A person A came to the bus stop at 8:10 am and found that he was 40 minutes before the arrival of the bus which was running late by 30 minutes. What was the scheduled arrival time (STA) of the bus?
Two trains P and Q arrived at station X on same day at 14:35 hours and 15:28 hours, running late by 21 minutes and 12 minutes respectively. Then the time difference between their scheduled arrivals (in minutes) is
Six persons A, B, C, D, E and F are sitting around a circular table such that C is sitting to the right of E, and F is to the right of A. If B is sitting to the left of D, and A and C are sitting adjacent to each other, then who is sitting opposite of D?
If the symbols $$\alpha, \beta, \gamma$$ and $$\delta$$ stand for arithmetical operations of addition, subtraction, multiplication and division respectively, then
$$\frac{(42\delta2)\beta(5\gamma4)}{(5\beta4)\alpha(4\delta4)}$$=
If $$a \times b$$ stands for $$\frac{1}{a} + \frac{1}{b}$$, then $$\sum_{n = 1}^{10}\left(1 \times \frac{1}{n}\right) = $$ then
If $$ C \triangle D = C^{2} + CD + D^{2} - (C + D)$$, then $$7 \triangle 8 =$$
If $$3^{x} = 9^{y} = 27^{z}$$ and $$xyz = 36$$, then $$x + y + z $$=
If $$2^{n-l} + 2^{n+l} = 320$$, then n =
If A : B = 2 : 3; B : C = 6 : 7 and C : D = 4 : 5, then D : A =
An urn contains 60 litres of mixture of milk and water in the ratio 3 : 1. How many litres of water is to be added to this mixture to make the ratio of milk and water as 1 : 3?
If the arithmetic mean of two surds is $$5 + 9\sqrt{2}$$ and one of them is $$1 + 12\sqrt{2}$$, then the square root of the second surd is
If $$\sqrt[3]{26 - 15\sqrt{3}} =x - \sqrt{y}$$, then $$3x + 2y$$ =
The smallest 5 digit number that leaves remainder 11 when divided by 111 is
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. Then the number is
If the LCM of 3, 4, 5, 6, $$x$$ is 120 and $$x$$ < 1201, then the largest value of $$x$$ among the following is
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
If $$m^{n} = 361$$, 'm' and 'n' being natural numbers, which of the following could be a value of $$\frac{(m-n)}{2}$$
$$\frac{0.099 \times 9.9 \times 0.99 + 0.000001}{0.099 \times 9.9 - 0.0099 + 0.0001}$$ =
The difference between the largest and the smallest of the following numbers is
$$\frac{2}{7}, \frac{2}{9}, \frac{3}{11}, \frac{1}{5}, \frac{5}{12}$$
If $$a = \frac{4}{9}, b = \frac{7}{12}, c = \frac{3}{7}, d = \frac{12}{17}$$ and $$e = \frac{1}{2}$$ then their descending order is
In an election contested by two candidates A and B, A polled 35% of the votes and is defeated by B by 15000 votes. What is the number of votes polled by B?
In an examination A scored 25% of marks and failed by 30 marks whereas B scored 50% of the marks and got 20 marks more than the minimum pass marks. What is the minimum percentage of the pass marks?
A man bought a horse and a carriage for Rs.3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. The cost of the horse is (in Rs.)
The profit earned by selling an article for Rs.900 is double the loss incurred when the same article is sold for Rs.450. At what price should the article be sold to make 25% profit?
P, Q and R together started a business. P invests three times as much as Q and Q invests two third of what R invests. What is the share of Q, if the total profit is Rs.12100 (in rupees)?
A, B, C, D start a partnership business where A, B and C invested $$\frac{1}{3}rd,\frac{1}{4}th$$ and $$\frac{1}{4}th$$ of the capital respectively and the rest of the capital by D. If the total profit at the end of the year is Rs.60 lakhs, what is the profit of D (in lakhs) ?
Pipe A and B can fill an empty tank in 6 hours and 9 hours respectively. If Pipe A is opened at 10 pm and B one hour thereafter then the tank will be fill ed at
A tank supplies water to a family for 50 days. Due to leak in the tank, 5 litres of water wastage every day and then the supply lasts for 10 days less. For how many days the supply last if 50 litres of water wastage every day?
