Qu@ntose

SOLUTION-

How many integral values can the expression (15x^2+2x+1)/(x^2-2x-1) not take? Solution- As we have to find the values that the equation cannot take,we can find range of possible values that equation will attain and then remove this range from R(R->Real numbers) =>(15x^2+2x+1)/(x^2-2x-1) = y =>(15x^2+2x+1)=y*(x^2-2x-1) =>(15x^2+2x+1)=y*x^2-2yx-y =>(15-y)x^2 +2*(y+1)*x + (1+y) = 0 Now for x to be real discriminant must be >=0 So, =>(2^2)*(y+1)^2 - 4(15-y)(y+1) >=0 =>(y+1)[y+1-15+y]  >=0 =>(y+1)(y-7) >=0 So, y = (-inf,-1] u [7,inf) So the given equation will not take integral values between (-1,7) i,e; 0,1,2,3,4,5,6 Hence,the given equation cannot take 7 integral values. 

A party was organized in a college in which three types of cold drinks were served. The served cold drinks were Pepsi, Coke and Sprite. There were 500 students in the college but 10% students did not drink any of the three cold drinks. A total of 750 bottles of cold drinks were served at the party. It is known that cold drinks were served in bottles only and no student drank more than one bottle of the same type of cold drink. The additional information is given below: (i) The number of students who drank Pepsi and Coke both was equal to the number of students who drank Pepsi and Sprite both. (ii) The number of students who drank Coke and Sprite but not Pepsi was twice the number of students who drank all the three cold drinks. (iii) The number of students who drank Pepsi and Sprite but not Coke was more than 50. (iv) The number of students who drank all the three cold drinks was at least 1. #Q1 If the difference between the numbers of students who drank Pepsi and Sprite but n

abc  is a three-digit number having 5 factors ,what would be the number of factors for abcabc and find the value of abc ? Solution- abcabc=abc*(1001) abcabc = abc*(7*11*13) As abc has odd factors abc must be  (prime)^4, where prime number must be less than 7, only such prime number is 5. abc = (5^4)=625 ANS Numbers of factors of abcabc = 5*2*2*2= 40 ANS 

 N filling pipes, P 1 , P 2 , P 3 ,.....P n (where n>10)  attached to a tank.The rate of filling of P i , where  i >1, is equal to thrice the combined rate of filling of all the lower numbered pipes. If the time taken by P n-3 to fill the tank is 128 minutes, find the time (in minutes) taken by P n   to fill the tank. Solution- It is given that, R i  = 3*(R 1  +R 2  +R 3  +...+R i-1 ) Where R i   is the rate of ith pipe. Now, T n-3  = 128 min R n-3 = 3*(R 1  +R 2  +R 3  +....R n-4 ) Let R 1  +R 2  +R 3  +...+R n-4 = x R n-3 = 3x R n-2  = 3*(x+R n-3 ) = 12x R n-2 = 3*(x + R n-3 + R n-2 ) = 48 R n = 3*(x + R n-3   + R n-2 +R n-1 ) = 192x Now we know that, rate*time=work R n-3  *time = work (constant) 3x*128 = work Now, for pipe P n , R n  *time = work 192x*time = 3x*128 time = (3x*128)/192x time = 2 minutes ANS