Question 1 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$&#160; and&#160; &#160;$\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>

Question 2 :
The mid-point of line segment joining thepoints (3, 0) and (-1, 4) is :

Question 3 :
The points $A$ $(x_1, y_1), B (x_2, y_2)$ and $C (x_3, y_3)$ are the vertices of $\Delta $ ABC.<br/>The median $AD$ meets $BC$ at $D$.<br/>Find the coordinates of points Q and R on medians BE and CF,&#160;respectively such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.<br/>

Question 4 :
Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x &amp; {\cos}^{2}x &amp; 4\sin2x \\ {\sin}^{2}x &amp; 1+{\cos}^{2}x &amp; 4\sin2x \\ {\sin}^{2}x &amp; {\cos}^{2}x &amp; 1+4\sin2x \end{vmatrix}=$

Question 5 :
If $sec\theta -tan\theta =\dfrac{a}{b},$ then the value of $tan\theta $ is

Question 6 :
IF A+B+C=$ \displaystyle 180^{\circ} &#160;$ ,then $ &#160;tan A+tanB+tanC $ is equal to

Question 7 :
If $\sin { A } =a\cos { B } $ and $\cos { A } =b\sin { B } $, then $\left( { a }^{ 2 }-1 \right) \tan ^{ 2 }{ A } +\left( 1-{ b }^{ 2 } \right) \tan ^{ 2 }{ B } $ &#160; is equal to

Question 8 :
If a line in the space makes angle $a, p$ and $y$ with the coordinate axes, then<br/>$\cos\,2a\,+\cos\,2b\,+\,\cos\,2y\,+\,\sin^2\,a\,+\,\sin^2\beta\,+\,\sin^2\,y\,$ equals

Question 10 :
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.<br/>$\dfrac { 13 }{ 3125 } $

Question 11 :
If we apply Euclid&#34;s division algorithm for $20, 8,$ then the correct answer will be

Question 12 :
Factorise the expressions and divide them as directed.$12xy(9x^2-&#160; 16y^2)\div&#160; 4xy(3x + 4y)$

Question 13 :
Divide the following and write your answer in lowest terms:&#160;$\dfrac{3x^2-x-4}{9x^2-16}\div \dfrac {4x^2-4}{3x^2-2x-1}$

Question 15 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is

Question 16 :
Solve : $\displaystyle \frac{9}{x}\, -\,&#160;\displaystyle \frac{4}{y}\, =\, 8$ and&#160;$\displaystyle \frac{13}{x}\, +\,&#160;\displaystyle \frac{7}{y}\, =\, 101$

Question 17 :
If the equations $y = mx + c$ and $x &#160;\cos &#160;\alpha + y \sin &#160;\alpha = p$ represent the same straight line, then

Question 19 :
A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium">&#160;<span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes&#160;</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail.&#160;</p><p>(iii) The value of $P (H) + P (T)$.</p>

Question 20 :
A bag contains $7$ black socks, $12$ white socks, and $17$ red socks. If you pick one sock at random from the bag, what is the probability that it will NOT be white?

Question 22 :
The ratio of areas of square and circle is givenn : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of

Question 23 :
In a circle of radius 21 cm an arc subtends an angle of&#160;$\displaystyle 56^{\circ} $ at the centre of the circle. The length of the arc is

Question 24 :
The crescent shaded in the diagram, is like that found on many flags. $PSR$ is an arc of a circle, centre $O$ and radius $24.0$ cm. Angle POR $=$ $48.2^{\circ}$.<br/>$PQR$ is a semicircle on $PR$ as diameter, where $PR$ $=$ $19.6$ cm<br/>$[\pi = 3.14] [\cos 24.1 = 0.91]$The area of the crescent is<br/>

Question 25 :
If the radius of a circle is $\displaystyle \frac{7}{\sqrt{\pi}}$ cm, then the area of the circle is equal to

Question 26 :
The ratio of the circumference of a circle to twice the diameter of the circle is&#160;

Question 27 :
If a right circular cone and a cylinder have equal circles as their base and have equal heights, then the ratio of their volumes is 2 : 3.<br>

Question 28 :
The maximum length of a pencil that can be kept in rectangular box of dimensions $12\ cm\times 9\ cm \times 8\ cm$, is

Question 29 :
A cone of height $7$ cm. and base radius $3$ cm. is carved from a rectangular block of wood of dimensions $10 cm. \times 5 cm. \times 2$ cm. The percentage of wood wasted is

Question 30 :
The surface area of the frustum cone is givenits base radius, R = 12 cm and top radius, r = 10 cm. The height of the cone is12 cm. Find the slant height of the cone.

Question 31 :
A conical vessel of height $10$ $mts$ and radius $5\ mts$. is being filled with water at uniform rate of $3/2$ $ cu.mts/min$. How long will it take to fill the vessel?