Q. The sum of first $n$ terms of an AP is $3n^2-n$. Find the ${25}^{th}$ term of this AP.

Q. A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $10$ cm, and its base is of radius $3.5$ cm, find the volume of wood in the toy. $[Use\pi =\frac{22}{7}]$

1. $425$
2. $290$
3. $474.83$
4. $205.33$

Q. Solve that following for x:

Q. Water is flowing through a cylindrical pipe, of internal diameter $2cm$, into a cylindrical tank of base radius $40cm$, at the rate of $0.4m/s$. Determine the rise in level of water in the tank in half hours.

Q. In fig., a circle is inscribed in triangle $ABC$ touches its sides $AB,BC$ and $AC$ at points $D,E$ and $F$ respectively. If $AB=12$ cm, $BC=8$ cm and $AC=10$ cm, then find the length of $AD,BE$ and $CF$.

Q. Find the ratio in which the $y-$axis divides the line segment joining the points $(-4,-6)$ and $(10,12)$. Also, find the coordinates of the point of division.

Q. In fig., $l$ and $m$ are two parallel tangents to a circle with centre $O$, touching the circle at $A$ and $B$ respectively. Another tangent at $C$ intersects the line $l$ at $D$ and $m$ at $E$. Prove that $\angle DOE={90}^o$

Q. Sum of the areas of two squares is $400c{m}^2$. If the difference of their perimeters is $16cm$, find the sides of the two squares.

Q. Show that the points $(-2,3),(8,3)$ and $(6,7)$ are the vertices of a right triangle.

Q. In fig., a circle with centre $O$ is inscribed in a quadrilateral $ABCD$ such that, it touches the sides $BC,AB,AD$ and $CD$ at points $P,Q,R$ and $S$ respectively, If $AB=29$ cm, $AD=23$ cm, $\angle B={90}^o$ and $DS=5$ cm, then the radius of the circle (in cm) is:

1. $11$
2. $18$
3. $6$
4. $15$

Q. How many three-digit natural numbers are divisible by $7$?

Q. For what values of k, the roots of the quadratic equation $(k+4)x^2+(k+1)x+1=0$ are equal?

Q. Solve the following quadratic equation for $x$: $4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

Q. A Group consists of $12$ persons, of which $3$ are extremely patient, other $6$ are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer more?

Q. A card is drawn at random from a well shuffled pack of $52$ playing cards. Find the probability that the drawn card is neither a king nor a queen.

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

Q. In fig., the area of triangle ABC (in sq. units) is:

1. $15$
2. $7.5$
3. $2.5$
4. $10$

Q. The horizontal distance between two poles is $15$ m. The angle of depression of the top of first pole as seen from the top of second pole is ${30}^o$. If the height of the second pole is $24$ m, find the height of the first pole. $[Use\sqrt{3}=1.732]$

Q. A box contains $90$ discs, numbered from $1$ to $90$. If one disc is drawn at random from the box, the probability that it bears a prime-number less than $23$, is:

1. $\frac{7}{90}$
2. $\frac{10}{90}$
3. $\frac{4}{45}$
4. $\frac{9}{89}$

Q. If the difference between the circumference and the radius of a circle is $37cm$, then using $\pi =\frac{22}{7}$, the circumference (in cm) of the circle is:

1. $154$
2. $44$
3. $14$
4. $7$

Q. Given A.P is $\frac{1}{3q},\frac{1-6q}{3q},\frac{1-12q}{3q}$. Find the common difference

1. $-2$
2. $1$
3. $-1$
4. $2$

Q. A bucket opens at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is $24cm$ and the diameters of its upper and lower circular ends are $30cm$ and $10cm$ respectively. Find the cost of metal sheet used in it at the rate of $Rs10$ per $100c{m}^2$. $[Use\pi =3.14]$.Insert answer in nearest integer.

Q. The probability of getting an even number, when a die is thrown once, is:

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{1}{6}$
4. $\frac{5}{6}$

Q. In a circle of radius 21 cm, an arc subtends an angle of ${60}^o$ at the centre. Find the sum of the length of the arc and area of the sector formed by the arc. $[Use\pi =\frac{22}{7}]$

Q. Construct a tangent to a circle of radius $4$ cm from a point on the concentric circle of radius $6$ cm.

Q. In fig., $PA$ and $PB$ are two tangents drawn from an external point $P$ to a circle with centre C and radius $4cm$. If $PA$ $\perp$ PB, then the length of each tangent is:

1. $4cm$
2. $3cm$
3. $5cm$
4. $6cm$

Q. The angle of depression of a car, standing on the ground, from the top of a $75m$ high tower, is ${30}^o$. The distance of the car from the base of the tower (in m.) is:

1. $25\sqrt{3}$
2. $50\sqrt{3}$
3. $75\sqrt{3}$
4. $150$

Q. In Fig., $AB$ and $CD$ are two diameters of a circle with centre $O$, which are perpendicular to each other. $OB$ is the diameter of the smaller circle. If $OA=7cm$, find the area of the shaded region. $[Use\pi =\frac{22}{7}]$

1. $60.5c{m}^2$
2. $63.5c{m}^2$
3. $66.5c{m}^2$
4. $56.5c{m}^2$

Q. Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14cm\times 7cm$. Find the area of the remaining card board. $[\text{Use}\pi =\frac{22}{7}]$

Q. A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is $14cm$ and the total height of the vessel is $13cm$. Find the total surface area of the vessel. $[Use\pi =\frac{22}{7}]$