hi , it's udit ....
pls help me in soving these....
*** when x + y + z = 6, x^2 + y^2 + z^2 = 8, x^3 + y^3 + z^3 = 5 then x^4 + y^4 + z^4 = ?? 0/1/9/ can not be det
*** how many natural numbers less than 100 can be expressed as a difference of two perfect squares in only one way ?? 25/28/35/38
*** when x^13 + x +90 is divided by x^2 x +n , remainder obtained is zero how many integral values of n is / are possible ?? 0/1/2/ infinite
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Answers for QQAD #118
i am not getting any answer for qqad 95
plz help me
aakhir ek pagal hi dusre pagal ka madad kar sakta hai
Actually I M Not Getting Any Region Bounded By These Two Curves
plz try to provide a diagram in he solutions to the geaometry and mensuration topics otherwise its real difficult to understand the sol
solution for part A:
How many integral values of p are there for which the inequality 3 - x-p > x^2 is satisfied by at least one negative x?
"by atleast one negative x"
This implies whatever values of p we find for the solution x<0 (i.e -ve)
taking x as negative the inequality looks like
solving this we will get 2 roots. Now we have to see how x^2+x+p-3 will behave between these roots and beyong these roots. At x=-1/2 we will get minimum value of x^2+x+p-3. Thus any value between the roots satisfy the inequality. now on sloving the equation x^2+x+p-3 the delta value is 13-4p. For real values of the solution 13-4p>=0.
thus p can be any integral less than equal to 3. So the number of solutions will be infinite.
hence (e) non of the foregoing is the answer
check fallas. might be i m wrong
In the end of the question it says for all x in (1,2). This means x=1 for case 1and x=2 for case 2
putting x=1 in the inequality we get
solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+7*p+1 will be less than zero (p= -7/2 will give ninimum value of the equation). Hence -6,-5,-4,-3,-2,-1 satisfy the inequality for x=1
putting x=2 in the inequality we get
solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -7,-6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+8*p+4 will be less than zero (p= -4 will give ninimum value of the equation).
Hence -7,-6,-5,-4,-3,-2,-1 satisfy the inequality for x=1
The common integral values from case 1 and 2 are
thus, (d) 6 is the answer
Hope the solution is correct...have given major fundae:)