TS ICET 2020 Question Paper Shift-1 (30th Sep)

In the followings, 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.

Is the positive integer 'n' even ?

(I) 12 n is an even integer.
(II) 11 n is an odd integer.

Among A, B, C, D and E, who is the heaviest?
(I) C is heavier than only A.
(II) D is lighter than B, but heavier than C and E.

What is the perimeter of the equilateral triangle?
(I) All the sides are equal.
(II) The area of the triangle is $$\frac{\sqrt{3}}{4}$$ Sq. units.

Find the value of x?
(I) $$x$$ is divisible by 2
(II) $$x$$ is divisible by 7

If $$a_{1} , a_{2} . .. .. a_{40}$$ are in arithmetic progression, then the common difference is
(I) $$a_{36} - a_{10} = 52$$
(II) $$a_{40} = 83$$

Which train is moving with a greater speed?
(I) A train P of length 300m crosses a man in 18 seconds,
(II) Another train Q of length 250m crosses a bridge of length 350m in 20 seconds.

what is the value of $$\frac{x^{3} + 3x^{2}y + y^{3}}{4xy^{2}}$$
(I) x = 43
(II) x : y = 7 : 9

What is relative speed of the boat?
(I) Speed of boat in still water is 2 kmph.
(II) The boat is moving against the current.

Is n a prime number?
(I) The sum of positive divisors of n is n + 1,
(II) n is a positive integer.

If a, b are positive integers such that ab = 84, what is the value of a?
(I) $$a > b$$
(II) $$9 <\frac{a}{b} <10$$

what is average of $$x, y, z$$ and t ?
(I) The average of $$x$$ and t is and the average of y and z is also 5.
(II) $$x, y, z$$ and t are integers $$\geq 1$$.

What is the interest earned in one financial year on a term deposit in a bank?
(I) The amount deposit is Rs.10000.
(II) The rate of interest is 6.5% per annum.

Does the Set A contain primes?
(I) A has 99 elements in it.
(II) $$A = \left\{100! + 2, 100! + 3, ..., 100! + 100 \right\}$$

Is n a perfect square of an integer?
(I) n leaves remainder 2 when n is divided by 4.
(II) n leaves remainder 1 when n is divided by 8.

What is the number of vertices of the regular polygon?
(I) The sum of the angles subtended by the sides at the centre of the polygon 2 $$\pi$$
(II) The number of diagonals of the polygon is 170.

Find the value of $$\sin^{2}\theta + \sin \theta \cos \theta+ \cos^{2}\theta$$
(I) $$\theta ∈ \left(0, \frac{\pi}{2}\right)$$
(II) $$\sin \theta = cos \theta$$

What is the least value of $$\theta$$?
(I) The matrix $$ = \begin{bmatrix} \mathbf{\tan \theta} & 0 & 0\\ 0 & 1 & 1 \\ 0 & 1 & 1 \end{bmatrix}$$ is singular
(II) $$0 < \theta < \frac{\pi}{4}$$

What are the co-ordinates of the point P?
(I) P lies on the line of $$y = x$$
(II) P is at a distance of $$\sqrt{18}$$ units from the origin.

Is g : ℝ $$\rightarrow$$ ℝ an even function?
(I) $$g(x)= ax^{5}+bx^{3}+cx^{2} + x$$
(II)a, b, c are integers

What is the distance between the towns A and C?
(I) It takes 60 minutes to go from A to B
(II) It takes 90 minutes to go B to C

For the following questions answer them individually

The number that does not fit in the following sequence is

Each of the questions from 36 to 45 follows a definite pattern, observe the same and fill in the, blanks with suitable ones.

Consider the following table that gives the production of different crops A, B, C, D, E by a state from 2010 to 2015 in million tonnes. Based on this information, answer questions 46 to 48 .

The percentage increase in production of crop 'A' over the entire period 2010 to 2015 is

The expenditure under five heads of account, A, B, C, D, E of a company is shown in the following Pie chart. Based on this data, answer the questions from 49-53.

The difference in the sectorial angles of expenditure between the heads of accounts under C and D is

If Rs. 120 lakhs is the total expenditure in an year, then the ratio of the expenditures under the heads B and E to that of C as is

In a particular year, the company decided to cutdown the expenditure under the head C to the extent of 5% and wanted to increase 2% in A and 3% in D. If the annual expenditure during that year is 96 lakhs, then the total expenditure towards the heads A and D (in lakhs of rupees) is

The average expenditure under various heads of the company is equal to the expenditure under which of the following heads of account:

In a class of 30 students, 15 can speak Marathi, 17 can speak Hindi and 13 can speak English, 5 students can speak both English and Marathi and two out of these can also  speak Hindi. 6 students speak only English and speak only Hindi. Based on this information answer the following questions.

