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An ice cream vendor puts a hemispherical scoop of ice cream on a cone which has radius 7 cm and height 15 cm. Find the volume of ice cream put on the cone.

If the side of a rhombus is 6 cm and its one diagonal is 8 cm. Find the area of the rhombus in ${cm}^2$.

A brick measures $20cm\times 10cm\times 5cm$. How many bricks will be required for a wall $20m$ long, $2m$ high and $\frac{1}{2}m$ thick?

<Two friends arguing>

Aju: A transversal is a line which intersects two lines at two distinct points.

Shubh: A transversal is a line which intersects two parallel lines at two distinct points.

If $\angle$e : $\angle$b : $\angle$c = 2 : 1 : 3 and AE is a straight line. What will be the value of $\angle$c?

In the following figure, AB =EF, BC = DE and $\angle$ B = $\angle$ E = ${90}^0$.

Prove that AD =FC.

Which among the following equations represents the given graph?

In the figure given below, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

Find the quantity of concrete required to make 70 cylindrical pillars of radius $5cm$ and height $10m$.

Which of the given equations will pass through the points (-2,2), (0,0) and (2,-2)?

Which of the following is false for a cone?

What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(where $x\ne 0,y\ne 0)$

Question 5 (iii)
It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $Rs20per{m}^2$, find:

(iii) Capacity of the vessel

$[Assume\pi =\frac{22}{7}]$

If $\sqrt{2}=1.414,then\sqrt{\frac{\sqrt{2}-1}{(\sqrt{2}+1)}}=$ ?

In the following figure, $\angle PQR={60}^{\circ },\angle PQR$ is bisected and the resultant angles are bisected again.

Find $\angle TQS+\angle SQU+\angle PQS.$

Question 56

Fill in the blanks to make the statement true.

___ $\times$ (-93) = 93

In the figure, P and Q are centres of two circles intersecting at B and C. ACD is a straight line. Then $\angle BQD$ =

If $x^{-2}=64,then{x}^{\frac{1}{3}}+x^0=$

How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 g, find the weight of the empty box in kg.

If a pool has to be constructed with a boundary of width $14m$ consisting of two straight sections $120m$ long joining semi-circular ends whose inner radius is $35m.$ If the cost of flooring the boundary by tiles is Rs. $50$ per square metre, then the cost incurred will be

What are the factors of $x^2+5x-24$?

Construct the angles of the following measurements:

$\left(i\right){30}^0\left(ii\right){75}^0\left(iii\right){105}^0\left(iv\right){135}^0\left(v\right){15}^0\left(vi\right)22{\frac{1}{2}}^{\circ }$

The range of $|x-2|+|x-5|$ is

Arrange the fractions in ascending order

$\frac{2}{3},\frac{4}{5},\frac{6}{5},\frac{9}{8}$

If the length of diagnal of a cube is $8\sqrt{3}cm$ then its surface area is

$\left(a\right)192c{m}^2\left(b\right)384c{m}^2\left(c\right)512c{m}^2\left(d\right)768c{m}^2$

$(3+\sqrt{5})(3-\sqrt{5})$ is rational.

In the construction of the bisector of a given angle, as shown in the figure below

ΔBEF $\cong$ ΔBDF by which congruence criterion?

If R be a relation $<$ from A={1,2,3,4} to B={1,3,5} i.e., (a,b) $\in R\iff a<b,thenRo{R}^{-1}$ is

a+b=10,a square+b square =58. Find a cube+b cube

O is a point inside a quadrilateral ABCD which isn't at the point of intersection of diagonals. Prove that

OA+OB+OC+OD>AC+BC

Question 2
Complete the table:
$$\begin{array}{cccc}& \text{First expression}& \text{Second expression}& \text{Product}\\ \left(i\right)& a& b+c+d& --\\ \left(ii\right)& x+y-5& 5xy& --\\ \left(iii\right)& p& 6p^2-7p+5& --\\ \left(iv\right)& 4p^2{q}^2& p^2-q^2& --\\ \left(v\right)& a+b+c& abc& --\end{array}$$

Factorise:
$25x^2-10x+1-36y^2$

The graph of the line x - y = 0 passes through the point

(a) $\frac{-1}{2},\frac{1}{2}$

(b) $\frac{3}{2},\frac{-3}{2}$

(c) (0, -1)

(d) (1, 1)

The length of the longest rod that can fit in a cubical vessel of side 10 cm,is
(a) 10 cm (b) 20 cm (c) $10\sqrt{2}$cm (d) $10\sqrt{3}$cm

If $x=\sqrt[3]{32+\sqrt{3}},then{x}^3+\frac{1}{x^3}=$

$\text{In the given figure ,}AB||CD,\angle BAE={65}^{\circ }and\angle OEC={20}^{\circ }.Find\angle ECO.$

$$\begin{array}{cc}TheWickerMan& 04:35\\ GhostoftheNavigator& 06:50\\ BraveNewWorld& 06:18\\ BloodBrothers& 07:14\\ TheMercenary& 04:42\\ DreamofMirrors& 09:21\\ TheFallenAngels& 04:00\\ TheNomad& 09:05\\ OutoftheSilentPlanet& 06:25\\ TheThinLineBetweenLove& 08:27\end{array}$$

Find the probability that a song will be (i) at least 7 minutes long (ii) less than 5 minutes long.

There are 50 people in a restaurant, 22 are male and 28 are female. What is the probability that a person chosen at random will be male?

An exterior angle of a triangle is ${110}^{\circ }$ and one of the interior of opposite angles is ${40}^{\circ }$ . Then the other two angles of a triangle are :-

If the sum of two consecutive numbers is 71 and the smaller number is x, find the other number.

Find the length of the tangent drawn to a circle of radius 8 cm, from a point which is at a distance of 10 cm from the center of the circle.

Using HCF and LCM answer the following question

A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad it is to be paved with square tiles of the same size find the least possible number of such tiles?