What is the value of $$x + y$$?
(I) $$3x - 4y - 5 = 0$$.
(II) $$8y - 6x + 10 = 0.$$
TS ICET 2022 Question Paper Shift-1 (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.
What is angle A in triangle ABC?
(I) $$\angle B= 40^{\circ}$$.
(II) Triangle ABC is isosceles.
Is the integer 3m + 4n even?
(I) 2m + n is an odd number.
(II) m + 2n is an odd number.
A sequence of integers is given by $$a_{n} = (a_{n-l} + 1)^{2}$$ , then what is $$a_{5}$$?
(I) $$a_{3} = 25$$
(II) $$a_{1}$$ is an odd integer.
Is the perimeter of the rectangle greater than 65 cm?
(I) Its length is less than 16 cm.
(II) Its breadth is greater than 10cm.
For real numbers a, b and c, is a = b = c ?
(I) a + 3b + 2c = 0.
(II) $$a^{2} + b^{2} + c^{2} = ab+ bc + ca$$.
How much money do the persons A and B together have?
(I) B has Rs.200 less than what C has.
(II) A has Rs.300 more than C has.
How many students passed in both Mathematics and English?
(I) 15 failed in both Mathematics and English.
(II) The number of failures in Mathematics exceeds the number of failures in English by 10.
Is $$x = y = z$$?
(I) $$x^{3} + y^{3} + z^{3} = 3xyz$$.
(II) $$x^{2} + y^{2} + z^{2} = xy + yz + zx$$.
What is the average of a, b, c, d?
(I) a + b + c = d + 15.
(II) 13 - c - 3d = a + b.
What is the GCD of the positive integers m, n?
(I) LCM of m, n is 165.
(II) Product of m, n is 165.
What is the area of the sector?
(I) Radius of the circular sector is 10 cm.
(II) The angle of the sector is $$\frac{\pi}{6}$$.
What is the area of the rectangle PQRS?
(I) PQ is twice of QR.
(II) PS = 4 cm.
What is the HCF of $$x$$ and y?
(I) Ratio of $$x$$ and y is 2 : 3.
(II) $$x$$ and y are two consecutive positive integers.
What is the value of $$x^{6} - y^{6}$$?
(I) $$x^{3} - y^{3} = 10$$.
(II) $$x^{4} - y^{4} = 5$$.
Is A a brother of B ?
(I) B is a sister of C.
(II) C is a brother of A.
In how many hours did David cover 600 miles?
(I) David covered the first half of the distance at 40 mph.
(II) David covered the last $$\frac{1}{4}$$th of the distance at 30 mph.
How many people are there in that room?
(I) If 4 persons leave the room, then there will be less than 15 persons in that room.
(II) If 3 more persons enter the room, then there will be more than 20 persons in that room.
Alex and Tony started a piece of work. After working for two days, Alex left. The remaining work was completed by Tony. In how many days did Tony complete the work?
(I) Tony can complete the work in 20 days working individually.
(II) Alex and Tony can complete the work in $$6\frac{2}{3}$$ days working 3 together.
Is D a brother of F ?
(I) B has two sons of which F is one.
(II) D's mother married to B
: 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.
PRLN : XZTV :: _________ : RTNP
QRS : VWX :: ___________ : MNO
Gum : Stick :: Needle : ____________
SUWY : LPTX :: PRTV : ________
ACER : BEHV :: ROSE : __________
PEN : 35 :: LAB : __________
SEV⑳ : UGX⓪ :: VEG⑧ : ________
AE : 26 :: DH : _______
$$\frac{X}{Y} : \frac{42}{52} :: \frac{P}{Q}$$ : __________
ALSO⑫ : CNUQ⑭ :: FIVE⑨ : __
In questions numbered 31 to 35 pick the odd thing out.
0, 1, 2, 3, 6, 11, 20, 37, 68, ________
Frog, Crocodile, Allegator, Whale, Tortoise, Toad, Turtle
Carrot, Cauliflower, Cabbage, Capsicum, Ladies finger, Brinjal, Bottle guard
31, 63, 127, 257, 511, 1023, 2047?
