If `(x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x|` show that `"Delta^"(x)=0a n d"Delta"(0)+S x ,w h e r eS` denotes he sum of all the cofactors of all elements in `"Delta"(0)a n d` dash denotes the derivative with respect of `xdot`

If (x)=|a_1+x b_1+x c_1+x a_2+x b_2+x c_2+x a_3+x b_3+x c_3+x| , show that ^(x)=0 and that(x)=(0)+S x ,w h e r eS denotes the sum of all the cofactors of all the element in (0)dot

If a\ a n d\ b denote the sum of the coefficients in the expansions of (1-3x+10 x^2)^n a n d\ (1+x^2)^n respectively, then write the relation between a\ a n d\ bdot

Let Delta_0 = |(a_11, a_12, a_13), (a_21, a_22, a_23), (a_31, a_32, a_33)|, (where Delta_0 !=0) and let Delta_1 denote the determinant formed by the cofactors of elements of Delta_0 and Delta_2 denote the determinant formed by the cofactors at Delta_1 and so on Delta_n denotes the determinant formed by the cofactors at Delta_(n-1) then the determinant value of Delta_n is (A) (Delta_0)^(2n) (B) (Delta_0)^(2^n) (C) (Delta_0)^2 (D) (Delta_0)^(n^2)

Write the coordinates of the orthocentre of the triangle formed by the lines x y=0\ a n d\ x+y=1.

Given that alpha , gamma are roots of the equation Ax^(2)-4x+1=0 and beta , delta are roots of the equation Bx^(2)-6x+1=0 . If alpha , beta , gamma and delta are in H.P. , then

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

Evaluate: (int0n[x]dx)/(int0n{x}dx)(w h e r e[x]a n d{x} are integral and fractional parts of xa n dn in N)dot

If alpha,beta,gamma,delta are the roots of the equation 9x^(4)+Kx^(2)-7x+4=0 and sum gamma delta=2 then K=

alpha and beta are the roots of the equation x^(2)-3x+a=0 and gamma and delta are the roots of the equation x^(2)-12x+b=0 .If alpha,beta,gamma, and delta form an increasing GP., then (a,b)-