If `omega` is a non-real complex cube root of unity and `(5+3omega^2-5omega)^(4n+3)+(5omega+3-5omega^2)^(4n+3)+(5omega^2+3omega-5)^(4n+3)=0,` then possible value of `n` is

Match the statements/expressions given in column I with the values given in Column II. Column I, Column II In R^2, if the magnitude of the projection vector of the vector alpha hat i+beta hat j on sqrt(3) hat i+ hat ji ssqrt(3) and if |alpha| is /are, (p) 1 Let aa n db be real numbers such that the function f(x)={-3a x^2-2,x<1b x+a^2, xgeq1 Differentiable for all x in Rdot Then possible value (s) of a is/are, (q) 2 Let omega!=1 be a complex cube root of unity. If (3-3omega+2omega^2)^(4n+3)+(2+3omega-3omega^2)^(4n+3)+(-3-2omega+3omega^2)^(4n+3)=0 , then possible values (s) of n is /are, (r) 3 Let the harmonic mean of two positive real numbers aa n db be 4. If q is a positive real number such that a ,5,q ,b is an arithmetic progressin, then the values (s)of|q-a| is /are, (s) 4 , (t) 5

Match the statements/expressions given in Column 1 with the values given in Column II. Column I, Column II In R^2, iff the magnitude of the projection vector of the vector alpha hat i+beta hat jon3 hat i+ hat ji s3 and if alpha=2+3beta , then possible value (s) of |alpha| is (are), p. 1 Let aa n db be real numbers such that the function f(x)={-3a x^2-2, x<1b x+a^2, xgeq1 is Differentiable for all x in Rdot Then possible value (s) of a is(are), q. 2 Let omega!=1 be a complex cube root of unit. If (3-3omega+2omega^2)^(4n)+(2+3omega-3omega^2)^(4n+3)+(-3+2omega+3omega^2)^(4n+3)=0 , then possible value (s) of n is (are), r. 3 Let the harmonic mean of two positive real numbers aa n db be 4. If q is a positive real number such tht a ,5,q ,b is an arithmetic progression, then the value (s) of |q-a| is (are), s. 4 , t 5

Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2))^(4n+3) + (2+3omega-3omega^(2))^(4n+3)+(-3+2omega+3omega^(2))^(4n+3)=0 , then the set of possible value(s) of n is are

If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=

If omega is a complex cube root of unity then (1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

If omega is complex cube root of unity (1-omega+ omega^2) (1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

If omega is an imaginary cube root of unity, then show that (1-omega+omega^2)^5+(1+omega-omega^2)^5 =32

If omega is an imaginary cube root of unity, then show that (1-omega)(1-omega^2)(1-omega^4) (1-omega^5)=9

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then omega + omega^(2)= …..