CBSE Class 10 Mathematics (Basic) — Short Answer Questions

26. Prove that $\sqrt{3}$ is an irrational number.

27. Find the ratio in which the x-axis divides the line segment joining the points $(-6, 5)$ and $(-4, -1)$. Also, find the point of intersection.

28. (A) If $x = h + a \cos \theta$, $y = k + b \sin \theta$, then prove that : $\left(\dfrac{x - h}{a}\right)^2 + \left(\dfrac{y - k}{b}\right)^2 = 1$.

28. (B) Prove that : $\dfrac{\tan A}{1 + \sec A} - \dfrac{\tan A}{1 - \sec A} = 2\csc A$.

29. (A) In the given figure, $\triangle ABC$ is a right triangle in which $\angle B = 90^\circ$, $AB = 4\text{ cm}$ and $BC = 3\text{ cm}$. Find the radius of the circle inscribed in the triangle ABC.

29. (B) In the given figure, if a circle touches the side QR of $\triangle PQR$ at S and extended sides PQ and PR at M and N respectively, then prove that : $PM = \frac{1}{2}(PQ + QR + PR)$.

30. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use $\pi = 22/7$)

31. Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that : (i) same number appears on both the dice ? (ii) different number appears on both the dice ?