Neha's *Fundu* Section

[vikram_k51]

Hi frens,
here are some of the doubts that i have.
Will be highly thankful if anyone throws some light on these.

1.Find the perimeter (in centimetres) of a square which is symmetrically inscribed in a semicircle of radius 10 cm.
a. sq.rt. (80) cm b. 80 cm c. 8 sq.rt (24) cm d. 16 sq.rt (5) cm


2. If a and b are the roots of the equation x2 + 2x - 1 = 0 and c and d are the roots of the equation x2 + 3x - 4 = 0, then find the value of (a + c ) (b+ d) (a + d) (b + c).
a.-46 b.-24 C.0 d.-64

3.Two circles with centres O1 and O2 and radii 6 cm and 8 cm cut each other at right angles. Find the length of the common chord.

a. 10 cm b. 4.8 cm c. 9.6 cm d. 5 cm

4.The marked price for a pair of shoes is 60% above the cost price. A shopkeeper sells the pair of shoes after giving a discount of x%. Now he raises the marked price by x% and gives a discount of (x + 5)%. If the profit earned in the second case is twice that of the first case, find the value of x.
a.20 b.25 c.10 d.15



6.How many numbers greater than a million can be formed by using the digits 7, 4, 6 and if 4 has to be used twice, 6 has to be used thrice and the rest only once?

a.720 b. 7! /3! c. 360 d. None of these

7 .From a group of 8 students, 3 students have to be selected. Mr. X is not selected unless Mr. Y is also selected. In how many ways can the 3 students be selected?
a.41 b. 21 c. 20 d. None of these
8. Given that N = (521)raised to 125 x (125)raised to 521, find the last two digits of N.
a.75 b.25 c.45 d. None of these

9.There are three containers - A, Band C each of one litre capacity. Initially, there were 400 ml alcohol in A, 500 ml alcohol in B, and 600 ml water in C. Also A(f)B means f fraction of A is poured into B.
The following process takes place.
1.C(1)A
2. A(0.5)B
3. A(0.66)C
4. B(0.66)C
Find the concentration at the end of the process in container C.
a. 30% b. 70% c. 50% d.60%
¬

10.In a right circular cone of vertical angle of 60° and height of 6 cm, a sphere of maximum volume is inserted. If the radius of this sphere is 2.33 cm, find the volume of the cone.
a. 18pi b. 15pi C. 24pi d. Cannot be determined
11.Alok and Atul are competing in 800 m race. Alok gives Atul a lead of 100 m. Initially, Alok runs

at x times of Atul's speed ( x is an integer > 1), but after crossing 600 m, he slows down to a

speed which is 1 / x time of Atul's speed. Atul continues to run at his original speed. If both of

them meet for the second time at a distance of 50 m from the finish line, then who wins the race and by what distance?
a. Atul, 33.33 m b. Alok, 37.5 m c. Atul, 37.5 m d. Alok, 25 m

12.A solid sphere of radius 7 cm is melted to form a number of small cones and cylinders. The requirement is such that the number of cones should be twice the number of cylinders. Also the radius of the cone must be equal to its height, which should be equal to the radius of the cylinder and also be half the height of the cylinder. If the height of one such cylinder is 4 cm, find the maximum number of cones which can be made out of the sphere.
a.18 b.21 c.36 d.42

13.A circle is inscribed in a trapezium whose two non-parallel sides are 10 cm and 12 cm long. Find the length of the line joining the mid-points of non-parallel sides.

a. 8 b. 10 c. 11 d. None of these

14.The initial mark-up percentage for a Parx shirt is 87.5%, which is sold after giving a discount of 20%. Due to some reason the cost price of making a shirt increases by 25%. Now a shirt is sold after raising the marked price by Rs. 500 and giving a discount of 25%. If the percentage profit still remains the same, find the new selling price of the shirt.
a. Rs. 800 b. Rs. 1 ,000 c. Rs. 1,200 d. Rs. 1,500

