`m^2-m+1=0` find the value of m

The mid-point of the segment joining (3m, 6) and (-4, 3n) is (1, 2m, -1). Find the values of m and n.

If .^(m+n)P_(2)=90 and .^(m-n)P_(2)=30 , find the value of m and .

Two blocks A and B are connected by a string as shown as shown in the figure . Friction coefficient of the inclined plane is 0.5 . The mass of the block A is 5 kg. If minimum and maximum values of mass of the block B for which the block A remains in equilibrium are m_(1) and m_(2) then find the value of (m_(2) - m_(1)) [in kg]

If A=[{:(,a,0),(,0,2):}], B=[{:(,0,-b),(,1,0):}], M=[{:(,1,-1),(,1,1):}] and BA=M^2 , find the values of a and b.

If tanA=m/(m-1) and tanB=1/(2m-1) , find the value of tan(A-B) .

If d/(dx)[(x^m-A_1x^(m-1)+A_2x^(m-2)-.......+(-1)^m A_m)e^x]=x^m e^x , find the value of A_r

If (a^(m))^(n)=a^(m).a^(n) , find the value of : m(n - 1) - (n - 1)

If m = 1, n = 2 and p = -3, find the value of : 2mn^(4)-15m^(2)n+p

If quadratic equation x^(2)-(m+1)x+6=0 has one root as x=3 , find the value of m and the other root of the equations.

If m=2 find the value of : (i) m-2 (ii) 3m-5 (iii) 9-5m (iv) 3m^2-2m-7