Two persons A and B start from a point P and walk at the speeds 3 kmph and 4 kmph respectively. B reaches the point Q and returns immediately to meet A at a point R in between P and Q. If P, Q R are collinear, then the distance between Q and R (in km) is
Walking at $$\frac{3}{4}$$ of his usual speed a person reaches his office 10 minutes late. What is the time (in minutes) taken by him to reach his office if he walks at his usual speed?
P works twice as fast as Q and R work together. Working together, all three can do a work in 21 days. In how many days can Q and R together do the work?
A, B and C individually can complete a job in 20, 15 and 25 days respectively. If only one or two persons can be assigned the job who would complete the job quickly?
ABCD is a quadrilateral. AC = 12 cm. The perpendicular distances from B and D to AC are 4 cm and 6 cm respectively. Then the area (in $$cm^{2}$$) of the quadrilateral ABCD is
The circumference of circle A is $$\frac{11}{7}$$ times the perimeter of a square with area 784 sq. cm. The area of another circle B whose diameter is half the radius of the circle A, is (in sq. cm.)
A solid metallic sphere of radius 6 cm is melted and moulded into smaller spheres of diameter 4 cm. The number of smaller spheres made are
The radii of the bases of a cylinder and a cone are in the ratio of 3 : 4, and their heights are in the ratio 2 : 3. Then the ratio of their volumes is
The curved surface area of a cylinder is 1056 sq.cm, and its height is 28cm. The volume of the cylinder (in $$cm^{3}$$) is
The surface area of a cylindrical pipe, open at both the ends is 628 sq.cm. Its length is greater than its radius by 15 cm. If the pipe is closed at one end then the amount of water (in $$cm^{3}$$) the pipe can hold (taking $$\pi = 3.14$$) is
One diagonal of a rhombus is 20 cm and side of the rhombus is 26 cm. Then the area of the rhombus (in sq.cm) is
If $$O \leq x \leq 14$$ and $$11x \equiv 3 (mod 14)$$ then $$x$$ =
What is the time 100 hours after 7 am?
If A = {3, 4, 5, 6, 7, 8, 9}, then the number of subsets of A not containing 6 is
For two sets A and B, if
$$n(A - B) = 14, n(B - A) = 16, n(A \cup B) = 40$$, then $$n(A \cap B)$$ =
If one of the roots of the cubic equation $$x^{3} + ax^{2} + bx + c = 0$$ is -1 , then
the product of the other two roots is
Suppose $$\alpha$$ and $$\beta$$, are the zeros of the polynomial
$$f(x) = x^{2} - 6x + k$$. Then the value of k, such that $$\alpha^{2} + \beta^{2} = 40$$ is
If $$x^{3} - 4x^{2} + ax + b$$ is exactly divisible by both $$x - 2$$ and $$x + 1$$, then (a, b) =
If the integer n is divided by 3, the remainder is 2. Then, the remainder when 7n is divided by 3 is
A person bought 29 postal stamps of Rs.5 and Rs.10 by paying Rs.200. The difference between the number of stamps be bought with that money is
Six years ago, the age of a person was two years more than five times, the age of his son. Four years hence, his age will be two years less than three times the age of his son. After how many years from now will their combined age be 100 years?
