CBSE Class class-10 Mathematics (Basic) — Very Short Answer Questions

21. If α, β are the zeroes of the polynomial $p(x) = x^2 - 3x - 1$, then find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$.

22. (A) In $\triangle ABC$, $DE \parallel BC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$ and $EC = x - 1$, then find the value of x.

22. (B) In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of x and y. ($\triangle ABC$: $AB = 4 \text{ cm}, BC = 6 \text{ cm}, AC = y$; $\triangle XYZ$: $XY = x, YZ = 7.2 \text{ cm}, XZ = 6 \text{ cm}$)

23. The coordinates of the centre of a circle are $(x - 7, 2x)$. Find the value(s) of 'x', if the circle passes through the point $(-9, 11)$ and has radius $5\sqrt{2}$ units.

24. (A) If $\tan \theta = \frac{24}{7}$, then find the value of $\sin \theta + \cos \theta$.

24. (B) If $\cot \theta = \frac{7}{8}$, then find the value of $\dfrac{(1 + \sin \theta)(1 - \sin \theta)}{(1 + \cos \theta)(1 - \cos \theta)}$.

25. Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.