8, 50, 181 72, 104, 128, 98
Note : Each of the questions from 36 to 45 follows a definite pattern, observe the same and fill in the blanks with suitable ones.
$$25, 20, 16\frac{2}{3}, .............. 12\frac{1}{2}, 11\frac{1}{9}, 10, 9\frac{1}{11}$$
2, 3, 5, 8, 12, 17, 23, ________
$$(1 - \sqrt{2}), - 1, (- 1 - \sqrt{2}), (- 3 - \sqrt{2})$$, ___________
6, 11 , 18, 27, 38, ___________ , 66
$$2+\sqrt{2}, 6,6+\sqrt{6}, 8 + 2\sqrt{2}, 10 +\sqrt{10}, ............., 14 + \sqrt{14}$$
$$\frac{1}{2}, \frac{8}{5}, \frac{27}{10}, \frac{64}{17}, ............., \frac{216}{37}, \frac{343}{50}$$
64, 32, 35, 5, 22, 11, 14, _________, 16, 8, 28, 4
2, 14, 3, 21, ________, 28, 5, 35, 61 42
4, 12, 48, 240, __________, 10080, 80640
2, 6, 20, 42, 110, 156, 272, ____________
The following graph shows the expenditure of a household on repairs in hundred rupees) during January to September. Based on this, answer the questions.
The percentage increase of the expenditure in the month of June than the month of March
Which month shows highest percentage increase in expenditure over its previous month?
The average expenditure per month in the given period (in rupees)
The Pie-chart shows the number of toys of six types A, B, C, D, E and F manufactured by a company. Based on this, answer the questions.
The percentage of toys of type E in the total number of toys of all types is
If the total number of toys produced is 72000, then the number of toys of type A is
The ratio between the number of toys of types A and E is
In an examination consisting of tests in three subjects Physics, Chemistry and Mathematics, the following data is obtained.
(i) Total number of candidates appeared :400.
(ii) Number of candidates failed in all the three subjects: 12.
(ii) Number of candidates failed only in Physics and Chemistry: 24.
(iv) Number of candidates failed only in Chemistry and Mathematics: 18.
(v) Number of candidates failed in Mathematics and Physics: 32.
(vi) Number of candidates failed in only Physics, only chemistry and only Mathematics are 40, 30 and 50 respectively.
How many candidates passed in Mathematics?
What is the percentage of candidates that failed in at least two subjects?
What is the percentage of candidates who passed in Chemistry?
What is the number of candidates that passed in all the three subjects?
The letters of the English alphabet A, B, C, .. . , Z are given ranks 1, 2, 3, ... , 26 respectively. Then they are coded as follows:
(i) A letter with rank 'n' is coded to the letter with rank r, where r is the remainder when 7n is divided by 26, here $$1 \leq r \leq 26$$.
(ii) For decoding reverse process is allowed.
Based on this coding process, answer the questions 56-60.
The word FINE is coded as
The code for the word PRISM is
The string of letters that are coded as NEST is
The number of letters in the alphabet that are coded to themselves as under the given code is
The string of letters that are coded as CRISP is
For the following questions answer them individually
If SOLAR is coded as QMJYP, then the code for EIGHT is
If TENDER is cod ed as SDMCDQ then the code for PURCHASE is
In a certain code language, if the word DISTANCE is coded as EDCINSAT, then in that language ACQUIRE is coded as
If PICTURE is coded as QEDVOSA, then ELEVEN is coded as
In a code language, if GATE is coded as 10042308, then LURE is coded i!n that language as
If April $$1^{st}$$ , 2022 is Friday, which day will it be after 208 days?
At what time between 7'o clock and 8'o clock will the two hands of the clock be at $$120^{\circ}$$ angle with each other?
What will be the angle between the minute and hour hands when the clock shows the time as 5:15 ( in degrees) ?
E is the mother of the brother of a sister of A's father, then E related to A as
A daily train is scheduled 12:15 pm at Station A. It came 15 minutes late on Sunday, another 20 minutes late on Monday, another 25 minutes late on Tuesday and another 30 minutes late on Wednesday. Then the time of arrival of the train at station A on Wednesday is
A local train arrives at station A for every 45 minutes when Mr X came to station A, an announcement says that a local train has departed from station A, 18 minutes back and the next train will come at 11:41 AM. Then the time of the arrival of Mr.X to station A is
Five persons A, B, C, D, E are sitting around a table facing the centre. A sits to the left of E and C sits to the right of B. D is between A and C then the person on the right of E is
For real numbers a and b define $$a \triangle b = a^{2} - b^{2} + ab$$. Then the number of real values of a such that $$a \triangle a = 4$$ is
For the natural numbers $$x$$ and y, define
$$x * y = \sqrt{xy} + \frac{1}{\sqrt{xy}}$$ and $$x \odot y = \sqrt{xy} - \frac{1}{\sqrt{xy}}$$, then $$\frac{(3*4)*(3 \odot 4)}{(3*4)\odot(3 \odot 4)}$$ =
If $$x \oplus y = (x + y + 1)^{2}$$ and $$x \ominus y = (x - y + 2)^{2}$$, then $$(1 \oplus 4) \ominus (2 \oplus 5)$$ =
$$(25x^{2})^{\frac{1}{5}}.(5x^{4})^{\frac{2}{5}}.\left(125x^{\frac{27}{5}}\right)^{-\frac{1}{3}}$$=
$$\frac{\left(a+\frac{1}{b}\right)^{x}\left(a-\frac{1}{b}\right)^{y}}{\left(b +\frac{1}{a}\right)^{x}\left(b -\frac{1}{a}\right)^{y}}$$=
If $$x:y = 3:4$$, then $$(4x + 5y): (5x - 2y)$$ =
The sum of the cubes of three positive integers is 8072. If the ratio of the first and the second as also of the second and the third is as 3 : 2. Then the sum of the three numbers is
$$\frac{4+3\sqrt{3}}{7+3\sqrt{3}} = a + \sqrt{b}$$, then $$a - \sqrt{b} =$$
If $$\left(\frac{a}{b}\right)^{x-1} = \left(\frac{b}{a}\right)^{x-3}$$, then the value of $$x$$ is
The product of divisors of 127 is
The number of positive divisors of 680 other than one and itself is
LCM of $$m = 17.23^{2}.43, n = 31^{2}.23.47$$ is
The number among the following which leaves the remainder 3 when divided by 5, 6 and 8 is
The sum of 5 consecutive even integers is 50. What is the sum of their squares?
If the numerator and the denominator of a fraction are increased by 10% and 20% respectively, the number becomes $$\frac{22}{45}$$ . What was the original number?
Whiich of the following fractions is largest?
$$\frac{5}{7},\frac{7}{11},\frac{9}{13},\frac{4}{9}$$
The descending order of the following fractions is
$$\frac{9}{10},\frac{5}{14},\frac{7}{9},\frac{6}{11},\frac{8}{13}$$
If $$x$$ is 16% less than y, then y is what percent more than $$x$$?
In the year 1990 the population of cities X and Y were same. From 1990 to 2000 the population of X increased by 60%, while population of Y decreased y 60%. In the year 2000 the population of Y is what percent of population of X?
Cost price of first article is thrice the cost price of second article. If there is gain of $$x\%$$ on second article and loss of $$x\%$$ on first article, then gain percent or loss percent, in the total transaction is
By selling an article for Rs.6800 a trader loses 15%. For how much should he sell to get a profit of 25% (in rupees)?
A, B and Center into partnership. A invests some money at the beginning, B invests double the amount that of A after 6 months and C invests thrice the amount that of A after 8 months. If the annual profit is Rs.27000, then C's share is (in rupees)
A, B, Center into a business with capitals Rs.8000, 9000, 12000 respectively.
After 3 months D joins the business with a capital of Rs.18000. If there is a profit of Rs.2550 at the end of the year, then the difference between the shares of A and D in the profit, in rupees, is
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours.
If all the pipes are opened at a time, in how many hours will the tank be filled?
