Let A = 3x²−8x+ 11, B = −2x²+ 12x, C = −4x²+ 7 and D = x²−x−11.

If (A+ B+ C)−D = px²+ qx+ r, then the value of (p + q+ r) is :

The correct option is 30.

Step 1: Write down the given algebraic expressions.

We are given four algebraic expressions:

$A=3x^2-8x+11$

$B=-2x^2+12x$

$C=-4x^2+7$

$D=x^2-x-11$

Step 2: Find the expression for (A + B + C).

Combine the like terms of A, B, and C:

$A+B+C=(3x^2-8x+11)+(-2x^2+12x)+(-4x^2+7)$

Grouping the terms by powers of x:

$A+B+C=(3-2-4)x^2+(-8+12)x+(11+7)$

$A+B+C=-3x^2+4x+18$

Step 3: Subtract D from (A + B + C).

Now, calculate (A + B + C) − D:

$(A+B+C)-D=(-3x^2+4x+18)-(x^2-x-11)$

Distribute the negative sign through the expression for D:

$(A+B+C)-D=-3x^2+4x+18-x^2+x+11$

Group and combine like terms:

$(A+B+C)-D=(-3-1)x^2+(4+1)x+(18+11)$

$(A+B+C)-D=-4x^2+5x+29$

Step 4: Compare with px² + qx + r to find p, q, and r.

We are given that:

$(A+B+C)-D=p{x}^2+qx+r$

Equating coefficients of like powers of x:

p = -4
q = 5
r = 29

Step 5: Calculate the value of (p + q + r).

$p+q+r=-4+5+29$

$p+q+r=1+29=30$

Thus, the required value of (p + q + r) is 30.