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Find the ${10}^{th}$ term from the end of the A. P. 4,9,14,........... , 254.

Edward opened a Recurring deposit account in a bank. He deposited ₹300 per month for 2 years. At the time of maturity he received ₹7725. What was the rate of interest?

The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Cards each marked with one of the numbers 4, 5, 6 ...20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. The probability of getting an even prime number is

Set up equations and solve them to find the unknown numbers in the
following cases:

(a) Add 4 to eight times a number; you get 60.

(b) One-fifth of a number minus 4 gives 3.

(c) If I take three-fourths of a number and add 3 to it, I get 21.

(d) When I subtracted 11 from twice a number, the result was 15.

(e) Munna subtracts thrice the number of notebooks he has from 50, he
finds the result to be 8.

(f) Ibenhal thinks of a number. If she adds 19 to it and divides the
sum by 5, she will get 8.

(g) Anwar thinks of a number. If he takes away 7 from
of
the number, the result is 23.

The value of $tan\theta \times cosec\theta \times cot\theta$ is

Refer to the following figure. Three squares are constructed on each side of the triangle as shown, with the length of each square equal to the side on which it is constructed. If the largest side is 13, sum of the areas of the three squares is___. [The angle opposite to the blue colour square is the right angle.]

Calculate the mean deviation about median for the following data

$\begin{array}{cccccc}{X}_i& 3& 9& 10& 12& 13\\ f_i& 3& 4& 5& 2& 4\end{array}$

The equation of a line which is parallel to line 2x = 3y - 4 and meets the y-axis at (0, 4) is .

Find the coordinates of the point on x-axis which is equidistant from the points (-2, 5) and (2, -3).

Identify the point which is invariant under reflection in x-axis.

A random survey of the number of children of various age groups playing in park was found as follows:



$\begin{array}{cc}\text{Age (in years)}& \text{Number of children}\\ 1-2& 5\\ 2-3& 3\\ 3-5& 6\\ 5-7& 12\\ 7-10& 9\\ 10-15& 10\\ 15-17& 4\end{array}$



Draw a histogram to represent the data above.

All the arcs in the following diagram are semicircles. The diagram shows two paths connecting A to B. Path I is the single large semi-circle and Path II consists of the chain of small semicircles.

The weight of 50 workers is given below:

$\begin{array}{cccccccc}Weightinkg& 50-60& 60-70& 70-80& 80-90& 90-100& 100-110& 110-120\\ Numberofworkers& 4& 7& 11& 14& 6& 5& 3\end{array}$

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the upper and lower quartiles.

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted

and the following data was obtained:

$$\begin{array}{cc}& \\ \text{Height in cm}& \text{Number of Girls}\\ \text{Less than 140}& 4\\ \text{Less than 145}& 11\\ \text{Less than 150}& 29\\ \text{Less than 155}& 40\\ \text{Less than 160}& 46\\ \text{Less than 165}& 51\end{array}$$

Find the median height.

In the given figure, $AD=BC$ and $DEC$ is an arc of the circle, centre of which is $O$ such that $\angle DOC={90}^{\circ }$. If $AB=20\sqrt{2}\text{cm}$ and the perpendicular distance of $AB$ from centre $O$ is $25\sqrt{2}\text{cm}$, then area of the shaded region is

Find the greatest number that will divide 445 572 and 669 leaving remainders 4 5 and 6 respectively

Find the ratio of the areas of two similar triangles $\Delta ABC$ and $\Delta PQR$ shown in the figure.

A man on the top of a tower, standing on the sea shore, finds a boat coming towards him takes 10 minutes for the angle of depression to change from ${30}^{\circ }$ to ${60}^{\circ }$. How soon will the boat reach the sea-shore?

In an A.P., first term is 1, last term is 11 and sum of n terms is 36, then n =

Define an elementary event.

The number of $3\times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$ has exactly two distinct solutions, is

The following table gives the GDP in Rupees (Crores) by the three sectors:

(i) Calculate the share of the three sectors in GDP for 1950 and 2000.

(ii) Show the data as a bar diagram similar to Graph 2 in the chapter.

(iii) What conclusions can we draw from the bar graph?

If $x=r\sin \alpha \cos \beta ,y=r\sin \alpha \sin \beta \text{and}z=r\cos \alpha ,$ then