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State whether the following quadrilaterals are similar or not:

A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.

If x=-⅓ is a zero of the polynomial p(x)=27x³-ax²-x+3,then find the value of a

Find the value m if x = - 4 is a zero of quadratic equation $4x^2–mx+5=0$.
[2 MARKS]

$\frac{\text{sin}\theta \text{cos}({90}^{\circ }-\theta )\text{cos}\theta }{\text{sin}({90}^{\circ }-\theta )}+\frac{\text{cos}\theta \text{sin}({90}^{\circ }-\theta )\text{sin}\theta }{\text{cos}({90}^{\circ }-\theta )}=$ ___

Find the angular elevation of the sun when a 10m long pole casts a shadow of length $10\sqrt{3}$ m on the ground.

$2.2d{m}^3$ of brass is to be drawn into a cylindrical wire of diameter $0.50cm$. Find the length of the wire.

In a year Raju gave the examination of maths 11 times and the number of marks obtained are listed below in the form of table in each of his examination

Which of the following has sum of its zeroes as zero?

If $9^{th}$ term of an AP is 15 and the common difference is 2, then the first term of the AP is

Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circumradius. [3 MARKS]

A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?

Find the distance between the points (0, 0), (a, b). [1 MARK]

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. [1 MARK]

In a²x² + ax, if 'a' is constant and 'x' a variable, this expression would become a polynomial in __ variable(s).

A group of 48 workers can complete a piece of work in 11 days. But 48 workers worked on first day, 44 workers worked on second day, 40 workers worked on third day and so on. Unfortunately, on the 10th day, they had to restart the entire work . Then, find the time taken by the remaining workers to complete the entire work.

The value of the constant $‘m^{\prime }$ is ___ if $y=–1$ is a root of the quadratic equation$7+4(m+2)y–y^2=0.$

The angle of elevation of an aeroplane from a point on the ground is ${45}^{\circ }$. After a flight of 15 seconds, the angle of elevation changes to ${30}^{\circ }$. If the aeroplane is flying at a height of 3000 m, then find the speed of the plane.

$(\text{Take}\sqrt{3}=1.732)$

Question 7
Find the point on the x-axis which is equidistant from (2, - 5) and (- 2, 9).

Which of the following is an example of an arithmetic progression?

Question 3
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

$\begin{array}{cc}\text{Expenditure (in Rs)}& \text{Number of families}\\ 1000-1500& 24\\ 1500-2000& 40\\ 2000-2500& 33\\ 2500-3000& 28\\ 3000-3500& 30\\ 3500-4000& 22\\ 4000-4500& 16\\ 4500-5000& 7\end{array}$

Three chairs and two tables cost Rs. 1850. Five chairs and three tables cost Rs. 2850. Then find the total cost of one chair and one table. [3 MARKS]

Shanti and Satya were partners in a firm sharing profits in the ratio of 4 :1. On 31st March, 2013 their Balance Sheet was as follows:

Balance Sheet of Shanti and Satya
as at 31st March, 2013

$\begin{array}{cccc}\text{Capital and Liabilities}& \text{Amount (Rs.)}& \text{Assets}& \text{Amount (Rs.)}\\ \text{Creditors}& 45,000& \text{Bank}& 55,000\\ \text{Workmen's Compensation Fund}& 40,000& \text{Debtors}& 60,000\\ \text{Satya's Current Account}& 65,000& \text{Stock}& \text{85,000}\\ \text{Capitals:}& & \text{Furniture}& 1,00,000\\ \text{Shanti}& 2,00,000& \text{Machinery}& 1,30,000\\ \text{Satya}& 1,00,000& \text{Shanti's Current Account}& 20,000\\ & \underset{–}{\overline{4,50,000}}& & \underset{–}{\overline{4,50,000}}\end{array}$

On the above date the firm was dissolved:

(1) Shanti took over 40% of the stock at 10% less than its than its book value and the remaining stock was sold for Rs. 40,000. Furniture realized Rs. 80,000.

(2) An unrecorded investment was sold for Rs. 20,000. Machinery was sold at a loss of Rs. 60,000.

(3) Debtors realized Rs. 55,000

(4) There was an outstanding bill for repairs for which Rs. 19,000 were paid.

Prepare Realisation Account.

Construct a cyclic quadrilateral ABCD in which AB = 8cm, AC = 9 cm, BC = 7 cm, and AD = 5.4 cm.

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

A pole has a height of 45 m and casts a shadow of x m. If a flag of 10 m is kept on the pole, the shadow of the arrangement will be 15 m in length. Find the value of x.

In a two digit number, the ten's digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.

If $tan\theta +sin\theta =m$ and $tan\theta -sin\theta =n,$ then $\frac{(m^2-n^2{)}^2}{mn}=$___.

The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c{m}^2$).

Rohit borrowed Rs. 625 from his friend Shyam. After 146 days, Rohit repaid a sum of Rs. 641.25. Find the rate of interest Shyam charged Rohit.

Solve the following inequation:

2 – 5 < 5 + 4 < 11; ε I

The average marks of the students in Mathematics of class $8^{th}$ is 45. But most of the students were given 60 out of 100.The Median of the class would be:

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, Bc = 8 cm and AC = 10 cm, find the lengths fo AD, BE and CF.

Solve the following systems of equations:

$\frac{1}{5x}+\frac{1}{6y}=12$

$\frac{1}{3x}-\frac{3}{7y}=8$

A man is employed to count Rs. 10710. He counts at the rate of Rs. 180 per minute for half an hour. After this he counts at the rate of Rs.3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Solve the following:
(a) The locus of a point whose x coordinate is always 7 is the equation.
(b) Show that the point (3,1) does not lie on the line 3x + 4y = 16. [4 MARKS]

A die is thrown once. The probability of getting a prime number is
(a) $\frac{2}{3}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{1}{6}$

The largest number which divides 70 and 125 leaving remainders 5 and 8, respectively is

Ashwarya bought 496, Rs 100 shares at Rs 132 each. Find :

(i) an investment made by her.

(ii) income of Ashwarya from these shares, if the rate of dividend is 7.5%.

(iii) how much extra must Aishwarya invest in order to increase her income by Rs 7,200?

The product of first two terms of an arithmetic sequence with common difference 6 is 135. Then the first term is

In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of the inscribed circle and the area of the shaded region.

[Use $\sqrt{3}=1.73and\pi =3.14$]