Match the columns - Column 'A' (i) Zero of polynomial x + 1 (ii) Linear polynomial (iii) Degree of polynomial x5-x4+3 (iv) The coordinates of x-axis (v) Coefficient of x in polynomial 5x2 (vi) Ordinate of point (5, 6) Column 'B' (a) 0 (b) 6 (c) 5 (d) 1+x (e) (x, 0) (f) -1

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प्र.4 सही जोड़ी मिलाइए - (Match the columns -)

• (i) बहुपद $x + 1$ का शून्यक $\to$ (f) $-1$
  • (Explanation: $x+1=0 \implies x=-1$)
• (ii) रैखिक बहुपद $\to$ (d) $1+x$
  • (Explanation: A linear polynomial has a degree of 1.)
• (iii) बहुपद $x^5 - x^4 + 3$ की घात $\to$ (c) 5
  • (Explanation: The highest power of the variable in the polynomial is 5.)
• (iv) $x$-अक्ष के निर्देशांक $\to$ (e) $(x, 0)$
  • (Explanation: Any point on the $x$-axis has a $y$-coordinate of 0.)
• (v) बहुपद $5x^2$ में $x$ का गुणांक $\to$ (a) 0
  • (Explanation: The term with $x^1$ is absent in $5x^2$, so its coefficient is 0.)
• (vi) बिन्दु $(5, 6)$ की कोटि $\to$ (b) 6
  • (Explanation: The ordinate of a point $(x, y)$ is its $y$-coordinate.)

प्र.5 एक शब्द/वाक्य में उत्तर दीजिए - (Answer in one word/sentence -)

(i) यदि बिन्दु $(+, +)$ के रूप का है, तो वह किस चतुर्थांश में होगा? * (i) In which quadrant a point lies, if the point is of the form $(+, +)$? * The point will lie in the First Quadrant.

(ii) रैखिक समीकरण $x = 3y$ को मानक रूप में लिखिए। * (ii) Write the linear equation $x = 3y$ in standard form. * The standard form $Ax + By + C = 0$ gives $\boxed{x - 3y + 0 = 0}$.

(iii) एक बिन्दु से होकर कितनी रेखाएँ खींची जा सकती हैं? * (iii) How many lines can pass through one point? * Infinitely many lines can pass through one point.

(iv) किसी समान्तर चतुर्भुज के विकर्ण परस्पर समान और लम्बवत् हों, तो वह चतुर्भुज होगा। * (iv) If the diagonals of a parallelogram are equal and perpendicular to each other, then quadrilateral will be. * The quadrilateral will be a square.

(v) वृत्त की सबसे बड़ी जीवा कहलाती है। * (v) Write the name of longest chord of a circle. * The longest chord of a circle is its diameter.

(vi) त्रिभुज का क्षेत्रफल संबंधी हीरॉन का सूत्र लिखिए। * (vi) Write the Heron's formula to find the area of a triangle. * Heron's formula for the area of a triangle with side lengths $a, b, c$ is: $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$ where $s$ is the semi-perimeter: $s = \frac{a+b+c}{2}$

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