Q. Find the values (s) of $k$ so that the quadratic equation $3x^2-2kx+12=0$ has equal roots.

Q. In figure, the chord $AB$ of the larger of the two concentric circles, with centre $O,$ touches the smaller circle at $C.$ Prove that $AC=CB.$

Q. The volume of a hemisphere is $2425\frac{1}{2}c{m}^3$. Find its curved surface area. $[Use\pi =\frac{22}{7}].$

Q. From a solid cylinder of height $7$ cm and base diameter $12$ cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. $[Use\pi =\frac{22}{7}].$

Q. A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) the queen of diamonds.

Q. The sum of first $20$ odd natural number is :

1. $210$
2. $400$
3. $100$
4. $420$

Q. The coordinates of the point P dividing the line segment joining the points $A(1,3)$ and $B(4,6)$ in the ratio $2:1$ are:

1. $(4,2)$
2. $(2,4)$
3. $(5,3)$
4. $(3,5)$

Q. Draw a triangle $ABC$ with side $BC=6$ cm, $\angle C={30}^o$ and$\angle A={105}^o$. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of $\Delta ABC$.

Q. In the figure, the sides $AB,BC$ and $CA$ of a triangle $ABC,$ touch a circle at $P,Q$ and $R$ respectively. If $PA=4$ cm, $BP=3$ cm and $AC=11$ cm, then the length of $BC$ (in cm) is:

1. $11$
2. $14$
3. $15$
4. $10$

Q. If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

1. $1:2$
2. $2:1$
3. $1:4$
4. $4:1$

Q. Prove that the parallelogram circumscribing a circle is a rhombus.

Q. If $1$ is a root of the equations $a{y}^2+ay+3=0$ and $y^2+y+b=0$, then $ab$ equals:

1. $3$
2. $-\frac{7}{2}$
3. $6$
4. $-3$

Q. Find the sum of all three digit natural numbers, which are multiples of $7.$

Q. If a point $A(0,2)$ is equidistant from the points $B(3,p)$ and $C(p,5)$ then find the value of $p.$

Q. If the coordinates of the one end of a diameter of a circle are $(2,3)$ and the coordinates of its centre are $(-2,5),$ then the coordinates of the other end of the diameter are:

1. $(-6,7)$
2. $(6,7)$
3. $(6,-7)$
4. $(-6,-7)$

Q. A point $P$ divides the line segment joining the points $A(3,-5)$ and $B(-4,8)$ such that $\frac{AP}{PB}=\frac{K}{1}.$ If $P$ lies on the line $x+y=0,$ then find the value of $K.$

Q. If the area of a circle is equal to sum of the areas of two circles of diameters $10$ cm and $24$ cm, then the diameter of the larger circle (in cm)is:

1. $26$
2. $34$
3. $17$
4. $14$

Q. A bucket is in the form of a frustum of a cone and it can hold $28.49liters$ of water. If the radii of its circular ends are $28cm$ and $21cm$, find the height of the bucket. $[Use\pi =\frac{22}{7}].$

Q. If the vertices of a triangle are $(1,-3),(4,p)$ and $(-9,7)$ and its' area is $15$ sq. units, find the value (s) of $p.$

Q. In the figure, a circle touches the side $DF$ of $\Delta EDF$ at $H$ and touches $ED$ and $EF$ produced at $K$ and $M$ respectively. If $EK=9$ cm, then the perimeter of $\Delta EDF$ (in cm) is:

1. $18$
2. $13.5$
3. $12$
4. $9$

Q. A number is selected at random from first $50$ natural numbers. Find the probability that it is a multiple of $3$ and $4.$

Q. In figure, $OABC$ is a square of side $7cm.$ If $OAPC$ is a quadrant of a circle with centre $O,$ then find the area of the shaded region. $[Use\pi =\frac{22}{7}].$

Q. The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is:

1. ${90}^0$
2. ${45}^0$
3. ${60}^0$
4. ${30}^0$

Q. Two dice are thrown together. The probability of getting the same number on both dice is:

1. $\frac{1}{2}$
2. $\frac{1}{12}$
3. $\frac{1}{3}$
4. $\frac{1}{6}$

Q. The $16$th term of an AP is $1$ more than twice its $8$th term. If the $12$th term of the AP is $47,$ then find its $n$th term.

Q. In the figure, an isosceles triangle $ABC,$ with $AB=AC,$ circumscribes a circle. Prove that the point of contact $P$ bisects the base $BC.$

Q. Tangents $PA$ and $PB$ are drawn from an external point $P$ to two concentric circle with centre $O$ and radii $8cm$ and $5cm$ respectively, as shown in figure. If $AP=15cm,$ then find the length of $BP.$

Q. Solve for $x:$ $4x^2-4ax+(a^2-b^2)=0.$

Q. In the figure, $PQ$ and $AB$ are respectively the arcs of two concentric circles of radii $7$ cm and $3.5$ cm and centre O. If $\angle POQ={30}^0$, then the area of the shaded region. $[Use\pi =\frac{22}{7}].$

Q. A kite is flying at a height of $45$ m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^0$. Find the length of the string assuming that there is no slack in the string.