Two taps A and B can fill a tank in 2 hours and 3 hours respectively. Both taps are turned on and after 45 minutes turned off due to power cut. After 30 Minutes, only tap A is turned on. Time taken by Tap A to fill the remaining tank is
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to Band B to C is 2:3 (in kmph) is
A started running towards south at 7:00 am, B started running towards south at 11:00 am. At what time will they meet if the speeds of A and B are in ratio 3 : 7?
A a lone can complete a job in 12 days. After working far 2 days A is joined by B and they completed the job in 6 days. Had B worked alone how many days are needed to complete the job?
A works twice as fast as B. working together they complete a job in 14 days.
In how many days will B, working alone complete the job?
ABCD is a quadrilateral in which the length of the diagonal AC = 1.4 meters and the lengths of the perpendiculars drawn from B and D on AC are 80 cm and 50 cm respectively. The area of ABCD ( in sq. m.) is
A rectangular lawn of dimension 80m $$\times$$ 60m has two roads each of 10m wide are made in the middle and parallel to its length and breadth. Then the area of the roads in sq. m is
Volume of a right circular cone having base radius 70 cm and curved surface
area 40040 $$cm^{2}$$ is
A wall of dimensions 25m $$\times$$ 2m $$\times \frac{3}{4}$$ m is to be built by using bricks each of whose dimensions are 20cm $$\times$$ 10 cm $$\times$$ 7.5 cm. The number of bricks are needed to build this wall is
A solid consists of a circular cylinder with a right circular cone exactly fitted on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone, then the height of the circular cylinder is
A metallic solid cylinder of 14cm diameter and 32cm height is cast into 77 solid cubes of equal size. Then the length of side of the cube (in cm) is
If the diagonals of a rhombus are 30 cm and 24 cm. Then its area, in sq. cm. is
The remainder when $$33^{32}$$ leaves upon division by 7 is
The digit in the units place of $$7^{300}$$ is
If A, B, C are three subsets of a set X, then
{(A - B) - C} - {A - (B - C)} =
(Here A' = X - A)
Let U = {x $$\mid$$ x is a natural number $$\leq$$ 20}. Define
A = {x $$\mid$$ x $$\in$$ U and x is a prime number},
B = {x $$\mid$$ x $$\in$$ U and x is an even number},
and C = {x $$\mid$$ x $$\in$$ U and x is a multiple of 3 }. Then $$(A \cup B) \cap C$$ =
If the roots of the equation $$x^{4} - 10x^{3} + 35x^{2} - 50x + 24 =0$$ are 1, 2, 3 and 4, then the roots of the equation $$24x^{4} - 50x^{3} + 35x^{2} - 10x + 1 = 0$$ are
How much is to be added to the polynomial $$(x + 2)(x + 4)(x + 6)(x + 8)$$ to make it a perfect square?
If $$(x - 1)$$ and $$(x - 2)$$ are the factors of $$x^{4} - 5x^{3} + 4x^{2} + ax + b$$ then, $$\frac{a}{b}$$ =
If$$(x^{2} - 3x + 2)$$ is a factor of $$x^{3} - 6x^{2} + ax+ b$$ then $$a^{2} + b^{2} =$$
The digits of a 3 digit number are in strict descending order. Then the largest prime that always, divides the difference of the given 3-diigit number and the 3 digit number obtained by reversing the digits of the given number is
If length and breadth are reduced by 2 units each, area of rectangle reduces by 22 sq. units, then the perimeter of the rectangle is
If the solution of the system of equations
$$\frac{x}{4} + 2y = 7; \frac{19}{x+\frac{y}{4}} = 4$$ is $$x=\alpha$$ and $$y=\beta$$, then $$\alpha^{2} + \beta^{2}$$
The third term of Geometric Progression is 4; then the product of its first 5 terms in that Geometric Progression is
If the ratio of the sum of the first 3 terms of a geometric progression to the sum of the first 6 terms is 8:35, then the common ratio of that geometric progression is
The radius of the circle is 21 cms. The angle subtended by an arc of the circle at the centre is $$60^{\circ}$$. The length of its arc is
$$4(\sin^{4} 30^{\circ} + \cos^{4} 60^{\circ}) - 3 (\cos^{2} 45^{\circ} - \sin^{2} 90^{\circ}) =$$
If $$A + B = \frac{\pi}{4}$$ , then $$(1 + \tan A) (1 + \tan B)$$ =
If the angles of a triangle ABC are in arithmetic progression then
$$\frac{\cos C - \cos A}{\sin A - \sin C}$$ =
