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What is the length of an arc which subtends angle $\theta$ (degrees) at the centre in a circle of radius r?

A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the point B if AB and BC are parallel to the coordinate axes.

Evaluate $\int \frac{2x+3}{\sqrt{4x+3}}dx$ (where $C$ is integration constant)

Question 4(c)

Find using distributive property:

$824\times 25$

Question 5

In the following figure, DE||OQ and DF||OR, show that EF||QR.

If $(2x^2+3y^2):(2x^2-3y^2)=11:5$, find the value of $(5x^4+7y^4):(5x^4-7y^4)$.

From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

The value of $\left[\right(\frac{cosA}{cotA})+sinA]$ is:

ΔABC is right angles at B and D is any point on AB. DE is perpendicular to AC. If AD = 4 cm, AB = 16 cm, AC = 24 cm find AE.

Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

1. 0

Solve the quadratic equation $4x^2+12x+9=81$ by completion of squares method.

Which of the following represent the solution set of the given inequation?

$-x^2+2x+15>0;x\in \text{R}$

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. What is the outer surface area of the cylinder?

A staircase consists of 20 steps. The length and breadth of each step is 100 $m$ and $\frac{1}{2}m$ respectively. The height of the lowermost step is $\frac{1}{2}m$ and the height of the subsequent step increases by $\frac{1}{2}m$. Find the volume in $m^3$ of the concrete required to make the staircase.

In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]

The product of roots of the equation ${\left(ax\right)}^2$ + ax + c = 0 where a is the variable is

Match the following columns:

$\begin{array}{cccc}& \text{Column A}& & \text{Column B}\\ \left(i\right)& \text{Ambedkar established the Depressed Classes Association}& \left(A\right)& \text{December, 1929}\\ \left(ii\right)& \text{Gandhiji began the Civil Disobedience Movement}& \left(B\right)& \text{August, 1930}\\ \left(iii\right)& \text{Gandhiji ended the Civil Disobedience Movement}& \left(C\right)& \text{March, 1930}\\ \left(iv\right)& \text{Congress adopted the demand for 'Purna Swaraj'}& \left(D\right)& \text{March, 1931}\end{array}$

A closed cylindrical tank is made up to a sheet of metal. The height of the tank is 1.3 m and radius is 70 cm. How much sq. m of sheet metal was required?

Which of the following relation do not represent a function?

A triangle ABC with sides BC =7cm, $\angle B={45}^{\circ },\angle A={105}^{\circ }$ is given. The image of constructing a similar triangle of $\Delta ABC$ whose sides are $\frac{3}{4}$ times the corresponding sides of the $\Delta ABC$ is given below. Then $\frac{A^{\prime }{C}^{\prime }}{AC}$ is equal to :

The monthly pocket money of 50 students of a class are given in the following distribution:

$\begin{array}{ccccccc}Monthlypocketmoney(inRs.)& 0-50& 50-100& 100-150& 150-200& 200-250& 250-300\\ Numberofstudents& 2& 7& 8& 30& 12& 1\end{array}$

Find the modal class and also give class mark of the modal class.

Figure shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If $\angle AOB={90}^{\circ }$, calculate:

(i) The height of the tunnel
(ii) The perimeter of the cross-section
(iii) The area of the cross-section.

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If $p=2^a\times 3^b\times 5^c$ and $a>b>c$ are natural numbers, then what is the unit digit of p?

How do we draw aangle?