Show that `|[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|`= 1

Using properties of determinants, prove that, |{:(1,1+p,1+p+q),(2,3+2p,1+3p+2q),(3,6+3p,1+6p+3q):}|=1

{:|( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)|:}=1

If x ,y \ a n d \ z are not all zero and connected by the equations a_1x+b_1y+c_1z=0,a_2x+b_2y+c_2z=0 , and (p_1+lambdaq_1)x+(p_2+lambdaq_2)+(p_3+lambdaq_3)z=0 , show that lambda=-|[a_1,b_1,c_1],[a_2,b_2,c_2],[p_1,p_2,p_3]|-:|[a_1,b_1,c_1],[a_2,b_2,c_2],[q_1,q_2,q_3]|

Show that the points P(-2,3,5) ,Q (1,2,3) and R (7,0,-1) are collinear

The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m - 1 and median q. Then p + q equals___

If sin (x + y) = p/sqrt(1 + p^(2)) " and " cos (x - y) = 1/sqrt(1 + q^(2)) "then show that " tan x " is a root of the equation " (p + q)z^(2) + 2(1 - pq) z- (p + q) = 0

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} .

Increasing order of Electron affinity for following configuration. 1s^2 , 2s^2 , 2p^3 (b) 1s^2 2s^2 2p^4 [c] 1s^2 , 2s^2 , 2p^6 , 3s^2 , 3p^4 (d) 1s^2 , 2s^2 , 2p^6 , 3s^2 , 3p^3

Elements A,B,C,D and E gave the following electronic configuration: A 1s^2 , 2s^2 , 2p^1 B 1s^2 2s^2 2p^6 3s^2 3p^1 C 1s^2 2s^2 2p^6 3s^2 3p^3 D 1s^2 2s^2 2p^6 3s^2 3p^5 E 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 Which among these will belong to the same group in the periodic table?

If one root is square of the other root of the equation x^2+p x+q=0, then the relation between pa n dq is p^3-q(3p-1)+q^2=0 p^3-q(3p+1)+q^2=0 p^3+q(3p-1)+q^2=0 p^3+q(3p+1)+q^2=0