If $$z^{x} = 4^{Y} = 16^{z}$$ and $$xyz = 1728$$, then $$5x + 3y + 2z$$ =
The sum of the first n terms of a sequence is given by $$5n^{2} + 2n$$. Then the $$10^{th}$$ term of this sequence is
If 9 times the $$9^{th}$$ term of an arithmetic progression is equal to 13 times the $$13^{th}$$ term, then the $$22^{nd}$$ term of the arithmetic progression is
$$\frac{\cos 690^{\circ} + \cot 210^{\circ} + \cos 420^{\circ}}{\sin 690^{\circ} + \sec 210^{\circ} +\tan 420^{\circ}}$$
$$\frac{1}{\sqrt{3}} \sin 300^{\circ} + \tan 855^{\circ} + \frac{3}{4} \sec 780^{\circ}$$ =
If in a $$\triangle$$ ABC, A + B = C, then $$\tan A. \tan B. \tan C$$ =
$$x + \frac{1}{x} = 2 \cos \theta \Rightarrow x^{3} + \frac{1}{x^{3}}$$
A man standing at 50m on the tower of a ship observes the angle of depression of 2 boats on either side of the ship to be $$30^{\circ}$$ and $$60^{\circ}$$ respectively. The distance (in meters) between the boats is
In the given figure $$l_{1}, l_{2}$$ are two intersecting lines at O and $$l_{3}$$ is a horizontal through O. The value of $$x$$ ( in degrees) is
In the given triangle if $$\angle ABC = \angle BDC = 90^{\circ}$$ and BD = AD,
Then $$x$$ =
The diagonal of a square is $$16\sqrt{2}cm$$. Its area (in sq. cm) is
The area of a rhombus whose side is 50m and one of its diagonals 80m (in sq.m.) is
In the following circle with center O, if $$\angle$$ ABC is $$115^{\circ}$$, then $$\angle$$ AOC =
The area of the circle centred at (1, 2) and passing through the point (4, 6) is (in sq. units)
A(4, 2), 8(6, 5), C(1, 4) are the vertices of $$\triangle$$ ABC. If the median from A meets BC at D, then $$AD^{2} : BC^{2} $$=
The equation of the perpendicular bisector of the line obtained by joining the points (1, 1) and (3, 5) is
A point C divides the line joining the points A(1 , 3) and B(21 7) internally in the ratio 3 : 4. The equation of the line passing through C and parallel to the line $$2x + 7y = 4$$ is
The equation of line passing through the origin and is inclined at an angle of $$30^{\circ}$$ to the X-axis
The equation of the line passing through the points $$(1, \sqrt{3})$$ and $$(\sqrt{3}, 3)$$ is
If m denotes the slope and c denotes the intercept of a line then (m, c) for the line $$7x - lly - 23 = 0$$ is
The intercept made by the linejoi1ning the points (1 , 11) and (-3, -5) on the Y-axis is
The equation of the line passing through the point of intersection of the lines
$$2x + 3y - 4 = 0; 5x - 2y + 6 = 0$$ having slope $$\frac{-2}{3}$$ is $$ax + by + c = 0$$, $$\frac{5a + 6b}{c}$$=
The arithmetic mean of the first twenty natural numbers is
After calculating the arithmetic mean of 25 integers as 73, it was observed that two integers were wrongly taken 76 and -23 instead of -76 and 23 respectively. Then the correct arithmetic mean is
The average height of 30 men is 158 cm and average height of another group of 40 men is 162 cm, then the average height of the combined group is
The median of the following set of observations is
1, 3, 5, 7, ... , 97
The median of the following frequency distribution is
The mode of the following data is
1, 13, 6, 9, 11, 13, 5,8, 13, 14, 5, 8, 13, 6, 13
The arithmetic mean and the median of a frequency distribution are 51 and 50 respectively. Then the value of the Mode is
The probability of getting 2 heads in a toss of 5 coins is
The probability that 3 boys and 3 girls can be seated in a row such that all the boys sit together side by side, is
A bag has 4 white, 5black and 6 red balls. The probability of drawing a ball which is wh ite or black is
Meanings (Sentences with dashes)
His ____________ services were appreciated by his colleagues.
The change was indiscernible.
The underlined word means
I don't know why she is always so belligerent towards me.
The underlined word means
He turned nostalgic at the mention of school.
The underlined word means
The mechanism of this watch is very intricate.
The underlined word means.
Synonyms and Antonyms
Synonym of ' incisive'
Choose appropriate synonym for 'debilitate'
Choose appropriate antonym for 'alacrity'
Synonym of 'Espionage'
Choose appropriate synonym for deadlock.
Verb (Tense and Voice)
Both the father and his son ___________ at the gym yesterday.
She ___________ lunch just now.
Just as I __________ into the bathroom, all lights went off.
Insert a verb in the present tense
The Earth __________ round the Sun.
Passive voice of 'I will contact you tomorrow.'
Phrasal Verbs & Idioms
I had to ___________ to clear the competitive exams.
Select the most appropriate meaning of the underlined phrase
A discussion was going on whether it was ethical to delve into social media posts to look for damaging details about an employee.
He _____________ as soon as he heard their car turn into the drive way.