The angle of elevation of top of a mountain cliff from a point 200 m from its foot is $$45^{\circ}$$. The height of the cliff (in meters) is
The area of an equilateral triangle is $$256\sqrt{3}$$ sq. cm., then the perimeter of that triangle is
If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 26 cm. then the area of the triangle in $$cm^{2}$$, is
If the angles of a quadrilateral are in the ratio 4 : 5 : 10 : 11, then the angles are
$$ABCD$$ is a parallelogram in which $$AB = 2x + 5; CD = y + 1; AD = y + 5$$ and $$BC= 3x - 4$$. Then the lengths of the sides of the $$ABCD$$ are
In the following circle with center O, if $$\ANGLE AOB = 30^{\circ}$$, then the area of the
shaded region (in sq.cm.) is
If a semi circle is drawn on the side of a square, which has a diagonal of length 12 cm, the area of the semi circle, in $$cm^{2}$$, is
If the triangle with the vertices $$A(2, x), B(2,6), C(2 + \sqrt{3}, 5)$$ is equilateral then value of $$x$$ is
The point which divides the line segment (3, 5), (4, 7) in the ratio 2 : 3 internally is
Let A (-2, -2), B (31, 6) and C (8, 2) be three points. Let the slope of $$AB = m_{1}$$
and the slope of $$AC = m_{2}$$. Then $$m_{1}$$ : m_{2}$$ =
The Y-intercept made by the straight line passing through the point (3, 2) and perpendicular to the line y=x is
The equation of the line passing through the point (1, 2) and perpendicular to the line $$x + y + 1 = 0$$ is
Equation of the line perpendicular to the line $$y = 3x + 17$$ and which makes an intercept of length 6 units on positive Y-axis is
The equation of a line which is parallel to X-axis and cuts the positive side of the Y-axis at 7 units from the origin is
The equation of the line passing through (p, q) and having slope as $$\sqrt{3}$$ is
In a statistical data 2, 4, 6, 8, 10 occur with frequencies 1, 3, 5, 7, 9 respectively, then the arithmetic mean is
The average age of 4 boys A, B, C, D is 13 years, while the average age of B, C, D is 14 years then the age of A is
The arithmetic mean of a data of 100 observations is 23. If each of the observations is multiplied by 5 and then 2 is added to each observation, then the arithmetk mean of the new data is
A data conSists of the natural numbers of the form 2k + 1 with frequency $$k for 1 \leq k \leq 15$$, then the median of the data is
The median value for the followi1ng data is
The arithmetic mean and median of a frequency distribution are 20 and 30 respectively. The mode of this distribution is
The mode of the following data is
The probability of getting at least one head on a toss of five coins is
While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Then the probability that missing cards to be of different colours is
When 5 boys and 6 girls sit at random in a row, then the probability that boys and girls sit alternatively is
Meanings (Sentences with dashes)
The company is obliged to give a refund if the tour is ___________.
The monks are expected to live a life of _____________.
___________ in the idea of democracy is the notion of individual liberty.
Have you heard of the ten-year old mathematical _________ who can solve the toughest problems in the shortest amount of time?
Air strikes against military bases ___________ a full scale invasion.
Synonyms and Antonyms
Choose the antonym for 'Despicable'
Select the most appropriate synonym for 'abeyance'
Antonym of 'sparse'
Synonym of 'manifest'
Antonym of 'pusillanimous'
Verb (Tense and Voice)
Passive voice of 'People say there is a secrete tunnel near the village:'
is
When _________ you start for the party?
Active form of the sentence 'Let the window be closed.'
Passive voice of 'Read the newspaper report.'
One of my friends __________ broken his fingers and is in a lot of pain.
Phrasal Verbs & Idioms
Let us not ___________ this issue any more.
The director riding high on the huge success of his film. The underlined part means.
He always abides by the decision of his parents. The underlined expression implies:
Life is not a bed of roses.
The given idiom means:
He was in fine feather joking with his employees.