Answer the questions 56 to 60 based on the following table, and the rules stated below:

i) If the first and last letters of a word are consonents then codes are interchanged;
ii) If the first and last letters of a word are vowels, and they are replaced by the symbol $$\beta$$;
iii) If two vowels come togher in a word then they are replaced by the symbols that come next to the vowel in the chardt

For the following questions answer them individually

In a certain code 16 means SWEET AND HOT 537 means COFFEE IS SWEET and 236 means TEA IS HOT. Then 536 means

At what time between 5.30 and 6.00 will the hours hand and minutes hand of a clock will be at right angle?

Mr.P left home for the bus stop 30 minutes earlier than usual. It takes 18 minutes, for P to reach the bus stop. If P reaches bus stop at 9.00 am, then at what time does P usually leave house for the bus stop?

An express train departs from station X at 5.00 am with maximum allocated speed 120 kmph. The train is scheduled to arrive station Z and return to station Y to halt at night. At what time the train will reach station Y, if the total waiting time between the stations of boarding is 45 minutes?

Eight persons A,B,C,D,E,F,G and H are sitting in a straight line facing North but not necessarily in the same order. F sits fifth to the right of A. D sits fifth to the right of E. E sits to the immediate right of A. H sits towards the left of D. B sits third to the right of G. G is an immediate neighbour of A . Which of the following is definitely true?

If $$a*b = (a + b) + (a - b)^{2}$$ and $$a \triangle b = (a + b)^{2} - (a - b)$$ then $$(3 \triangle 5):(3 * 5) =$$

For real numbers $$x$$, y, define two binary operations $$\odot$$ and $$\ominus$$ by

$$x \odot y = x^{2} + y^{2} + 3xy - 5$$
$$x \ominus y = 3x + 4y + 5xy + 6$$ then
$$(1 \odot 2) \ominus (2 \odot 3) = $$

Three persons A, B and C invested their annual savings in a bank at 20% rate of simple interest per annum. If each of them gets an equal amount after 10, 15 and 20 years, respectively. Then the ratio of their initial investments is

The GCD of 3240, 3600 and $$x$$ is 36 and the LCM of these three number is
$$2^{4} \times 3^{5} \times 5^{2} \times 7^{2}$$ then $$\sqrt{6x}=$$

Three bicycles are fitted with wheels that can make 6, 5 and 10 revolutions per minute respectively. One spoke on each wheel is painted blue. All three bicycles start moving at the same time, and the poke of the wheels painted blue is in the same position for all 3 bicycles. After how much time, will all the three wheels be a1igned in the same manner as they were at the starting? ( in seconds)

The rational number that represents the recurring decimal number $$0.2\overline{34}$$ is

Six persons A, B, C, D, E and F are of different heights. No two among them, are of same height. It is also known that

i) A is taller than B but shorter than C
ii) Dis taller than E who is in turn is taller than F
iii) F is taller than A

Who is the shortest?

If the following fractions are arranged in descending order (of their magnitudes), the
middle one is

$$\frac{2}{3}, \frac{5}{7}, \frac{9}{13}, \frac{9}{14}, \frac{7}{9}$$

In a ready made cloth stores a customer has got 10% discount on his dress, but has paid 2.5 %. CGST and 2.5% SGST on the discounted rate. Had he got Rs.200 as discount and then paid the said taxes, he would have paid Rs.42 more. The price (in Rupees of the dress before the discount is

A dealer sell items at a 20% profit. If the cost of items doubles and the profit percent becomes half its present value, then the actual profit now is what percent of the previous profit?

An item is sold at a profit of 30% to its cost price. Had the profit been 30% of the present selling price, the, vendor would have gained Rs. 540 more. What is the present selling price? (In rupees)

A and B started a business with B's investment 2.5 times that of A. Ratio of time period of the investment of A and B was 3 : 1 and the total investment made by both of them was Rs.28000. If the annual profit earned was Rs.2500 less than A's investments, the difference between their annual profit is (in rupees)

Three persons A, B, C start a business with capitals Rs.8 lakhs Rs.10 lakhs and Rs.12 lakhs. After 6 months C has taken back Rs.4 lakhs from the capital and after another 2 month B withdraws an amount of Rs.2 lakhs from the capital. Then A's share in a profit of R.574000, at the end of the year, in Rupees

An overhead tank is connected by 3 pumps A, B and C. The pumps A and B can fill the tank in 4 hours and 5 hours respectively, where a C can empty the Tank in 2 hours. If A. B and C are opened in order at 5.00 am; 6.00 am and 7.00 am when will the tank be empty?

Two pipes A and B can fill a cistern in 12 minutes and 18 minutes respectively. Both are kept open for 2 minutes and A is closed. In how many minute will the tank be full?

