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If $1c{m}^3$ of cast iron weighs $21g,$ find the weight of a cast-iron pipe of length $1m$ with a bore of $3cm$ in which the thickness of the metal is $1cm.$

The area of the floor of a room is 15$m^2.$ If its height is 4 m, then the volume of the air contained in the room is

The equation x - 2 = 0 on number line is represented by

The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

Find the value of k for which the point (1, -2) lies on the graph of the linear equation $x-2y+k=0.$

Using ruler and compasses only, draw an angle of measure ${135}^{\circ }$.

If angles C,B and A of a right angled triangle ABC, right angled at A, form an increasing A.P.. then, sinA x cosB =

Shalini deposited Rs. 4,00,000 in a bank where she was promised an interest of 10%. She deposited it for a period of two years. Find the difference in the amount if the interest is calculated in a compounded manner to the amount interested in a simple manner.

A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. The length of the pipe is

In $\Delta ABC,\angle B=\angle C$ and ray AX bisects the exterior angle $\angle DAC.$ If $\angle DAX={70}^{\circ },$ then $\angle ACB$=

One side other than the hypotenuse of a right angled isosceles triangle is 4 cm. The length of the perpendicular on the hypotenuse from the opposite vertex is

The angles of a quadrilateral are in the ratio $2:4:5:7.$ Find the angles.

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point

What is the area of the right triangle with lengths of perpendicular sides equal to 2 cm each?

The measure of the angle between the coordinate axes is

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is:

Write the equation of a line passing through the point $(3,5)$ and parallel to $x$-axis.

___ is the sum of money at simple interest that amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years.

Find the LCM and HCF of the following integers by applying the prime factorization method : 8, 9 and 25

Two angles whose arms are perpendicular are either_____or_____.

Which of the following points lie on the negative side of x-axis?

The product of infinite terms in $x^{\frac{1}{2}}.x^{\frac{1}{4}}.x^{\frac{1}{8}}...........\infty$ is

If $A$ is a proper subset of $B$, then $n\left(A\right)$$n\left(B\right)$.

Water is flowing continuously from a tap having a bore of internal diameter
8 $\times$ ${10}^{-3}$ m. Calculate the diameter of the water stream at a distance 2 $\times$ ${10}^{-1}$ m below the tap. Assume that water velocity as it leaves the tap is 4 $\times$ ${10}^{-1}$ m/s

Question 4.2
Fill in the blank to make the following statements true:

- 53 + = - 53

Factorise:
$21x^2+5x-6$

An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.

In the given figure, $\frac{QR}{QS}=\frac{QT}{PR}and$ $\angle 1=\angle 2$. Which of the following is true?

Construct a square of side 4cm.

Question 14(iv)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$


Are the median distance calculated in (ii) and (iii) same?

Let a, b, c be the sides of a triangle, no two of them are equal and $\lambda \in R$. If the roots of the equation $x^2+2(a+b+c)x+3\lambda$( ab + bc +ca ) = 0 are real, then

Determine the length of a chord which is at a distance of 6 cm from the centre of a circle of radius 10 cm.

In the given figure, AB is a diameter of a circle with centre O and DO||CB.

If $\angle BCD={120}^{\circ },$ calculate

(i) $\angle$BAD, (ii) $\angle$ABD,

(iii) $\angle$CBD, (iv) $\angle$ADC.

Also, show that $△$AOD is an equilateral triangle.

Which graph correctly shows the positions of points (3, 5), (1, −3), (−4, 0), and (−2, −5)?

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points, without finding the centre of the circle. Justify the construction.

Factorise:
$27a^2-48b^2$

A motor boat has a speed of 18 $\frac{km}{hr}$ in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in $km/hr.$

The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____.

The number of diagonals that can be drawn in a nonagon.

A quadrilateral can be divided into two congruent triangles. If the opposite sides are non-parallel, the quadrilateral is called ___.

Find the value of ${(\frac{1}{2a}+\frac{3}{4b})}^2$

If a + b = 5 and a - b = 1 find the value of a² + b²/2ab