[vineet.nitd]

Originally Posted by AC_here

Checking option (b)

B^2 = ( x + y - z)^2
A = (x-y)(x- 3y+ 2z)

Put y = z = 0 then B^2 = x^2 = A

Hence (b) is False

Read the conditions for option (b) in the problem again .Dont be in haste .

[vineet.nitd]

Originally Posted by doomsayer

ans :b

when x>y>z >0 then b reduces into x+y+z
and (x+y+z)^2 > x² + 3y² - 4xy - 2yz + 2zx
so b is the ans

How... ? Are you sure ? Check again ..!!

[AC_here]

Originally Posted by vineet.nitd

Read the conditions for option (b) in the problem again .Dont be in haste .

You are right , the condition is x > y > z > 0

Correcting though..

B^2 - A = (x + y -z)^2 - (x - y)(x - 3y + 2z)
= -2y^2 + z^2 + 2xy + 4yz
= 2y(x-y) + z(z + 4y)
> 0

Hence (b) is true

Answer is (b)

[Aarav]

Any one can post the questions after 12 noon.

Quant Question # 4

Let [x] denotes the greatest integer that is less than or equal to x, e.g. [3.45] = 3, then [1/3] + [2/3] + [2^2/3] + [2^3/3] +...+ (101 terms) equals

(a) 1/3( 4^50 - 1) - 50 (b) 1/3( 4^51 - 1) - 51 (c) 2/3( 4^50 - 1) - 50
(d) none of the above


Quant Question # 5

There are 11 books on a shelf. How many ways are there to choose 4 of them so that no two of the chosen books stand next to each other?

(a) 70 (b) 165 (c) 495 (d) none of these

Quant Question # 6

We are given a system of n linear equations in n variables, n > 1. Which of the following
statements MUST BE FALSE?

(a) The system of equations has an odd number of solutions.
(b) The system of equations has no solution.
(c) The system of equations has an infinite number of solutions.
(d) The system of equations has exactly n solutions.

[krsh.vik]

Originally Posted by Aarav

Any one can post the questions after 12 noon.

Quant Question # 4

Let [x] denotes the greatest integer that is less than or equal to x, e.g. [3.45] = 3, then [1/3] + [2/3] + [2^2/3] + [2^3/3] +...+ (101 terms) equals

(a) 1/3( 4^50 - 1) - 50 (b) 1/3( 4^51 - 1) - 51 (c) 2/3( 4^50 - 1) - 50
(d) none of the above

ans is d
actual ans is
2/3(4^50 -1) -101 + 1/3

[Aarav]

Originally Posted by krsh.vik

ans is d
actual ans is
2/3(4^50 -1) -101 + 1/3

Please check your mistake. I'm sure it's a small one.

[Destiny's_Child]

Soln to prob 3 to 6

3) The expn reduces to 1+2+5 +10 + 21 + 42......... (99 terms)

= 1 + 2 + (4+1) + (8+2) + (16+4+1) +(32+ 8 +2)

= (1+2+4)...99terms + (1+2 +4)....97 terms + (1+2+4)...(95 terms) + .........(1+2+4)+1

= 2^99 - 1 + 2^97 - 1 + 2^95 - 1 .................+ 2^3 -1 + 2^1 - 1

= (2^1 + 2^3 + 2^5 +.........2^99)(50 terms) - 50

= [2(4^50 - 1)]/3 - 50 ---- Ans

4) Here when we keep 7 books, 8 spaces are ceated for keeping 4 boooks so that these books wont be together

So Ans would be 8C4 = 70

5)Here equations would have either one solution (i.e odd number of solutions), no solution or infinitely many solutions.

So the answer is
The equation will have exactly n solutions

[warrior]

Originally Posted by Aarav

Quant Question # 5

There are 11 books on a shelf. How many ways are there to choose 4 of them so that no two of the chosen books stand next to each other?

(a) 70 (b) 165 (c) 495 (d) none of these

Quant Question # 6

We are given a system of n linear equations in n variables, n > 1. Which of the following
statements MUST BE FALSE?

(a) The system of equations has an odd number of solutions.
(b) The system of equations has no solution.
(c) The system of equations has an infinite number of solutions.
(d) The system of equations has exactly n solutions.

#5

its like x+y+z+w =11 where x>=0 y,z,w >0

so we have 11C3 =165 as the no of solu

#6

it should be (d) as the it can 1 , no or infinitely many solun but not exactly n

[Aarav]

Seems most of the people have done these questions before. Or have they? It requires a little discipline of 15 minutes daily to be here, and people are not even willing to do that. Get out of your comfort zones ... CAT prepration requires that.

[warrior]

Originally Posted by Aarav

Any one can post the questions after 12 noon.

Quant Question # 4

Let [x] denotes the greatest integer that is less than or equal to x, e.g. [3.45] = 3, then [1/3] + [2/3] + [2^2/3] + [2^3/3] +...+ (101 terms) equals

(a) 1/3( 4^50 - 1) - 50 (b) 1/3( 4^51 - 1) - 51 (c) 2/3( 4^50 - 1) - 50
(d) none of the above

all the even power of 2 leaves a remainder of 1 and od power the remainder of 2 when divided by 3.


now this 1/3 or 2/3 part will always be eliminated

now sum of all = 2^102-1/3 = 4^51-1/3

of these 101 terms ie. upto 2^100/3

we have 51 even and 50 odd terms

51/3+ 100/3 = 151/3

ans (4^51-1/3) - 151/3 (D) none of these