If `c<1` and the system of equations `x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=0` is consistent, then the possible real values of `b` are `b ∈(-3 3/4)` b. `b ∈(-3/2,4)` c.`b∈ (-3/4,3)` d. none of these

If (a(b+c-a))/(loga) = (b(c+a-b))/(logb) = (c(a+b-c))/(logc) , then prove that b^(c ) . c^(b) = a^(c ).c^(a) = a^(b).b^(a) .

If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(c,a,b),(b,c,a)| , then the value of k, is 1 b. 2 c. 3 d. 4

If a= ^(20)C_(0) + ^(20)C_(3) + ^(20)C_(6) + ^(20)C_(9) + "…..", b = ^(20)C_(1) + ^(20)C_(4) + ^(20)C_(7) + "… and c = ^(20)C_(2) + ^(20)C_(5) + ^(20)C_(8) + "…..", then Value of (a-b)^(2) + (b-c)^(2) + (c-a)^(2) is

If (a+b-c)/(a+ b) =(b+c-a)/(b+c) = (c+a-b)/(c+a) and a+b+cne 0, then prove that a = b = c.

The correct order of increasing bond length of C-H, C-O, C-C and C=C is

The correct order of increasing bond length of C-H, C-O, C-C and C=C is-

Choose the correct combination of labelling the number of carbon compounds in the substrate molecules, involved in the citric acid cycle 1. (A) 4C, (B) 6C, (C) 5C, (D) 4C, (E) 4C 2. (A) 6C, (B) 5C, (C) 4C, (D) 3C, (E) 2C 3. (A) 2C, (B) 3C, (C) 4C, (D) 5C, (E) 6C 4. (A) 4C, (B) 5C, (C) 6C, (D) 4C, (E) 4C

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

If a,b and c are real numbers, and Delta ={:|( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) |:}=0 Show that either a+b+c=0 "or" a= b= c .

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c