Official Quants Group|CAT:2022|MBA:2023-2025

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 In a convex octagon,two diagonals are drawn at random.The probability that the diagonals intersect inside the octagon is ? 

In an examination of 100 questions,a student is awarded 3 for correct,-2 for wrong and -1 for un-attempted. How many differrent scores are possible?

 Find the minimum value of x^1/2.y^1/3.z^1/4 , when 6x + 4y + 3z = 13. (x, y and z are real numbers) .(Please provide the solution for this. Thanks in advance)

 If 'p' and 'q' are the roots of the eqn 6x^2-5x+1=0 then find the value of (p+q)+2(p^2+q^2)+3(p^3+q^3)...to infinity. 

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Solution pls

  How to study Geometry, Trigonometry, time and distance. Answer is here https://m5mej.app.goo.gl/TMGw 

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Approach

(CAT 2006)
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
(1) 3
(2) 3.5
(3) 4
(4) 4.5
(5) 5 

(CAT 2007)
Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight member joint family is nearest to:
(1) 23 years
(2) 22 years
(3) 21 years
(4) 25 years
(5) 24 years 

 (CAT 2007)
Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.

How many units should Mr. David produce daily?
(1) 130
(2) 100
(3) 70
(4) 150
(5) Cannot be determined

(CAT 2008)
Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to
(1) 6:15 am
(2) 6:30 am
(3) 6:45 am
(4) 7:00 am
(5) 7:15 am 

(CAT 2005)
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

At what time do Ram and Shyam first meet each other?
(1) 10:00 a.m.
(2) 10:10 a.m.
(3) 10:20 a.m.
(4) 10:30 a.m.

At what time does Shyam overtake Ram?
(1) 10:20 a.m.
(2) 10:30 a.m.
(3) 10:40 a.m.
(4) 10:50 a.m.

In a ∆ABC,AD & BE are medians and G is the centroid, ∠AGE = 30°, AD=12cm & BE= 18cm. Find the area of the triangle? 

In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle? 

2x + 3y + 5 = 0 and 6x – 4y + 9 = 0 are two lines. If a point is at a distance of 1 unit from each of the two given lines, then how many such points exist?
a) 1
b) 3
c) 4
d) 2 

A goat is tied at the corner of a rectangular shed of dimensions 14 m x 7 m, with a rope 21 m long. If the goat can graze on the ground around and outside the shed as far as it is permitted by the rope, find the area (in sq.m.) on which it can graze.
a) 1232
b) 1560.5
c) 1260
d) 1543.5Â