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The letter "S" on a billboard is being painted. If the letter is drawn using circles as shown, find the area to be painted. (Radius of the inner circles = 3 ft;

Radius of the outer circles = 5 ft)

The Mean and Standard Deviation of the heights and weights of 20 persons are given below

In which characteristics are they more variables?

The sum of four consecutive numbers in an A.P. with common difference $d>0$ is 20. If the sum of their squares is 120, then the middle terms are __ and __.

Cuboids can be formed by stacking ___ .

The zeroes of the polynomial $x^2-x-12$ are ___, ____.

If three numbers are consecutive positive integers and 5 times the square of the largest number is greater than 2 times the sum of the squares of other two numbers by 75 , then find the sum of the largest and the smallest of these numbers.

Find the mean of the step deviations:

$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

Two AP's have the same common difference. The first term of one of these is -1 and that of the other is -8 then the difference between their 4th term is

The roots of the equation $x^2+2x–15=0$ are

The following is the trial balance of Mr. Deepak as on March 31, 2011. You are required to prepare Trading and Profit and Loss account and a Balance sheet as on date
$\begin{array}{cccc}\text{Account Title}& \text{Amt. (Rs.)}& \text{Account Title}& \text{Amt. (Rs.)}\\ \text{Drawings}& 36,000& \text{Capital}& 2,50,000\\ \text{Insurance}& 3,000& \text{Bills Payable}& 3,600\\ \text{General Expenses}& 29,000& \text{Creditors}& 50,000\\ \text{Rent and Taxes}& 14,400& \text{Discount Received}& 10,400\\ \text{Lighting (Factory)}& 2,800& \text{Purchase Return}& 8,000\\ \text{Travelling Expenses}& 7,400& \text{Sales}& 4,40,000\\ \text{Cash in Hand}& 12,600& & \\ \text{Bills Receivable}& 5,000& & \\ \text{Sunday Debtors}& 1,04,000& & \\ \text{Furniture}& 16,000& & \\ \text{Plant and Machinery}& 1,80,000& & \\ \text{Opening Stock}& 40,000& & \\ \text{Purchase}& 1,60,000& & \\ \text{Sales Return}& 6,000& & \\ \text{Carriage Inwards}& 7,200& & \\ \text{Carriage Outwards}& 1,600& & \\ \text{Wages}& 84,000& & \\ \text{Salaries}& 53,000& & \end{array}$
Closing Stock Rs. 35,000.

Show that the sum of an AP whose first term is a ,the second term is b and the last term is c, is equal to (a+c)(b+c-2a)/2(b-a)

If 3 cot A = 4, Check whether

Prove that the line joining the points (2, 1) and (1, 2) and the line joining the points (3, 5) and (4, 7) are not parallel. What are the coordinates of their point of intersection?

which of the following pairs of lines in a circle cannot be parallel ?

(a) Two chords (b) A chord and a tangent

(c) Two tangents (d) Two diameters

Rohit can row downstream 32 km in 4 hours and 4km upstream in an hour. Find his speed of rowing in still water and speed of the current.

The height of a tree is $\sqrt{3}$ times the length of its shadow. Find the angle of elevation of the sun. [1 MARK]

If AD, BE and CF are the medians of an equilateral triangle ABC, then which of the following statements is true?

Question 3 (ii)

Are the following pair of linear equations consistent? Justify your answer.

$\frac{3}{5}x-y=\frac{1}{2}and\frac{1}{5}x-3y=\frac{1}{6}$

Check whether 14ⁿ can end with the digit zero...for any real integer n

If three coins are tossed simultaneously, then the probability of getting at least one head and tail is _____.