`|(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|=0` where `a,b` and `c` are in AP.

Show that |[x+1,x+2,x+a], [x+2,x+3,x+b],[ x+3,x+4,x+c]|=0 where a ,\ b ,\ c are in A.P.

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)^3,(x-c)^3),((x+a)^3,(x+b)^3,(x+c)^3)| =0, a,b and c being distinct real numbers.

If f(x)=|(x+c_1,x+a,x+a),(x+b,x+c_2,x+a),(x+b,x+b,x+c_3)| then show that f(x) is linear in x. Hence deduce f(0)= (bg(a)-ag(b))/((b-a)) where g(x)=(c_1-x)(c_2-x)(c_3-x)

If int _(0)^(2)(3x ^(2) -3x +1) cos (x ^(3) -3x ^(2)+4x -2) dx = a sin (b), where a and b are positive integers. Find the value of (a+b).

Let Delta(x)=|(x+a,x+b,x+a-c),(x+b,x+c,x-1),(x+c,x+d,x-b+d)| and int_0^2 Delta(x)dx=-16, where a,b,c,d are in A.P. then the common difference (i) 1 (ii) 2 (iii) 3 (iv) 4

Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 where alpha,beta,gamma are in AP

If a-2b+c=1 , then the value of |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}| is

Choose the correct answer in questions 17 to 19: If a, b, c are in A.P., then the determinant [{:(x+2,x+3,x+2a),(x+3,x+4,x+2b),(x+4,x+5,x+2c):}] is : (a) 0 (b) 1 ( c) x (d) 2x

Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the value of 5A+4B+3C+2D+E is equal to a. zero b. -16 c. 11 d. -11