Find the number of distinct rational numbers `x` such that `oltxlt1 and x=p//q` , where `p ,q in {1,2,3,4,5,6}` .

Is 0 is rational number ? So , express, 0 in the form of p/q where p and q are both integers and q ne 0

Find the unit vector in the direction of vector vec (PQ) , where P and Q are the points (1,2,3) and (4,5,6) , respectively.

Find the unit vector in the direction of vector vec(PQ) , where P and Q are the points (1,2,3) and (4,5,6) , respectively.

Let P = {x:x is a prime natural number is less than 9} and Q = {2, 4}, then find PxxQ .

If a, b, c are distinct positive rational numbers and they are in A.P., then the roots of the equation ax^(2) +2bx+x=0 are-

Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists unique pair of real numbers (x , y) such that P(x)Q(y)=20 , then the value of (6x+10 y) is _____.

Let p and q be real numbers such that p!=0,p^3!=q ,and p^3!=-qdot If alpha and beta are nonzero complex numbers satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha//beta and beta//alpha as its roots is A. (p^3+q)x^2-(p^3+2q)x+(p^3+q)=0 B. (p^3+q)x^2-(p^3-2q)x+(p^3+q)=0 C. (p^3+q)x^2-(5p^3-2q)x+(p^3-q)=0 D. (p^3+q)x^2-(5p^3+2q)x+(p^3+q)=0

If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, then find the value of p and q , where p and q are real.

Determine the degrees and the number of terms of each of the following polynomials : (1+3x+3x^(2)+x^(3))^(q) , where q = 2

Consider the number, N 5768P02Q If N is divisible by 4, them find the ordered pairs of (P,Q).