Find the values of x and y.
I) $$2x + 3y = -2$$
II) $$-x - \frac{3y}{2} = 1$$
TS ICET 2021 Question Paper Shift-1 (20th Aug)
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 value of $$\cos^{2} \theta - \sin^{2} \theta$$?
I) $$\sin^{2} \theta = \frac{7}{25}$$
II) $$\theta$$ lies in first quadrant
A is a non-empty set and R,S are two relations defined on A. Is R $$\cap$$ S a reflexive relation?
I) R and S are reflexive relations
II) R is symmetric relation
R is a relation defined on A, where A is the set {a,b,c,d,e}.
Is R symmetric?
I) $$R \subseteq A \times A$$
II) $$R = \left\{(x,y) \mid x \ is \ vowel \ and \ y = e \right\}$$
How many colors have been used to paint the outer surface of the cube?
I) Each face of the cube is painted using only one color, and no two adjacent faces have the same color.
II) At least two pairs of opposite faces have the same color.
Is 5 a root of the poly1101nial $$p(x)$$?
I) $$p\left(p\left(p(7)\right)\right) \neq 0$$
II) $$p(7) = 21$$ and $$p(21) = 5$$
What is the value of the positive two digit number?
I) The number is six times the sum of its digits.
II) The number obtained by reversing the digits is less than the original number by nine.
What will be the population in the city A in 2025?
I) In 2020 the population of the city A was 10 million.
II) In 2015 the population of the city A was much less than that of 2020.
If a and b are two digit numbers that share the same digits except in reverse order, then what is the sum of a and b ?
I) a - b = 45
II) The difference between the two digits in each number is 5
Is $$\frac{1}{a_{1}},\frac{1}{a_{2}},\frac{1}{a_{3}} ...$$ a Geometric Progression?
I) $$a_{1},a_{2},a_{3}$$.....is an Arithmetic Progression.
II) $$a_{1},a_{2},a_{3}$$.....is a Geometic Progression..
What are the values of x, y and z ?
I) $$x : y : z = 1 : 2 : 5$$
II) $$x + y + z = 64$$
In which quadrant the angle $$\theta$$ lies ?
I) $$\tan \frac{\theta}{2} + \cot \frac{\theta}{2} = -3$$
II) $$\sec \theta > 1$$
If the median of the set S is 19, what is the range of S?
I) S={18, 28, 11, $$x$$, 15, y }
II) Arithmetic mean of the elements of S is 20
Who is the tallest person among a, b, c ?
I) a is taller than c
II) c is shorter than b
$$x$$ and y are integers, $$x$$ is even and y is odd. Is the integer z odd?
I) $$xyz + 1$$ is odd
II) $$xy + yz + zx$$ is even
What is the area of the square?
I) The ratio of the length of a diagonal and the length of a side is $$\sqrt{2} : 1$$
II) The area of the circumcircle of the square is $$18 \pi cm^{2}$$
Is the square matrix A non singular ?
I) A is a 3$$\times$$3 matrix
II) The elements of A are distinct positive integers
What is the length of the rectangle R ?
I) Area of the rectangle R is 1200 sq. ft.
II) The cost of fencing the plot R along the side is Rs.56000 at the rate of Rs.400 per foot.
If $$If x \neq 0$$, is $$\frac{1}{x} > 1$$
I) $$\frac{x}{y} > y$$
II) $$x^{3} > x^{2}$$
A, B, C, D are points on the circumference of a circle. What is the area of quadrilateral ABCD?
I) Radius of the circle is $$\frac{\sqrt{2}}{2}$$
II) ABCD is a square
For the following questions answer them individually
Island : water :: Oasis : ________
If A, N, G, E, L are removed from English alphabet, then which letter occurs in $$13^{th}$$ place from the end?
How many consonants are there between e and u in English alphabet?
POST : VUYZ :: CPME : _____
DCAB, ______ , ABDC, BDCA
TLRIA : WOULD :: BEYOND : _____
$$L \otimes N \otimes P : 12\otimes14\otimes16 :: U \otimes W \otimes Y : $$_____
DECA :: ______ : MORE : OSXM
RAT : OXQ :: OLX : _______
30 : 42 :: 56 : _________
Note : In questions numbered 31 10 35 pick the odd thing out.