Articles & Prepositions
He is hard ___________ hearing.
He may 1ot be brilliant but he is good ________ English.
We had to walk _________ the forest to reach the village.
Spread the quilt ____________ the bed. Don't just put it there.
__________ the conversation, she left the room at once.
Computer Terminology
The process of dividing a disk into tracks and sectors is called _________.
The file extension of MS-WORD document in office 2007 is ________.
MOOCs stands for
Which of the following is not a memory device?
The full form of URL is ________.
Business Terminology
'Pareto' principle is also known as ___________.
A start-up that is valued at a billion dollars or more is called ________.
An ordered list of topics to be considered at a meeting, along with the name of the person responsible for each topic, is known as ____________.
A egal document that protects a company's secrets by holding the employees responsible is _________.
Export import policy of the government is formulated by
Read the Passage and answer the questions
Conservation technology is a growing field, and right up in the forefront are drones, or unmanned aerial vehicles, which are either operated by a remote controller or programmed to fly unaided. Drones have had a long history of use in the military and by large tech companies in mapping roadways, and their applications in conservation and ecology are growing.
Drones have various uses in wildlife conservation and monitoring, especially given the smaller sizes and more-affordable costs associated with this technology in modern times. Examples include using drones for elephant population monitoring and in measuring forest biodiversity. They are also widely used in monitoring illegal activities such as poaching or deforestation. Kaziranga National Park was the first protected area in India to utilize drones in targeting rhino-poachers.
UAVs are a so used to track wildfires and their spread, playing a role in disaster mitigation. Recent applications include the use of drones in pest management, where pesticides are loaded into drones for spraying large swaths of cropland, as seen during the locust swarm.
Drones can help counter issues related to safety of manned aerial surveys since there is no pilot involved and they can be flown into remote locations which might otherwise be inaccessibile. In the event of a crash scenario, their smaller sizes are likely to cause less damage which means ground staff who operate them do not face the risk of injury.
This passage is mainly about using drones for __________.
The first use of drones by Kaziranga National Park was in observin ____________.
Which of the following is NOT the use of drones?
UAV stands for ___________.
The Risk of crashes whille using drones is lower because of their ___________.
Read the Passage and answer the questions
Although nature must supply the initial force of desire, nature is not, in the civilised man, the spasmodic, fragmentary, and yet violent set of impulses that is in the savage. Each impulse has its constitutional ministry of thought and knowledge and reflection, through which possible conflicts of impulses are foreseen, and temporary impulses are controlled by the unifying impulse which may be called wisdom. In this way education destroys the crudity of instinct, and increases through know edge the wealth and variety of the individual's contacts with the outside world, making him no longer an isolated fighting unit, but a citizen of the universe, embracing distant countries, remote regions of space, and vast stretches of past and future within the circle of his interests. It is th is simultaneous softening in the insistence of desire and enlargement of its scope that is the chief moral end of education.
'Spasmodic' in the passage stands for a/an
Nature in the civilised men does not share the ______ of the savage.
Wisdom is an impulse that
Education makes man a ________ citizen.
The moral purpose of education is
Read the Passage and answer the questions
Theorists adopting psychodynamic approach hold that inner conflicts are crucial for understanding human behaviour, including aggression. Sigmund Freud, for example, believed that aggressive impulses are inevitable reactions to the frustrations of daily life . Children normally desire to vent aggressive impulses on other people, including their parents, because even the most attentive parents cannot gratify all of their demands immediately. Yet children, also fearing their parents' punishment and loss of potential love, come to repress most aggressive impulses. The Freudian perspective, in a sense, sees us as 'steam engines'. By holding in rather than venting 'steam', we set the stage for future explosions. Pent up aggressive impulses demand outlets. They may be expressed towards parents in indirect ways such as destroying furniture, or they may be expressed toward strangers later in life.
The word 'inevitable' in the passage is closest in meaning to
The word 'they' in the passage refers to
According to the passage, Freud believed that children experience conflict between a desire to vent aggression on their parents and
The word 'gratify' in the passage is closest in meaning to
Freud describes people as 'steam engines' in order to make the point that people
