Question 1 :
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients.$2s^2-(1+2\sqrt 2)s+\sqrt 2$<br/>
Question 2 :
If $\alpha , \beta$ are the roots of equation $x^2 \, - \, px \, + \, q \, = \, 0,$ then find the equation the roots of which are $\left ( \alpha ^2  \, \beta ^2 \right )  \,  and  \,  \,  \alpha \, + \,\beta $.
Question 3 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>
Question 4 :
If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.
Question 6 :
<br/>Let $\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$ any point on the cartesian plane then match the following lists:<br/> <br/><table class="table table-bordered"><tbody><tr><td> LIST - I    </td><td> LIST - II</td></tr><tr><td> $\mathrm{A})$ The distance from $\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td> $\mathrm{B})$ The distance from $\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td> $\mathrm{C})$ The distance from $\mathrm{P}$ to origin is </td><td> 3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$ </td></tr><tr><td> </td><td>4)$ |x_{1}|$                                   </td></tr></tbody></table>
Question 8 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 9 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 10 :
A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is
Question 11 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.
Question 12 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 15 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.
Question 16 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 17 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 18 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 19 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 20 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 21 :
If an arc of a circle subtends an angle of<b></b>$ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)
Question 22 :
Choose the correct answer from the alternative given.<br/>A can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is:
Question 23 :
The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long is
Question 24 :
The area of a sector formed by two mutually perpendicular radii in $\odot \left( 0,5cm \right) $ is ............... ${cm}^{2}$.
Question 25 :
If the diameter of a circle is increased by 200% then its area is increased by<br>
Question 26 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 28 :
The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point
Question 29 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 30 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is
Question 31 :
The probability expressed as a percentage of a particular occurrence can never be
Question 32 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 33 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 34 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 35 :
What is the maximum value of the probability of an event?
Question 36 :
The angles of elevation of the top of $12$m high tower from two points in opposite directions with it are complementary. If distance of one point from its base is $16$m, then distance of second point from tower's base is?
Question 37 :
Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of$ \displaystyle 30^{\circ} $ with the ground. If the length of the broken part is 20 meters , then the remaining part of the tree is of length
Question 38 :
A kite is flying with the string inclined at$\displaystyle 45^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is
Question 39 :
If the altitude of the sun is $60^{\circ}$, the height of a tower which casts a shadow of length 30 m is :<br/>
Question 40 :
What is the length of the chord of a unit circle which substends an angle $\theta$ at the centre ?