Note : Each of the questions from 36 to 45 follows a define pattern, observe the same and fiil in the blanks with suitable ones.
$$10_{2}, 100_{2}, 110_{2}, 1000_{2}, 1010_{2}$$, _______
$$a^{1/z}, b^{1/c}, c^{1/x}, d^{1/d}$$, _________
$$1\frac{8}{9}, 2\frac{2}{9}, 2\frac{5}{9}, 2\frac{8}{9}, 3\frac{2}{9}$$, _______
1, 5, 9, 15, _________
3, 5, ______ , 17, 33, _______
$$\frac{3}{8}, \frac{15}{24}, \frac{35}{48}$$, _______
525, 646, 477, 702, _______ , 774
36, 150, 392, 1452, _______
$$\frac{3}{5},\frac{8}{10},\frac{15}{17},\frac{24}{26},\frac{35}{37}$$, _____
2500, 250, 3750, 187.5, _______
The following chart indicates biscuit tins produced and their value in 2016 to 2020. Based on the information answer questions.
In which year the value of a biscuit tin is minimum?
The difference of cost per tin in the year 2018 and 2020. in rupees, is
The percentage increase in the cost per tin from 2016 to 2020 is
The following Pie chart shows the income of a state under different heads. Based on the information given in the chart answer questions.
If the Excise tax collected in that year is Rs.1250 crores then sales tax collected in that year in rupees (in crores)
The percentage of income tax in the total income of the state, collected to two decimal places is
If the Income Tax collected in the year is Rs.175 crores, then the total income of the state in that year (Rupees in crores) is
The percentage of the total income collected through commercial tax, income tax and others together in the sales tax collected in that year is
If the total income of the state is Rs. 12000 crores, then the difference of commercial tax and income tax in that year (Rupees in crores)
The following Venn diagram represents the 1200 employees of a company. Each of the employee is a member of at least one of three clubs A, B and C. Using the given data, answer the questions.
How many employees are members of club C only?
How many employees are not members of club B?
The 26 letters of the English alphabet are written around a circle in anticlockwise direction. Then each vowel is coded as the $$2^{nd}$$ vowel from it (for example, A is coded as I, E is coded as O etc) and each consonant is coded as $$4^{th}$$ consonant from it (for example, B is coded as G, C is coded as H etc). For decoding reverse process is adopted. Based on this information, answer the questions from 56 to 60
The letter that is coded as T is
The code word for WORD is _________
The code word for TABLET is ______
The string of letters that is coded as PRIME is
The string of letters that is coded as TSICET is
For the following questions answer them individually
If MASK is coded as HVNF, then the code for GLOVE is
In a certain code language, if the word REJECTION is coded as SGMIHZPWW, then how is the word MECHANIC coded in that language?
If TRIGONOMETRY is coded as UTLKTTVUNDCK. then TRIANGLE will be coded as
If ISOLATED is coded as EOKHWPAZ, then which word is coded as LKOEPERA?
If ENGLAND is coded as 1234526 and FRANCE is coded as 785291 then the code for GREECE is
If today is Sunday what day it was 126 days ago?
If the length of the minute hand of a clock is 14 cm, then the area swept by the minute hand in 15 minutes is (in sq. cm)
The smaller angle between the two hands of a clock at 3.49 pm, in degrees is
A man goes to a park and sees a girl who he recognised to be his relative. The girl was the daughter of his sister's husband's wife. How is the girl related to the man?
Two local trains arrived at a station at 12.30 pm and 2.40 pm each running late by 20 minutes and 40 minutes respectively. What was the difference (in minutes) in their original scheduled times of arrivals?
A person comes for a job interview at 10.20 am, which was 40 minutes before the scheduled time which, in fact, was already delayed by 20 minutes. What was the original scheduled time of the inte1view?
Five friends A, B, C, D and E are posing for a photograph standing in a line in some order such that
i) D is to the right of E
ii) B is to the left of E and to the right of A
iii) D is to the left of C
What is their order of standing ?
