Question 1 :
The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is
Question 3 :
Without plotting the points indicate the quadrant in which they will lie, if ordinate is $5$ and abscissa is $3$?
Question 4 :
The points (1, -1), $\displaystyle \left ( -\frac{1}{2},\frac{1}{2} \right )$ and (1, 2) are the vertices of an isosceles triangleSay yes or no.
Question 7 :
If the perimeter of equilateral triangle is $42\sqrt 5$ cm. Calculate its sum of two sides
Question 8 :
If $x=7+4\sqrt 3$, then the value of $\sqrt x+\dfrac {1}{\sqrt x}$ is
Question 9 :
The product of a non-zero rational and an irrational number is<br>
Question 10 :
If $\left (x + \dfrac {1}{x}\right ) = 2\sqrt {3}$, then the value of $\left (x^{3} + \dfrac {1}{x^{3}}\right )$ is
Question 11 :
If $\dfrac {a^{2} + 2ab + b^{2}}{a^{2} - b^{2}} = 2a + 2b$, what is the value of $a - b$?
Question 13 :
The polynomial $\displaystyle p(x)=2x^{4}-x^{3}-7x^{2}+ax+b$ is divisible by $\displaystyle x^{2}-2x-3$ for certain values of $a$ and $b$. The value of $(a + b)$ is:
Question 14 :
If $\dfrac { x }{ 3 } =\dfrac { 16 }{ y } =4$, then $x+y=$
Question 15 :
Which of the following equations has the vertex of $(3, -3)$?
Question 16 :
Express $y$ in terms of $x$, given $-2x + y - 7 = 0$. Check whether the point $(-3, -2)$ is solution of this equation.<br/>
Question 17 :
When two line segments meet at a point forming right angle they are said to be ..........to each other.
Question 19 :
Which of the following will form the sides of a triangle?
Question 20 :
For $a,b,c,d\in N$, the area of the parallelogram bounded by the lines $y=ax+c,y=ax+d,y=bx+c$ and $y=bx+d$ is $18$ while the area of the parallelogram bounded by the lines $y=ax+c,y=ax-d,y=bx+c$ and $y=bx-d$ is $72$. The least possible value of $a+b+c+d$ will be:
Question 21 :
A rectangle and a rhombus are on the same base and between the same parallels. The ratio of their areas is :
Question 23 :
Coordinates of the centre of the circle which bisects the circumferences of the circles $x^{2}+y^{2}=1:\x^{2}+y^{2}+2x-3=0$ and $x^{2}+y^{2}+2y-3=0$ is
Question 25 :
If s is the semi-perimeter of a $\Delta A B C$ whose sides are a,b,c then s=.............?<br><br>
Question 26 :
Two sides of a right triangle containing the right angle are $100 cm$ and $8.6 cm$. Find its area
Question 29 :
If the arithmetic mean of first $n$ natural numbers is $15$, then $n$ is equal to:
Question 30 :
The mean of $12$  observations is $14$. By an error one observation is registered as $ 24$  instead of $-24$. Find the actual mean.
Question 31 :
A coin is tossed $5$ times. The probability of $2$ heads and $3$ tails is:
Question 32 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 33 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 34 : A die is thrown $400$ times, the frequency of the outcomes of the events are given as under.<br/><table class="wysiwyg-table"><tbody><tr><td>outcome<br/></td><td>$1$<br/></td><td>$2$<br/></td><td>$3$<br/></td><td>$4$<br/></td><td>$5$<br/></td><td>$6$<br/></td></tr><tr><td>Frequency<br/></td><td>$70$<br/></td><td>$65$<br/></td><td>$60$<br/></td><td>$75$<br/></td><td>$63$<br/></td><td>$67$<br/></td></tr></tbody></table>Find the probability of occurrence of an odd number.<br/>
Question 35 :
From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
Question 36 :
The height of a cone is $9 cm$ and the radius of the base is $7 cm$. The cone is melted and a cuboid is formed. The length of the base of the cuboid is $11 cm$ and breadth is $6 cm$. Find the height of the cuboid.<br>
Question 37 :
In the above question the cylinders formed will have their volumes in the ratio of
Question 38 :
If the base area and the volume of a cone are numerically equal, then its height is 3 units.<br>
Question 39 :
A rod of 2 cm diameter and 30 cm length is converted into a wire 3 m length of uniform thickness. The diameter of the wire is:
Question 40 :
The radius of a sphere is 9 cm It is melted and drawn into a wire of diameter 2 mm Find the lenght of the wire in meters
Question 41 :
Sixteen cylindrical cans each with a radius of $1$ unit are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box in square units?
Question 42 :
Circumference of the base of a cylinder is 88 cm and height of the cylinder is 42 cm Its volume is
Question 43 :
A capsule of medicine is in the shape of a sphere of diameter $3.5mm$. How much medicine (in ${mm}^{3}$) is needed to fill this capsule?