15.
If |x + 2| = |x -1| + |x – 4 |, then how many distinct values of x are possible?
a.0 b.1 c.2 d.3

16.The metro trains which travel at a uniform speed between stations A and B run at a regular interval of 12 min. If Aakash, walking along the railway track at uniform speed, observes that every 10 min there is a train coming from the opposite direction and passes him, then what is the time-gap between one train that overtakes him from behind and the immediately next train overtaking him?
a. 15 min b. 16 min c. 13.5 min d. None of these

Direction for questions 17 and 18: Answer the questions based on the following information.
An internet connection from Sify costs Rs. 2,500 for 250 hr of use or a validity period of one year, whichever expires first. A customer can connect to the internet only by dialling a local number which is billed Rs. 2 per local call of 3 min.

17.Given that the customer does not surf for more than 20 hr per month, what is the telephone bill he pays if he wants to minimize the fixed cost per hour of use?

a. Rs. 8,400 b. Rs. 9,600 c. Rs. 10,000 d. Rs. 12,000

18. If Dishnet provides an internet connection through cable and charges an installation cost of Rs. 4,000 plus Rs. 20 per hour of usage, what is the minimum usage level for Dishnet connection to be economically viable for the customer?

a.10 b.24 c.7.5 d. None of these

19.Find the smallest side of a prism of volume 3,600 units if its edges are in the ratio
5 : 12 : 13 : 15.



20. Find the quadratic equation whose roots are a and b , given that a + 1/b and b + 1/a are the roots of the quadratic equation 14x2 - 45x + 81 = O?

a. 2x2 - 8x + 7 = 0 b. 2x2 - 5x + 7 = 0

C. 2x2 - 8x + 5 = 0 d. 2x2 - 5x + 5 = 0

21.A circle A of radius 10 cm is inscribed in an equilateral triangle XYZ. Another circle B of radius 6 cm is drawn such that it is concentric of circle A. If a third circle C is drawn in such a way that it touches circle A internally and B touches C internally, then find the radius of circle 'C'.
a.8cm b.10cm c.7cm d.9cm

22.An equilateral triangle is inscribed in a circle of radius 4 cm. Find the possible dimensions of a rectangle having its area equal to that of the triangle.
a. 4 sq rt 3 ,2 sq rt 3 b. 3 sq rt 3 , 2sq rt 2 c. 6sq rt 3 ,4 d.sq rt ( 12sq rt 3 ) , sq rt ( 12 sq rt 3 )


23.In the question 22, what would be the area of the circle inscribed in the triangle?
a. 4pi cm2 b. 2picm2 . c. 3pi cm2 d. None of these

24. What is the least value of (x - 2)(x - 4)2(x - 6) + 6, for real values of x?
a. 0 b. 1 c. 2 d. 3

Thaanks and regards,
Vikram

[doofus3]

3.Two circles with centres O1 and O2 and radii 6 cm and 8 cm cut each other at right angles. Find the length of the common chord.

a. 10 cm b. 4.8 cm c. 9.6 cm d. 5 cm

hey! some of these questions are really easy. you should try them~

this i got orally by using pythogarus theorem.
the answer is 9.6cm.

i recommend you to go through all of them again and try to solve them on ur own.
if you cant, then you will have to brush up on ur basics

[vikram_k51]

Sorry for some silly questions in the lot.Please ignore them
Hey doofus3 thanks for the advice buddy .

[rajsharma]

Good Job! INIce to hav this thread going on.

[Mohit102]

Hi,

Found while going thru the mailing list. Can someone help me with the following question.

How can it necessarily be 14:11.

We get 14:11 when we assume that Vijay has completed 220m and Ajay has completed 280 m which satisfies the conditions given.

But We can get 220/S1 = 120/S2 which gives ratio of 11:6 when Vijay completes 220m and Ajay completes 120 m. This also satisfies the given conditions.

Mohit

[quote=pagalneha]These r all actual CAT questions that have appeared sometime.




2. Ajay and Vijay are at a distance of 100 mts., when 3rd time they meet ,they are at a distance of 20mts from Vijay’s side and each of them have completed at least 100 mts., what are the ratio of the speed of Ajay and Vijay.