If 24 & 32 = -2 and 52 & 68 = -4. then 76 & 36 =
For $$a, b \ \epsilon \ R$$, define $$a * b = a + b + ab$$. Then $$5 * (-5 * 6) =$$
If $$a * b = (a+b)^{2} - (a-b)^{2}$$, then $$\left((1 * 2) * 3\right) * 4 =$$
If $$x^{x\sqrt{x}} = \left(x\sqrt{x}\right)^{x}$$, then $$x$$ =
If $$3^{x} = 9^{y} = 27^z$$ and $$xyz = 2304$$, then $$3x + 2y + z =$$
If $$A : B = 2 : 3; B : C = 3 : 4; C : D = 4 : 5$$, then $$D : A =$$
The ratio of the volumes of a cylinder and a cone having same base radius and same height is
If $$x = \sqrt{3}-\sqrt{2}$$, then the value of $$\frac{1}{x^{4}}-x^{4}$$ is
$$\frac{1}{\sqrt{18}+3}+\frac{1}{\sqrt{27}+\sqrt{18}}+\frac{1}{\sqrt{36}+\sqrt{27}}+...+\frac{1}{\sqrt{900}+\sqrt{891}} =$$
If $$2^{2}$$ divides 19!, then the largest positive integer k is
The remainder when $$(48)^{5}$$ is divided by 5 is
What is the least number that should be subtracted from 5337 to make it a perfect square?
If the LCM and the GCD of two positive integers are 4641 and 21 respectively, and if one of the numbers is greater than 300 then the other number is
The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is _______
If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes $$\frac{7}{9}$$ and if both the numerator as well as the denominator are increased by 1, the fraction betomes $$\frac{4}{5}$$. What is the original fraction?
If the fraction $$\frac{19}{21}, \frac{21}{25}, \frac{25}{29}, \frac{29}{31}$$ and $$\frac{31}{37}$$ are arranged in the ascending order, then the largest fraction is
The ascending order of the following rational numbers is
$$A = \frac{4}{9};B = \frac{7}{12};C = \frac{3}{7};D = \frac{8}{15};E = \frac{1}{2}$$
The price of petrol is increased by 40%. By how much percent should a citizen reduce his purchase so as not to increase his expenditure?
In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?
A person sold a cow at a gain of 15%. Had he bought it for 25% less and sold it for Rs.600 loss, he would have made a profit of 32%. The cost price of the cow is (in rupees)
The cost price of 15 articles is equal to the sale price of the 12 articles. What is the final outcome of this transaction?
Three persons A, B and C enter into a business. A invests some money at the beginning, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs.27000, C's share in rupees is
A person started a business with Rs.900000. After sometime, another person B joined him by investing Rs.400000. At the end of the year they share their profit in the ratio 9 : 2. After how many months B joined A?
An electric pump can fill a tank in 5 hours. Because of a leak it took 6 hours to fill the tank. In how many hours the leak can empty the tank (in hours)?
Two pipes A, B can fill a tank independently in 4, 6 hours respectively. Both the pipes are opened at the same instant and after $$x$$ hours pipe A is stopped. If the total time taken to fill the tank is $$3\frac{1}{2}$$ hours, then $$x$$ is
If a car is moving at 5 meters per second, the time taken for it to cover a distance of 60 km is
A person goes from city-A to city-B at 60 kmph speed and returns from city-B to city-A at 40kmph speed. If the total journey time is 5 hours the distance between A and B (in km)
Two persons A and B can complete a piece of work in 4 days; B and another person C' in 6 days and A, B, C together in 3 days. If A and C' alone work on the same piece of work the number of days required to complete it is:
Ravi alone can complete a piece of work in 30 days. After working for 10 days
Ravi invites Ramu to join the work. If they together finish the work in the next 8 days, then Ramu alone can require the number of days to complete the work is
A man walks 89 meters along the diagonal of a rectangular field. If, the length of the field is 80 meters, find the cost of fencing the field at the rate of Rs.100 per meter (in rupees)?