A car covers a given distance moving at a speed of 35 kmph. However, if it were to halt for a fixed number of minutes every hour, its average speed would work out to 28 kmph. For how many minutes does the car stop per hour?

Three Engineers or four Technicians can complete a project in 43 days. How many days will it take for seven Engineers and five Technicians to complete the same project?

A and B can complete a piece of work independently in 12 and 16 days respectively. Both of them start the work and after 4 day B leaves. In how many days, will A complete the work.

A rectangular field has its length and breadth in the ratio 5 : 4. A man riding on a bicycle complete one lap of the field along its perimeter at a speed of 10.8 kmph in 4 minute and 36 seconds. The area of that field (in sq. meters) is

What is the radius of a spherical ball which is formed by melting a metallic cylinder of base diameter 8 inches and height 160 inches if conversion wastage result in 10% of weight loss? (in inches)

A rectangular park is of dimensions 8Om $$\times$$ 60m. The two walking paths 10m wide are to be constructed in the middle of the park parallel to its length and breadth. If the cost of construction of the path is Rs.300 per sq.m. Then the total cost (in lakhs) is

A vessel is in the form of a cylinder surmounted by a hemisphere. If the diameter of sphere is same as diameter 14 cm of the cylinder and if height of the cylinder 17 cm, then the volume of the vessel (in $$cm^{3}$$) is

From a rectangular sheet of paper of dimension 30cm $$\times$$ 20cm, squares of equal side 3 cm is cut out from each corner, and the remaining parts are folded on 4 side to form open rectangular box. Then the volume of the box (in $$cm^{3}$$) is

What is the contrapositive of the following statement?
'If two triangles are congruent, then they are similar'

In a group of athlete in a school, 21 are on basket ball team, 26 are on hockey team and 29 are on foot ball team. If 14 play hockey and basket ball, 12 play foot ball and basket ball, 15 play hockey and foot ball and 8 play all the three how many play only foot ball?

If the function given by $$f(x) = x+2$$ with domain $$\left\{x : 2 \leq x \leq 5\right\}$$, then the intervals of domain and range of $$f^{-1}$$ are respectively

If $$A = \left\{1, 2, 3 \right\}$$ and R is the relation given by
   $$R = \left\{ (1, 1), (2, 2), (3, 3), (1, 2), (2, 1) \right\}$$, then

If $$13 \sin \theta = 12$$ and $$\theta$$ is acute then $$\frac{\cosec \theta + \cot \theta}{\tan \theta + \sec \theta} =$$

$$\sin A + \sin B = $$

Two boys A and B are opposite side of a tower of height 150mts. They measure the angle of elevation of top of the tower as $$30^{\circ}$$ and $$60^{\circ}$$. Then the distance between the boys (in mts)

If $$(x) = x^{2} + 6x + K_{1}$$ and $$g(x) = x^{2} + 5x + K_{2}$$ have common factor $$x - a =$$ then a =

The sum of at two digit number n and the number formed by reversing its digits is 99. When 5 is added to n then it becomes 5 less than 6 times the sum of digits of n. Then the number n is

A machine cost Rs.875000. If the value of the machine depreciates 15% of its cost in the first year, $$13\frac{1}{2}\%$$ of it cost in the second year, $$12\%$$ of its cost in the third year and so on, then its value at the end of 10 years is (in rupees)

If $$(1 + x + x^{2})^{n} = \sum_{r=0}^{2n} a_{r}x^{r}$$, then $$a_{0} + a_{2} + a_{4} + ... = $$

If $$\omega$$ is cube root of unity, then $$\begin{vmatrix} 1+\omega & \omega^{2} & -\omega\\ 1+\omega^{2} & \omega & -\omega^{2}\\ \omega^{2} +\omega& \omega& -\omega^{2} \end{vmatrix} =$$

In a parallelogram ABCD, the length of the adjacent sides AB and BC are 14 cm and 12 cm. If the diagonal AC = 22 cm, then its area (in sq.cm.) is

One of the angle of a triangle $$\frac{2}{5}$$ of the sum of the adjacent angle of a parallelogram. The remaining angles of the triangle are in the ratio of 5 : 7. The value of the second largest angle of the triangle is

If (3, -6), (5, 7) and (13, 4) are the mid point of the sides BC, CA and AB of triangle ABC and if the centroid of the triangle is (a, b), then a + b =

If (17, 16) (14, 16) and (17, 20) are the vertices of a triangle, then the, its circum centre is

A data consists of 100 observations $$x_{1},x_{2},... x_{100}$$. If $$\sum_{i=1}^{100}(3x_{i}+17)^{2}=22500$$ and $$\sum_{i=1}^{100}(3x_{i}+17)= 900$$, then the standard deviation of $$x_{},x_{2},... , x_{100}$$ is

Which of the following two variables likely to have maximum positive correlation coefficient ?

