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For the following AP's, write the first term and the common difference.
(i) -5, -1, 3, 7....
(ii) $\frac{1}{3}$,$\frac{5}{3}$,$\frac{9}{3}$,$\frac{13}{3}$,…
(iii) 0.6, 1.7, 2.8, 3.9,…

Trigonometric 3 ideidentit

In $\Delta ABC,\angle A={60}^{\circ },BC=10cm.$ Find the circumdiameter of the triangle. $[sin{60}^{\circ }=0.87]$

Find the radius of the incircle of $△ABC\text{if}BC\perp AQ$

Find the sum of the roots of the equation $-3x^2+9x-3=0$.

Question 115

A school playground is divided by a 2 m wide path, which is parallel to the width of the playground and a 3 m wide path which is parallel to the length of the ground as given in the figure below. If the length and width of the playground are 120 m and 80 m respectively, find the area of the remaining playground.

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.

For terms $a^2{b}^2,a^3{b}^3$ and $a^3{b}^2$, $a^3{b}^3$ is known as ___

Solve the following systems of equation graphically:

x+ y = 3

2x + 5y = 12

Five liters of 31.2% acid solution has to be made out of a 40% and a 18% acid solution. How many litres of each of the 40% and 18% solution need to be mixed?

If the equation $x^2+2(k+2)x+9k=0$ has real equal roots, then values of $k$ are

Show that (x+3) is a factor of p(x) =69+11x-x²+x³.

Jax buys Jane a toy that costs ₹ 10. Which of the given notes will he use?

Divide 27 into two parts such that the sum of their reciprocals is $\frac{3}{20}$.

A shopkeeper buys a table listed at Rs. 2,500 and gets successive discounts of $20\%$ and $10\%$. He spends Rs.60 on transportation and sells it at a profit of $20\%$. Find selling price of the table.

The order of the matrix A is 3 $\times$ 5 and that of B is 2 $\times$ 3. The order of the matrix BA is

Find the L.C.M. of the following expressions by division method.

m⁴ + 3m³ − m − 3 and m³ + m² − 5m + 3

Insert five arithmetic means between 20 and 32.

Select the linear equations in one variable.

Draw a plan and calculate the area of a level ground using the information given below.

Which value of $p$ gives the solution $x=-14$ and $y=5$ for the linear equation $4y-x=2p$?

Square tiles of equal dimensions are to be laid in a lavish bathroom of size 90 inch ×126 inch . What should be the minimum dimension of a tile so that it covers the floor perfectly? How many such tiles are required?

In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.

Sam's mother takes a morning stroll every day. She walks an average of $1.5$ kilometers every day. How many miles does she walk in a day on average?

An athletic track 14 m wide consists of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Calculate the area of the track.

Out of the following which is a skew- symmetric matrix

If ratio of the sum of first n terms of two A.P is 7n+1:4n+27,then find the ratio of their 9th terms.

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The element of second row and third column in the inverse of $\begin{array}{c}\left[\begin{array}{ccc}1& 2& 1\\ 2& 1& 0\\ -1& 0& 1\end{array}\right]\end{array}$ is