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2024 BOARD EXAM QUESTIONS
1. If the sum of zeroes of the polynomial $p(x)=2x^2-k\sqrt{2}x+1$ is $\sqrt{2}$, the the value of k is:
(a) $\sqrt{2}$
(b) 2
(c) 2$\sqrt{2}$
(d) $\frac{1}{2}$
2. The zeroes of the polynomial $x^2+px+q$ are twice the zeroes of the polynomial $4x^2-5x-6$. Then value of p is:
(a) $-\frac{5}{2}$
(b) $\frac{5}{2}$
(c) $-5$
(d) $10$
3. Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial.
Reason (R): A polynomial of degree n (n>1) can have at most n zeroes.
4. If the sum and the product of zeroes of a quadratic polynomial are $2\sqrt{3}$ and 3 respectively, then a quadratic polynomial is:
(a) $x^2+2\sqrt{3}x-3$
(b) $(x-\sqrt{3})^2$
(c) $x^2-2\sqrt{3}x-3$
(d) $x^2+2\sqrt{3}x+3$
5. If $\alpha$ and $\beta$ are the zeroes of the polynomial $6x^2-5x-4$, then $\frac{1}{\alpha}+\frac{1}{\beta}$ is equal to:
(a) $\frac{5}{4}$
(b) $-\frac{5}{4}$
(c) $\frac{4}{5}$
(d) $\frac{5}{24}$
6. Assertion (A): Zeroes of a polynomial $p(x)=x^2-2x-3$ are -1 and 3.
Reason (R): The graph of polynomial $p(x)=x^2-2x-3$ intersects x-axis at (-1,0) and (3,0).
7. For what value of k, the product of zeroes of the polynomial $kx^2-4x-7$ is 2?
(a) $-\frac{1}{14}$
(b) $-\frac{7}{2}$
(c) $\frac{7}{2}$
(d) $-\frac{2}{7}$
8. If one of the zeroes of the quadratic polynomial $(\alpha-1)x^2+\alpha x+1$ is -3, then the value of $\alpha$ is:
(a) $-\frac{2}{3}$
(b) $\frac{2}{3}$
(c) $\frac{4}{3}$
(d) $\frac{3}{4}$