Ans ratio-14:11

[awr]

[quote=Mohit102]Hi,

Found while going thru the mailing list. Can someone help me with the following question.

How can it necessarily be 14:11.

We get 14:11 when we assume that Vijay has completed 220m and Ajay has completed 280 m which satisfies the conditions given.

But We can get 220/S1 = 120/S2 which gives ratio of 11:6 when Vijay completes 220m and Ajay completes 120 m. This also satisfies the given conditions.

Mohit

Originally Posted by pagalneha

These r all actual CAT questions that have appeared sometime.




2. Ajay and Vijay are at a distance of 100 mts., when 3rd time they meet ,they are at a distance of 20mts from Vijay’s side and each of them have completed at least 100 mts., what are the ratio of the speed of Ajay and Vijay.



Ans ratio-14:11

The very fact that they are meeting for the 3rd time suggests that the total distance covered by both of them till they meet for the third time is d + 2d + 2d = 5d = 5*100 = 500.
Hence the distance covered by both should add to this figure..

[Mohit102]

[quote=awr]

Originally Posted by Mohit102

Hi,

Found while going thru the mailing list. Can someone help me with the following question.

How can it necessarily be 14:11.

We get 14:11 when we assume that Vijay has completed 220m and Ajay has completed 280 m which satisfies the conditions given.

But We can get 220/S1 = 120/S2 which gives ratio of 11:6 when Vijay completes 220m and Ajay completes 120 m. This also satisfies the given conditions.

Mohit



The very fact that they are meeting for the 3rd time suggests that the total distance covered by both of them till they meet for the third time is d + 2d + 2d = 5d = 5*100 = 500.
Hence the distance covered by both should add to this figure..

Thanks for the reply. I might be totally wrong but would be great if you could point out where I am going wrong.

But they can meet 3times as
2d + d + 40

2d for both reaching the opposite end as both covers atleast 100 mt. - 1 Meeting Point

Now d will be covered by Vijay while Ajay is coming back from Vijay's original starting po
int. - 2 Meeting Point

Now finally at 3rd meeting point, If Vijay is fast enough to meet Ajay at a distance of 20m then it will become the 3rd meeting point.

and that will satisfy the minimum 100 m travel condition for both.

[Mohit102]

Hi,

Found some questions that I would like to share..

1) Two ants are moving on the graph y = x and y = | x |. The two ants move with speeds of 5 cm/s and 6 cm/s respectively. [Assume that the scale in a graph is 1 unit = 1 cm]. The first ant starts from the coordinates (-5,- 5) and the second ant starts simultaneously from the coordinates (-10, 10). Both the ants are travelling in the direction, on which path the origin lies.

2) If the first ant after reaching the origin, no longer travels along y = x but travels along y = _x, towards the second ant, where do the 2 ants meet?

3) The remainder obtained when 231 is divided by 31 is :

4) If a clock takes 30 seconds to strike 6, how long will it take to strike 12?

I could not solve the 4th one.. Any suggestion in that regard would be highly appreciated.

Answers

1. (20,20)
2. (20/11, -20/11)
3. 2
4. 66

[catasp2005]

Originally Posted by Mohit102

Hi,


4) If a clock takes 30 seconds to strike 6, how long will it take to strike 12?

I could not solve the 4th one.. Any suggestion in that regard would be highly appreciated.

Answer
4. 66

to strike 6, no. of gaps = 5. so for 5 gaps it takes 30 seconds .....
So to strike 12 it will hv 11 gaps , & for 11 gaps, time reqd = 30/5 * 11 = 66 sec....

[Mohit102]

Thanks for clarification catasp2005...

Here are few more...

Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. The weight of dry grapes available from 20 kg of fresh grapes will be




Let ABC be a 3-digit number, where A>0, such that the number is equal to the sum of factorials of the three digits. The value of B is
The number of positive integer valued pairs (x, y), satisfying
4x - 17y = 1 and x 1000 is:

Answers

1. 2.5 Kgs

2. 4

3. 59