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

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

Match the following lists (where [x] represents the greatest integer function) and then choose the correct code. Codes : {:(,"a b c d"),((1),"s r q p"),((2),"q p s p"),((3), "s r p q"),((4),"p p q r"):}

The vertices of a triangle are (p q ,1/(p q)),(q r ,1/(q r)), and (r p ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are

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 (2 , -3 , 1) is the centroid of the triangle ABC with vertices A (-3 , p , 2) , B (2 , -4 , q) and C (r , 3 , 5) , find the values of p , q , r .

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?

Let p , q , r in R^(+) and 27pqr ge (p+q+r)^(3) and 3p+4q+5r=12 . Then the value of 8p+4q-7r=

Consider int(x^(3)+3x^(2)+2x+1)/(sqrt(x^(2)+x+1))dx =(ax^(2)+bx+c)sqrt(x^(2)+x+1)+lambda int(dx)/(sqrt(x^(2)+x+1)) Now, match the following lists and then choose the correct code. Codes: {:(,a,b,c,d),((1),q,p,s,r),((2),s,p,q,r),((3),r,q,p,s),((4),q,s,p,r):}