If a fair die is thrown 3 times, the probability that the sum of the number turned up 14 is

If A, B and C are any three events in a sample space S then $$P(A \cup B \cup C)=$$

If A and B are two mutually exclusive event of a sample space S such that AUB = S and P(B)= 2P (A) then P(A) =

Choose the correct word/Correct Meaning of the Word/Fill in the Blanks with correct word /Phrase / Verb /
Preposition

The following authority that decides policy bank interest rates on periodical basis is ______.

A business's short-term assets minus accounts receivable and inventory, divided by short-term liabilities i known as __________.

Value added services means ________.

A: Why did Ranjit leave suddenly for Dubai?
B: Well, I smell a rat!

In this conversation B is

The files were destroyed. (Change the voice)

A: Why don't we have a short walk.
B: Sorry, I am totally done up.
In this conversation 'B' implies

A: "I'm a pprehensive of the future"
B: "You seem to have everything one could possibly want. So why are you so apprehensive?"
'B' implies that 'A' is

Unexpectedly, the officer who is the winner of many awards proved to be a man of straw.

The underlined expression means

A: It is strange . I thought the audience were educated, but they could not follow
what I said. I was thoroughly disappointed.
B: Don't cast your pearls before the swine.
'B' is

Read the following passage and answer questions

The difference between a physician and a quack is this - a physician knows and admits that his powers are limited. He can aid nature. He can help her remove obstruction and clear away abnormal growth; but he cannot recreate a broken constitution, or make a perforated a lung do the work of a sound one. But a quack with his pills, and his plasters, and his potions, will undertake to cure all the ills that flesh is heir to. In like manner the genuine reformer knows that the living law is the thought of the people, and that all Parliament can do is to fit thought to the life of the nation. It is not so much speed in legislation that is wanted, as still. It is not quantity, but quality, that is required. The highest interests of the State would often be better served by the wise and liberal administration of old laws than by high pressure production of new and imperfect one. Obstruction or no obstruction, necessary legislation will come in due time if people want it. Free speech is more precious than all the measures in the ministerial portfolio. Error of opinion may be tolerated as long as there is the right to combat it. Discussion is a bulwark against oppression, and the sheet-anchor of liberty.

Unlike a quack a physician

Read the following passage and answer questions

Each of us has locked within us all that is necessary to achieve wealth and greatness. It's merely a matter of learning to use these hidden assets, of investing them so to speak, so we can cash in on them. The tragic thing is that so many go through life without ever putting them to use. Sometimes, trouble and adversity is necessa1y to make people use their resourcefulness and brain power to achieve success. A book keeper lost his job as Christmas was approaching. He had no money to buy his 10 year old son a gift. Instead of merely despairing, he went to work making the boy a gift. Using two wheels from a discarded baby carriage a few pieces of lumbar from the basement, and some bright red paint he constructed a toy that captured the attention of the entire neighbourhood. Other children wanted similar toys. The demand grew so fast that the unemployed book keeper turned his basement into a factory, then moved his production to a real industrial plant. The toy the book keeper designed was called the 'Scooter'. Have you searched carefully for any 'hidden' resources you've overlooked simply because they  weren't in some form you could bank immediately? Have you some plan or idea which might prove of great value if you brought it into the open and put it to use? Somewhere you have unused assets. Put them to work for you and make yourself financially independent.

How did the book keeper become rich?

Read the following passage and answer questions

Leading investors have joined the growing chorus about governments and companies rusting into producing biofuels as a solution for global warming saying that many involved in the sector could be jeopardising future profits if they do not consider the long-term impact of what they are doing carefully.

It is essential to build sustainability criteria into the supply chain of the green fuel project in order to ensure that there is no adverse effect on the surrounding environment and social structures. The report produced by the investors expresses concern that many companies may not be fully aware of the potential pitfalls in the biofuel sector.

Production of corn and soya beans has increased dramatically in the last years as an eco-friendly alternative to fossil fuels but environmental and human rights campaigners are worried that this will lead to destruction of rain forests. Food prices could also go up as there is increased competition for crops as both food stuff and sources of fuel. Last week the UN warned that biofuels could have dangerous side effects and said that steps need to be taken to make sure that land converted to grow biofuels does not damage environment or cause civil unrest. There is already great concern about palm oil, which is used in many foods in addition to being an important biofuel, as rain forests are being cleared in some countries and people driven from their homes to create palm oil plantations.

An analyst and author of investors' report says that biofuels are not a cure for climate change but they can play their part as long as governments and companies manage the social and environmental impacts thoroughly. There should also be greater measure taken to increase efficiency and to reduce demand.

Who are jeopardizing future profit ?

"Potential pitfalls" means

Increase in production of com and soya bean will not lead to

Sustainability of supply chain in green fuel project is necessary for

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