CTET Paper II (Mathematics and Science) 4 Jan 2022 Solved Paper

Concept:The coefficient of a term is the number multiplied by the variable. To find the coefficient of $y^{2}$, simplify the whole expression by expanding and collecting like terms.Explanation:Start with the expression: $(4x - 7y)(4x + 7y) - (3x - 2y)^{2} + (x^{2} + y^{2})$First, use the difference of squares: $(4x - 7y)(4x + 7y) = 16x^{2} - 49y^{2}$.Next, expand the square: $(3x - 2y)^{2} = 9x^{2} - 12xy + 4y^{2}$. Then subtract it: $-(9x^{2} - 12xy + 4y^{2}) = -9x^{2} + 12xy - 4y^{2}$.Finally, add the last term: $+(x^{2} + y^{2})$.Combine all parts: $(16x^{2} - 49y^{2}) + (-9x^{2} + 12xy - 4y^{2}) + (x^{2} + y^{2})$.Group $y^{2}$ terms: $-49y^{2} - 4y^{2} + y^{2} = -52y^{2}$.The complete simplified expression is $8x^{2} + 12xy - 52y^{2}$.Answer:The coefficient of $y^{2}$ is $-52$, which corresponds to option A.