$PQ$ is a chord of length $4\ \text{cm}$ of a circle of radius $2.5\ \text{cm}$. The tangents at $P$ and $Q$ intersect at a point $T$. Find the length of $TP$.
Prove that $6\sqrt{3}$ is irrational.
The common difference of the A.P.: $3,\,3+\sqrt{2},\,3+2\sqrt{2},\,3+3\sqrt{2},\,\ldots$ will be:
The discriminant of the quadratic equation $3x^2 - 4\sqrt{3}\,x + 4 = 0$ will be:
The number of solutions of the pair of linear equations $\tfrac{4}{3}x + 2y = 8$, $2x + 3y = 12$ will be:
In the figure $DE \parallel BC$. If $AD = 3\,\text{cm}$, $DE = 4\,\text{cm}$ and $DB = 1.5\,\text{cm}$, then the measure of $BC$ will be:
If a tangent $PQ$ at a point $P$ of a circle of radius $5 \,\text{cm}$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \,\text{cm}$, then length of $PQ$ will be:
The product of $\sqrt{2}$ and $(2-\sqrt{2})$ will be:
The value of $\dfrac{1+\cot^2 \theta}{1+\tan^2 \theta}$ will be:
If $3 \cot A = 4$, then the value of $\dfrac{1 - \tan^2 A}{1 + \tan^2 A}$ will be:
The modal class of the following table will be: \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class Interval} & 0\text{--}5 & 5\text{--}10 & 10\text{--}15 & 15\text{--}20 & 20\text{--}25 \\ \hline \text{Frequency} & 2 & 7 & 11 & 8 & 6 \\ \hline \end{array} \]
The median class of the following frequency distribution will be: \[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-Interval} & \text{$0$--$10$} & \text{$10$--$20$} & \text{$20$--$30$} & \text{$30$--$40$} & \text{$40$--$50$} \\ \hline \text{Frequency} & \text{$7$} & \text{$8$} & \text{$15$} & \text{$10$} & \text{$5$} \\ \hline \end{array}\]
If $\tan \theta = \tfrac{3}{4}$, then the value of $\cos \theta$ will be:
