List of top Questions asked in CAT- 2022

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4), and (−2, 8), respectively. Then, the coordinates of the vertex D are

If \((3+2\sqrt2)\) is a root of the equation ax2 + bx + c = 0 and \((4+2\sqrt3)\) is a root of the equation ay² + my + n = 0,where a,b,c,m and n are integers, then the value of \((\frac{b}{m}+\frac{c−2b}{n})\) is

The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD,in cm,is

Ankita buys 4kg cashews, 14kg peanuts, and 6kg almonds when the cost of 7kg cashews is the same as that of 30kg peanuts or 9kg almonds. She mixes all three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent buying almonds is

The average of a non-decreasing sequence of N numbers \(a_1,a_2,…,a_N\) is 300.If \(a_1\) is replaced by \(6a_1\), the new average becomes 400.Then,the number of possible values of \(a_1\) is

Suppose k is any integer such that the equation \(2x^2+kx+5=0\) has no real roots and the equation \(x^2+(k−5)x+1=0\) has two distinct real roots for x. Then, the number of possible values of k is

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

Consider six distinct natural numbers such that the average of the two smallest numbers is 14 and the average of the two largest numbers is 28. Then,the maximum possible value of the average of these six numbers is

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

Let r be a real number and \(f(x) = \begin{cases} 2x - r & \text{if } x \geq r \\ r & \text{if } x < r \end{cases}\).Then, the equation \(f(x)=f(f(x))\) holds for all real values of x where

Two ships meet mid-ocean,and then,one ship goes south and the other ship goes west,both travelling at constant speeds.Two hours later,they are 60 km apart.If the speed of one of the ships is 6km per hour more than the other one,then the speed,in km per hour,of the slower ship is

The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
[1] Women may prioritize cooking because they feel they alone are responsible for mediating a toxic and unhealthy food system.
[2] Food is commonly framed through the lens of individual choice: you can choose to eat healthily.
[3] This is particularly so in a neoliberal context where the state has transferred the responsibility for food onto individual consumers.
[4] The individualized framing of choice appeals to a popular desire to experience agency, but draws away from the structural obstacles that stratify individual food choices.

The four sentences (labelled 1, 2, 3 and 4) below, when properly sequenced, would yield a coherent
paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. Fish skin collagen has excellent thermo-stability and tensile strength making it ideal for use as bandage
that adheres to the skin and adjusts to body movements.
2. Collagen, one of the main structural proteins in connective tissues in the human body, is well known for
promoting skin regeneration.
3. Fish skin swims in here as diseases and bacteria that affect fish are different from most human pathogens.
4. The risk of introducing disease agents into other species through the use of pig and cow collagen proteins
for wound healing has inhibited its broader applications in the medical field

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1,2,3, or 4) the following sentence would best fit.
Sentence: This has meant a lot of uncertainty around what a wide-scale return to office might look like in practice.
Paragraph: Bringing workers back to their desks has been a rocky road for employers and employees alike. The evolution of the pandemic has meant that best laid plans have often not materialised. ___(1)___ The flow of workers back into offices has been more of a trickle than a steady stream. ___(2)___ Yet while plenty of companies are still working through their new policies,some employees across the globe are now back at their desks,whether on a full-time or hybrid basis. ___(3)___ That means we're beginning to get some clarity on what return-to-office means - what's working,as well as what has yet to be settled. ___(4)___.

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Most were first-time users of a tablet and a digital app.
Paragraph: Aage Badhein’s USP lies in the ethnographic research that constituted the foundation of its development process. Customizations based on learning directly from potential users were critical to making this self-paced app suitable for both a literate and non-literate audience. ____(1)____ The user interface caters to a Hindi-speaking audience who have minimal to no experience with digital services and devices. ____(2)____ The content and functionality of the app are suitable for a wide audience. This includes youth preparing for an independent role in life or a student ready to create a strong foundation of financial management early in her life. ____(3)____ Household members desirous of improving their family’s financial strength to reach their aspirations can also benefit. We piloted Aage Badhein in early 2021 with over 400 women from rural areas. ____(4)____ The digital solution generated a large amount of interest in the communities.

Consider the arithmetic progression 3,7,11,…and let \(A_n\) denote the sum of the first n terms of this progression.Then the value of \(\frac{1}{25}∑^{25}_{n=1}A_n\) is

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm, then, the area of the triangle EOD, in sq. cm, is

Five students,including Amit,appear for an examination in which possible marks are integers between 0 and 50,both inclusive.The average marks for all the students is 38 and exactly three students got more than 32.If no two students got the same marks and Amit got the least marks among the five students,then the difference between the highest and lowest possible marks of Amit is

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

A donation box can receive only cheques of ₹100,₹250 and ₹500. On one good day,the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained,is

A glass contains 500cc of milk and a cup contains 500cc of water.From the glass,150cc of milk is transferred to the cup and mixed thoroughly. Next,150cc of this mixture is transferred from the cup to the glass.Now,the amount of water in the glass and the amount of milk in the cup are in the ratio

List of top Questions asked in CAT- 2022

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