((xi))a,a^(2),a^(3),a^(4)

Which of the following are Aps? If they form an AP, find the common difference d and write the next three terms. (i) 24m8m16,….. (ii) 2,5/2, 3, 7/2 ,….. (iii) -1.2, -3.2, -5.2, -7.2 ,…….. (iv) -10,-6,-2,2 ,……….. (v) 3,3+sqrt(2), 3+2sqrt(2), 3+3sqrt(2) ,.......... (vi) 0.2, 0.22, 0.222, 0.2222,..... (vii) 0,-4, -8,-12 ,.......... (viii) -1/2, -1/2, -1/2, -1/2 ,........... (ix) 1,3,9,27,....... (x) a,2a, 3a, 4a,....... (xi) a, a^(2), a^(3), a^(4) ,......... (xii) sqrt(2), sqrt(8), sqrt(18), sqrt(32) ,...... (xiii) sqrt(3), sqrt(6), sqrt(9), sqrt(12) ,...............

Without expanding the determinant, prove that: |{:(alpha xi, beta psi, gamma zeta),(xi^(2), psi^(2), zeta^(2)),(1,1,1):}| =|{:(alpha, beta, gamma),(xi,psi, zeta),(psi zeta,zeta xi, psi zeta):}|

sum_(i=1)^(2n) sin^(-1)(x_i)=npi then the value of sum_(i=1)^n cos^(-1)x_i+sum_(i=1)^n tan^(-1)x_i= (A) (npi)/4 (B) (2/3)npi (C) (5/4)npi (D) 2npi

(xi) a^(2) sin 2B + b^(2) sin 2A = 4Delta

Find x and y if (x^(4)+2xi)-(3x^(2)+yi)=(3-5i)+(1+2yi)

Giving reasons for your selection, select pairs out of the following four waves in a medium in a medium which will give rise to (i) beats (ii) destructive interference (iii) stationary waves. 1. xi_(1)=Acos2pi(v_(1)t+(x)/(lambda_(1))) 2. xi_(2)=Acos[2pi(v_(1)t+(x)/(lambda_(1)))+pi] 3. xi_(3)=Acos2pi(v_(2)t+(x)/(lambda_(2))) 4. xi_(3)=Acos2pi(v_(2)t-(x)/(lambda_(2)))

If (x_i y_i) ,i = 1,2,3,4 are concyclic points on xy=c^(2) and if y_1. y_2.y_3. y_4 =4 then c^(2) =