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question_answer1) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] \[{{x}^{2}}+4x+5\]has two zeroes. Reason [R] A quadratic polynomial can have atmost two zeroes.
question_answer2) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] The factor of \[\frac{3}{2}{{x}^{2}}-8x-\frac{35}{2}\] is \[\frac{1}{2}\left( x-7 \right)\left( 3x+5 \right)\] Reason [R] The factors are calculated by dividing the coefficients by 2 and expression is obtained by splitting the middle term
question_answer3) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] A quadratic polynomial having 4 and 3 as zeroes is \[{{x}^{2}}-7x-12\] Reason [R] The quadratic polynomial having a and P as zeroes is given by \[p\left( x \right)={{x}^{2}}-\left( \alpha +\beta \right)x+\alpha \,.\,\beta \]
question_answer4) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] Zeroes of \[f\left( x \right)={{x}^{2}}-4x-5\]are 5, -1 Reason [R] The polynomial whose zeroes are \[2+\sqrt{3},\,2-\sqrt{3}\]is \[{{x}^{2}}-4x+7\]
question_answer5) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If \[\alpha \] and \[\beta \]are the zeroes of the polynomial\[{{x}^{2}}+2x-15\], then \[\frac{1}{\alpha }+\frac{1}{\beta }\] is \[\frac{2}{15}\]. Reason [R] If \[\alpha \] and \[\beta \]are the zeroes of a quadratic polynomial \[a{{x}^{2}}+bx+c\], then \[\alpha +\beta =-\frac{b}{a}\] and \[\alpha \beta =\frac{c}{a}\]
question_answer6) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If one zero of the polynomial \[p\left( x \right)=\left( k+18 \right){{x}^{2}}+11x+4k\] is the reciprocal of the other zero, then k = 6 Reason [R] If \[\left( x-\alpha \right)\] and \[\left( x-\beta \right)\] are the factor of the polynomial p(x), then \[\alpha \] and \[\beta \]are the zeroes of the p(x)
question_answer7) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If the zeroes of \[{{x}^{2}}+px+q\] are two consecutive integers, then \[{{p}^{2}}-1=4q\] Reason [R] If \[\alpha \], \[\beta \]are zeroes of \[\left( x-a \right)\left( x-b \right)-c\], then a, b are zeroes of \[\left( x-\alpha \right)\left( x-\beta \right)+c\]
question_answer8) . Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If the zeroes of the polynomial \[f\left( x \right)=\left( {{k}^{2}}+4 \right){{x}^{2}}=4kx+\left( {{k}^{3}}-9 \right)\]are equal in magnitude but opposite in sign, then value of k is zero Reason [R] A quadratic polynomial whose zeroes are \[\alpha \] and \[\beta \]is \[{{x}^{2}}+\left( \alpha +\beta \right)x+\alpha \beta \]
question_answer9) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If m and n are the zeroes of the polynomial \[3{{x}^{2}}+11x-4\], then \[12\left( {{m}^{2}}+{{n}^{2}} \right)+145mn=0\] Reason [R] If \[\alpha \] and \[\beta \]are the zeroes of the polynomial\[a{{x}^{2}}+bx+c\], then \[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=\frac{{{b}^{2}}}{ac}+2\]
question_answer10) Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. Assertion [A] If \[{{x}^{2}}+x-12\] divides \[{{x}^{2}}+x-12\] exactly, then \[a=-8\] and b = - 5 Reason [R] When a polynomial \[p\left( x \right)\]is completely divided by \[\left( x-\alpha \right)\], then \[p\left( x \right)=0\].
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