Two poles of heights 78 meters and 30 meters stand up in a play ground. If their feet are 55 meters apart, find the distance between the tops (in meters)
From a right circular cylinder of height 21 meters and the base diameter of 20 meters a cone of same dimensions is removed. The volume of the remaining portion will be ( in $$m^{3}$$)
If a hemisphere has radius 24 cm, then its total surface area. in $$cm^{2}$$ is
The area of a square field is 3136 sq.m. This is to be fenced on all the four sides by a barbed wire three times (at different heights) leaving space for 2 gates of width of 1 meter each. If the cost of fencing is Rs.150 per metre the total cost (in rupees is)
The amount (in sq.m.) of canvas required to erect a conical tent whose height is 8.4 m and having area of the base as 38.5 sq.m is (taking the approximate 22 value of $$\pi$$ as $$\frac{22}{7}$$)
If the lateral surface area and the total surface area of a right circular cylinder are in the ratio 7 : 9 and its base radius is 4 cm, then the height of the cylinder (in cm) is
If $$n^{2} - 1$$ is divisible by 8, then n is
$$4212_{7}+5136_{7}-2354_{7}=$$
The statement $$p \wedge(\sim q)\rightarrow$$ p is a _____
Consider the following statement,
p: A is good at mathematics
q: A is good at English
for the statement p $$\rightarrow$$ q, the statement
'A is good in mathematics and A is not good in English" is
In a town of 840 persons, 450 persons read Hindi newspaper, 300 read English newspaper and 200 both. Then the number of persons who read neither Hindi nor English news paper is
If a set A has 4 elements, and the number of binary relations on A which are anti symmetric is $$2^{\alpha} \times 3^{\beta}$$, then $$\alpha + \beta = $$
Let $$f : R \rightarrow R$$ be defined as $$f(x) =3x^{2} - 7$$ for all $$x \epsilon R$$ then f is
A line makes intercept -3 from on the y-axis and has slope is $$\frac{3}{5}$$. Then, its equation is
The points $$(p + 1, 1), (2p + 1, 3)$$ and $$(2p + 2, 2p)$$ lie on the same straight line only if $$p =$$
If $$\tan \alpha = \cot \beta = 1$$ and $$\alpha, \beta$$ are both acute angles, then the value of $$2\alpha + \beta$$
is
If $$13 \sin \theta = 12$$ and $$\theta$$ acute, then $$\frac{cosec \theta + \cot \theta}{\tan \theta + \sec \theta} =$$
$$\frac{1+\sin \theta + \cos \theta}{1+\sin \theta - \cos \theta} =$$
Seen from the top of a tower 100 meters tall the angles of depression of two points A and B on the ground which are on the opposite sides of the tower are $$30^{\circ}$$ and $$60^{\circ}$$ respectively. The distance AB in meters is:
If a polynominal in $$x$$ leaves remainder -2 and 19 when divided by $$(x + 3)$$ and $$(x - 4)$$ then the remainder it leaves when it is divided by $$x^{2} - x -12$$ is
The roots of the equation $$\sqrt{6} x^{2} - 5x + \sqrt{6} = 0$$ are
If $$(x - 5)$$ is a factor of the polynominal $$p(x)$$, then a factor of the polynomial $$p(x^{3} - 3)$$ is
A number when divided by 5, leaves 3 as remainder. When the square of that number is divided by 5, then the remainder will be
Three pens and four pencils cost Rs.18. Four pens and three pencils cost Rs.17. Then, the cost of 14 pens and 14 pencils (in rupees) is
If $$\mid x - 2\mid + \mid x - 3\mid < 4$$, then the range of $$x$$ is
The sum of n terms of a progression is $$S_{n} = 5n^{2} + 2n$$. Then, the $$n^{th}$$ term $$t_{n}$$?