Their government imposed emergency on account of economic crisis.
The equivalent of the underlined word is :
They have _____________ the decision for another month.
Articles & Prepositions
I waited for _________ hour and left.
__________ Ganges flows through India.
______ Alps are in Switzerland.
I ran ________ him on my way back home.
Is there ________ university in your town?
Computer Terminology
A tiny wafer of silicon containing miniature electric circuits that can store millions of bits of information is known as __________.
India's first super computer is called ___________.
A program arranged in rows and columns that manipulates numbers is known as __________.
The first mechanical computer designed by Charles Babbage was called _____________.
A device that transfers data between computer networks to provide access to the internet is known as ________.
Business Terminology
Expected profitability of a company or a single product is assessed by a __________.
A type of correspondence used when a business firm has to convey a common matter to a large audience is known as __________.
A series of workers and machines in a factory by which a succession of identical items is progressively assembled is called ___________.
Which company/ business did Elon Reeve Musk acquire in 2022?
A financial statement that shows sales, cost of sales, gross margin,
operating expenses and profits or losses is known as ____________.
Read the Passage and answer the questions
Walls and wall building have played a very important role in Chinese culture. Not only towns and villages, the houses and the temples within them were somehow walled. The houses also had no windows overlooking the street, thus giving the feeling of wandering around a huge maze. Thus, a great and extremely laborious task of constructing a wall that runs the length of the country must not have seemed such an absurdity.
Various dynasties contributed to constructing and refurbishing of a wall whose foundations had been laid many centuries ago. It was during the $$4^{th}$$ and $$3^{rd}$$ century B.C. That each warring states like Chin, the Chao and the Yen started building walls to protect their kingdoms both against one another and against northern nomads. They also laid foundations on which Chin Shih Huang Di would build his first continuous Great Wall.
Throughout the centuries many settlements were established along the border. The garrison troops were instructed to reclaim wasteland and to plant crops in, it, build roads and canals. All these undertakings greatly helped increase the country's trade with many remote areas and also with southern central, and western parts of Asia.
Chinese towns resemble a maze because
Constructing a wall that ran the length of the country
The Great Wall of China
Crops were planted
The Great Wall helped in
Read the Passage and answer the questions
Before the grass has thickened on the roadside and leaves have started growing on the tree as is a perfect time to see, how dirty Britain has become. The pavements are stained with chewing gum, the gutters are full of discarded fast-food cartons. Years ago, I remember travelling abroad and being saddened by plastic bags, discarded bottles and soiled nappies at the edge of every road. Nowadays, Britain seems to look at least as bad.
The problem is that the rubbish created by our increasingly mobile lives lasts a lot longer than before. It stays in the undergrowth for years; a reminder of what a tatty little country we have become now.
It is estimated that 10 billion plastic bags have been given to shoppers. These will take anything from 100 to 1000 years to rot. However, it is not as if there is no solution to this. A few years ago, the Irish government introduced a tax on non -recyclable carrier bags and in three months reduced their use by 90%. When he was a minister, Michael Meacher attempted to introduce a similar arrangement in Britain. The plastics industry protested, of course, the idea was killed before it could draw breath.
It is perfect time to see Britain before the trees have leaves because
According to the writer
Micheal Meacher
Passage is about
Choose the synonym for the word 'tatty'.
Read the Passage and answer the questions
Presumption is our natural and original disease. The most wretched and frail of all creatures is man, and the proudest. He sees himself lodged in the dirt and filth of the world, nailed and riveted to the worst part of the universe, and yet in his imagination will be placing himself above the circle of the moon, and bringing heaven under his feet.
It is by the vanity of the same imagination that he equals himself to God; attributes to himself divine qualities, withdraws and separates himself from the crowd of other creatures, cuts out the shares of animals and distributes to them such portion of faculties and force as himself thinks fit.
All that seems strange to us and that we do not understand, we condemn. The same thing happened also in the judgment we make of beasts; they have several conditions like to ours; from those we may by comparison draw some conjecture: but those qualities which are particular to themselves, how know we what to make of them.
In this passage, 'presumption' means
Who or which is the weakest and the most arrogant among living creatures?
Man's greatness is at its best _____________.
We condemn what we cannot ___________.
Our judgement of the animal is ____________.
