Karnataka SSLC 10th Maths Question Paper 2024

By definition, the degree of a polynomial is the highest power of the variable present in it. A cubic polynomial is of the form $ax^3 + bx^2 + cx + d$ where $a \neq 0$. The highest power is 3.

For any quadratic equation $ax^2 + bx + c = 0$, the discriminant is defined as $D = b^2 - 4ac$.

From the trigonometric identity $1 + \tan^2 A = \sec^2 A$, it follows that $\sec^2 A - 1 = \tan^2 A$.

$7 \times 11 \times 13 + 13 = 13(7 \times 11 + 1) = 13(77 + 1) = 13 \times 78$. Since the number has factors other than 1 and itself (it is the product of 13 and 78), it is a composite number.

For lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be parallel, the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$. Here, $\frac{1}{2} = \frac{k}{4}$. Solving for $k$, we get $k = \frac{4}{2} = 2$.