IIFT 2022 Slot 1: Past Year Question Paper (July 21) - CAT MCQ

Two pipes can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that clue to leakage at the bottom of the tank, it took 36 minutes more to fill the tank. When the tank is full, in what time the leak will empty it?

A potential recruit get a total of 55% marks. There are 6 performance parameters with maximum marks of 100 in each parameter. The recruit gets marks in the ratio of 10:9:8:7:6:5 respectively in different parameters. In the first 3 parameters, the criteria for clearing performance core is 55% of the maxinuun marks and for next 3 parameters is 50% of the maximum marks.

How many parameters has the recruit cleared?

The sides of a triangle are 21, 20 and 13 cm. The given triangle is divided into two triangles by the perpendi ular on the longest side from the opposite vertex. What is value of 30% area of the smaller triangle formed?

The cost of setting up a utility bag factory is Rs. 1200. The cost of running the factory is Rs. 125 per 105 bags. The cost of raw material is 80 paise/per bag. The bag are old at Rs. 3.25 each. 900 bags were made, but only 785 bags were sold. Other companies can advertise on both sides of the bag. What is the approximate sum to be obtained from the advertisements being printed on the bags, to give a profit of 12%?

An investor lent-out a certain sum on simple interest and the same sum on compound interest at the same rate of interest per annum. He noticed that the ratio of the difference of the compound interest and the simple interest for 4 years to the difference of the compound interest and the simple interest for 3 years is 20:8. The approximate rate of interest per annum is given by,

Find the largest 5 digit number which when divided by 4, 9, and 11 leaves the same but largest remainder for all the three numbers ?

Four sprinters start running from 4 points which are 4 corners of an imaginary rectangle along straight lines and meet at a point 'O' which falls inside the rectangle as shown in the figure, after the first three sprinters run 55m, 65m and 75m respectively.
What is the approximate distance that the fourth sprinter will run to meet the other three sprinters at point O?

Let integer α be one of the roots of ax² + 2x + 3 = 0 and integer β be one of the roots of 5x² + bx + 8 = 0. It is also given that α = β². Which of the following statement is true if b = -14?

Find the value of x such tha

An integer is called a perfect square if it is square of another integer. The number of perfect square points (i.e. both coordinates are perfect squares that lie exactly within the circle (x − 12)² + (y − 10)² = 64 is

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using digits 2,3,4,5, 7 such that each n-digit number has the
(i) first and last digits are same
(ii) first and thrrd are prime numbers
(iii) second should be greater than or equal to 4.
What should be the minimum value of n such that the above is possible?

Pot "A" contains 5 blue and 10 green balls and another pot "B" contains 7 blue and 2 green balls. A biased dice with six sides numbered 1 to 6 is rolled. The probability of eah odd out ome is same and the probability of each even outcome is same. But the probability of an odd outcome is twice than the probability of an even outcome. If the face 1 or 2 or 3 comes up, a ball is taken from the pot "A" else a ball is taken from the pot "B". Find the probability of drawing a green ball.

In 1920, the "Sahitya Shakti" society was established by 500 members who read Premchand. In 1921, due to internal conflict, it removed all 200 members who also read Shakespeare. In 1922, further the member who also read Tolstoy numbering 100 left the society. In 1923, the society added only those ex-member who read both Shakespeare and Premchand but not Tolstoy after which the Sahitya Shakti society consisted of 350 members. Which of the following is true?

It is given that  Which of the following is true?

Find tan⁴ α + tan⁴ γ using the information given below:

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60 degrees. When he retires 'y' metre from the bank perpendicular to the tree, he finds the angle to be 45 degrees. When he further retires 15 - 5√3 metre perpendicular to the tree, he finds the angle to be 30 degrees. Find the height of the tree in metres?

20. Let a - d, a, a + d, a + 2d be four terms of an arithmetic progression with integer entries and a, a + d, a + 2d, a + 3d be another four terms of the same arithmetic progression. Let x = a(a - d)(a + d)(a + 2d) + d⁴ and y = a(a + d)(a + 2d)(a + 3d) + d⁴. Then x + y is equal to ?

A green liquid is mixed with a blue liquid in the proportion 4 : 5 and the mixture is sold at Rs. 20 per litre at a 20% profit. If the green liquid costs Rs. 4 more per litre than the blue liquid, what does the green liquid cost per litre approximately.

Two trains of equal length are running on parallel lines in the same direction at 54km/hour and 40km/hour. The slower train started first and then the faster train started after some time. The faster train passes the length of the slower train in 36 seconds completely. The length of each train is?

AB and CD are two chords intersecting at point E. Ram started from point A with a speed of 2km/hr. After reaching point E, Ram moved to point D with same speed and covered ED in one-fifth of the time taken for AE. Similarly. Shyam moved from point C to point B through point E. If Shyam takes in total 18 hours to cover the whole distance from C to B through point E with same speed. what is the time Shyam took to cover BE?

Find the area of the shaded region. Given that ABCD is a square with side length 'b' units and E is the midpoint of AB.

A large solid iron sphere of diameter 1 Om i melted and 2/5 of the melted amount is recast into seyeral mall spheres of diameter 2m. What is the ratio of the total urface area of the smaller spheres and the surface area of the lasge sphere.

To change one s mind from 'negativity to 'positivity or to change one's behaviour permanently, which of the following is the most effective way?

Vhat is the most effetive way to permanently reprogram one subconsious mind?

Which of the following about using willpower to bring permanent changes in behaviour' is not correct according to passage?

According to passage, the sub on cious mind .... :

The term "currency manipulation" by the developing and newly industrialized economies a mentioned in the pa sage can be explained as ..............