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What should be added to the quadratic polynomial x²-5x+4 so that 3 is a zero of the resulting polynomial ?

Find the standard deviation for the following data:

$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 6& 10& 14& 10& 10\end{array}$

In the adjoining figure O is the center of the circle. $\angle$AOD = ${120}^{\circ }$. If the radius of the circle be 'r', then find the sum of the areas of quadrilaterals AODP and OBQC:

1250 persons went to see a circus-show. Each adult paid Rs. 75 and each child paid Rs. 25 for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to Rs. 61,250.

An accurate clock shows $8$ o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows $2$ o'clock in the afternoon?

If the distance between the points P (x, 2) and Q (3, –­6) is 10 units, then x = _____.

If domain of $f\left(x\right)$ is $[0,1],$ then domain of $f\left(\right\{x{\}}^3+1),$ (where $\{.\}$ represents fractional part function) is

What term should be added to $a^2+2ab$ to make it a perfect square?

1. 256

What is the probability of not picking a face card when you draw a card at random from a pack of 52 cards?

On a square handkerchief, nine circular designs each of radius 7 cm are made (see the given figure). Find the area of the remaining portion of the handkerchief.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $\angle AOB=$ ___

The two geometric means between the numbers 1 and 64 are

Find the sum to $n$ terms of the AP:

5, 2, -1, -4, -7, ...

If $x\in (\pi ,\frac{3\pi }{2})$, then $\sqrt{\frac{1-\sin x}{1+\sin x}}$ is equal to

In the figure, given below, AD = BC,

$\angle BAC={30}^{\circ }$ and

$\angle CBD={70}^{\circ }$. Find: $\angle BCA$

A man 1.8 metres tall, looking down from the top of a telephone tower sees the top of a building 10 metres high at an angle of depression 40° and the foot of the building at an angle of depression 60°. What is the height of the tower? How far is it away from the building?

A man buys Rs. 20 shares paying $9\%$ dividend. The man wants to have an interest of $12\%$ on his money. The market value of each share is:

The point P which divides the line segment joining the point A (2, -5) and B (5, 2) in the lies in the ratio 2:3 quadrant.

Consider the following distribution of $S{O}_2$ concentration in the air (in ppm = parts per million) in 30 localities. We wish to find the mean SO₂ concentration using step assumed mean method. Fill the following table. Determine the assumed mean(a) and proceed.

$$\begin{array}{cccc}ClassInterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a\\ 0.00-0.04& 4& 0.02& -0.08\\ 0.04-0.08& 9& 0.06& A.........\\ 0.08-0.12& 9& 0.10& B........\\ 0.12-0.16& 2& 0.14& 0.04\\ 0.16-0.20& 4& 0.18& C........\\ 0.20-0.24& 2& 0.22& 0.12\\ Total& \sum f_i=30& & \end{array}$$

The value of A, B and C respectively are:

Each of the equal sides of an isosceles triangle is 25 cm. Find the length of its altitude if the base is 14 cm.

Solve each of the following systems of eqautions by the method of cross-multiplication:

ax+by=a-b

bx-ay=a+b

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.