If the $$5^{th}$$ and $$9^{th}$$ terms of a Geometric Progression are $$\frac{1}{9}$$ and $$\frac{1}{729}$$, then the first term of that Geometric Progression is
The coefficient of $$x^{7}$$ in the binomial expansion of $$\left(x^{3} - \frac{2}{x^{2}}\right)^{5}$$ is
Find the term independent of $$x$$, where $$x \neq 0$$, in the expansion of $$\left(\frac{3x^{2}}{2} -\frac{1}{3x}\right)^{15}$$
If $$A = \begin{bmatrix}2 & 2 & 1\\1& 0 & 2\\2 & 1 & 2\end{bmatrix}$$ is the inverse of $$B = \begin{bmatrix} -2 & a & 4\\ 2 & 2 & -3\\ 1 & 2 & -2\end{bmatrix}$$ then a =
If $$A = \begin{bmatrix}1 & 2 & 3\\ 0& 1 & 2\\0 & 0 & 1\end{bmatrix}, B = \begin{bmatrix}x\\ y\\ z\end{bmatrix}$$ and $$AB = \begin{bmatrix}6\\3\\ 1\end{bmatrix}$$ then $$x + y + z =$$
$$\lim_{x \rightarrow 0}\frac{2 \sin x - \sin 2x}{x^{3}} =$$
If $$y = \frac{x^{3} - 3}{7x^{2} + 2}$$, then $$x = 2$$, $$\frac{dy}{dx} =$$
In the adjacent figure $$\angle A=90^{\circ}$$ and $$AD \perp BC$$. If $$AC=10\sqrt{3}$$ and $$AD = 5$$ then $$DC =$$
In the quadrilateral ABCD, AB = AD. The bisectors of $$\angle$$ BAC and $$\angle$$ CAD meet the sides BC and CD at points E and F respectively. If CE = 6 cm, BE = 4 cm and BD = 15 cm, then the length of EF (in cm) is
A, B, C are three points on the circumference of a circle. If AB = 6 cm, AC = 8 cm and $$\angle BAC =90^{\circ}$$ then the radius of the circle (in cm) is
The perimeter of the triangle ABC with the vertices $$A(3, 2); B(-3, 2); C(0, 2 - 3 \sqrt{3})$$
The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2. 3), B(6, 7) and C(8, 3) is
The Arithmetic Mean of the following distribution is
$$x_{i}$$ : 1 2 3 ....21
$$f_{i} : 1^{2} 2^{2} 3^{2} .....21^{2}$$
The median of the observations 7, 8, 7, 9, 7, 14, 15, 6, 8, 14, 9, 17, 15, 16 is
If the Mean and Median of a set of observed data are 36 and 44 respectively, the Mode of that data is
The standard deviation of the data is 73, 74, 75, .... 85
If the standard deviation of the data : 7, 10, 13, 16, ... , 121 is $$\sigma$$ then the standard deviation of the data 50, 71, 92, .... 848 is
From the data of 8 comparable observations, the sum of the squares of the deviations in their ranks is found to be 31.5. Then coefficient of rank correlation is:
A pair of unbiased dice is thrown. The probability that there is either there appear same number on both or a sum of the numbers on their faces less than six, is
If two unbiased dice are thrown simultaneously, then, the probability of getting a total of 8 with at least one prime number
A box contains 5 red and 3 green and 4 black balls. Two balls are drawn in succession without replacement. Then, the probability that they are green and black in color is
If A and B are two events such that $$P(A) = \frac{3}{8}; P(B) = \frac{1}{3}$$ and $$P(A \cap B) = \frac{1}{4}$$
Then $$P(\overline{A} \cap \overline{B}) =$$
Choose the correct word/correct meaning of the word/Fill in the blanks with correct word/ verb/phrase/preposition.
Incredible
Contentious
Imperative
Retrograde
Lethargic
Tactical
A critical judge of any art and craft is ________.
A person who attacks popular beliefs or established customs is a/an_______.
Our boss is interested in making money and nothing else. Behind all his actions, he has a ________ motive.
I tried in vain to please him by all means. But he appears to be quite ________.
The full form of LOGO is ________
Liability is _________.
The assets and cash in a business are called
A kilobaud is ___________.
A financial statement that reports a company's assets, liabilities and shareholders' equity at a given time is called ______.
Pict01ial representation of step by step sequence for solving a problem is called _________.
A failure or flaw in the software programme is called ______.
One gigabyte is equal to _________.
ROM stands for _______.
HTML stands for _________.
A: My new car cost me an arm and a leg.
'A' means that the car ___________
A: I know she is working full-time. How is she able to teach her kids for two days?
B: She is capable of managing to get the best of both worlds.
The car hit the boy and to add insult to injury it drove off without stopping.
The underlined idiom means
Change the following sentence into passive voice:
"Open the door."
Change the following sentence into indirect speech
He said to his son, "Cross the road always at zebra crossing."
On of the students _______ brilliant.
He was murdered in cold blood.
The underlined idioms means
I was late to the office as the car ________.
We _______ to our holidays.
This work is __________.
Though I shouted, there was no response from the old man. He seems to be hard ________ hearing.
I don't know how she puts _______ his cruelty.
I'd rather _______ than go to a movie in this pandemic situation.
Dinesh has been working in this institution ______ 2009.
No sooner had I reached the station, _____ the train arrived.
Read the following passage and answer the questions.
The ability to speak in words and to enunciate clearly is a blessing which the creator has bestowed on man alone. No other living creature can speak. This is a blessing which should be highly prized and respected. The English language as well as the organised languages of other people. and nations, is replete with words which cany every conceivable shade of meaning. It is possible to choose the right words; word which will attract and not repel. There is no excuse for the careless use of words which will offend the sensibilities of others. The appropriate use of words is regarded as a sign of education and culture. The person who is able to use the proper words at the proper time has developed a very important factor in the achievement of a pleasing personality. While the inappropriate use of words can repel, the appropriate use of words, together with a pleasing and motivating tone for voice and pleasant facial expression, can go a long way toward gaining for one the attention, respect, confidence and liking of other persons.
What can man alone do?
What is the nature of an 'organised language'?
Why is it necessary to use appropriate words?
What is inexcusable?
Appropriate use of words is a sign of
Read the following passage and answer the questions.
When I worked in a second-hand book shop-so easily pictured, if you don't work in one, as a kind of paradise, where charming old gentlemen browse eternally among calf-bound folios - the thing that chiefly struck me was the rarity of really bookish people. Our shop had exceptionally interesting stock, yet I doubt whether ten percent of our customers knew a good book from a bad one. First edition snobs were much commoner than lovers of literature, but oriental students haggling over cheap text books were commoner still, and vague-minded women looking for birthday presents for their nephews were commonest of all.
Many of the people who came to us were of the kind who would be nuisance anywhere but have special opportunities in a bookshop. For example, the dear old lady who 'wants a book for an invalid (a very common demand, that), and the other dear old lady who read such a nice book in 1897 and wonders whether you can find her a copy. Unfortunately she does not remember the title or the author's name or what the book was about, but she does remember that it had a red cover. But, apati from these there are two well-known types of pest by whom every second hand bookshop is haunted. One is be decayed person smelling of old bread crusts who comes every day, sometimes several times a day, and tries to sell you worthless books. The other is the person who orders large quantities of books for which he has not the smallest intention of paying. In our shop we sold nothing on credit, but we would put books aside, or order them if necessary, for people who arrranged to fetch them away later. Scarcely half the people who ordered books from us ever came back.
what do you mean by "calf-bound folios"?
What did the author discover in the second-hand book shop?
What does the author mean by "First edition snobs"?
The tone of the author in the passage is
"Unfortunately she does not remember the title or the author's name or what the book was
about, but she does remember that it land a red cover. "What does it tell about the lady?
Read the following passage and answer the questions.
Since we now know what a terrible evil war is, we must spare no effort to prevent its recurrence. To this reason must also be added an ethical one: In this, course of the last two wars, we have been guilty of acts of inhumanity which make one shudder, and in any future war we would certainly be guilty of even worse. This must not happen!
Let us dare to race the Situation. Man has become superman. He is a superman because he not only has at his disposal innate physical forces, but also commands, thanks to scientific and technological advances, the latent forces of nature which he can now put to his own use. To kill at a distance, man used to rely solely on his own physical strength; he used to bend the bow and to release the arrow. The superman has progressed to the stage where he can use the energy released by the combustion of a given combination of diemical product$. This enables him to employ a much more effective projectile and to propel it over far greater distances.
However, the superman suffers from a fatal flaw. He has failed to rise to the level of superhuman reason which should match that of his superhuman strength. He requires such reason to put this vast power to solely 1easonable and useful ends and not to destructive and murderous ones. Because he lacks it, the conquests of science and technology become a mortal danger to him rather than a blessing.
"This must not happen" what does this refer to in the passage?
Man has become a 'super man', because of ________
What is the 'fatal flaw' of the super man
In the author's opinion, the scientific and teclmological conquests have turned out to be ________ to the humanity.
What does the author think of war in the modern context?
