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Consider two triangular parks ABC and EFG such that a path from one corner of the park bisects the other side of the park as shown in the figure. If the dimensions of the park ABC are AB = 4 m, BC = 6 m and AC = 3 m and that of park EFG are EF = 2 m, EG = 3 m and FG = 1.5 m.

Then, which of the following is true?

If centroid of the triangle formed by the points $(0,-2),(2,-y)$ and $(1,4)$ is same as the centroid of the triangle formed by the points $(1,0),(x,-3)$ and $(3,1)$, then centroid of the triangle formed by the points $(x,y),(2x-1,-y)$ and $(-x,1-y)$ is

Three
tankers contain 403 litres, 434 litres and 465 litres of diesel
respectively. Find the maximum capacity of a container that can
measure the diesel of the three containers exact number of times.

The monthly household incomes of 8 families are given as:

{45000, 50000, 75000, 60000, 48000, 54000, 68000 and 150000}

Find the average income. Does the mean income give a fair idea of the average household income?

1. If log 2, log (2^x-1) and log (2^x+3) are in AP then find the value of x.

If $x=acosec\theta$ and $y=bcot\theta$, then which of the following equations is true ?

The sum of four consecutive numbers in A.P. is $32$ and the ratio of the product of the first and last terms to the product of two middle terms is $7:15$ . Find the number .

A man invests some money partly in $9\%$ stock at 96 and partly in $12\%$ stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:

How to solve a linear equation

In fig., CP and CQ are tangents from an external point C to a circle with center O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4 cm, find the length of BC

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

In the given figure, DE || BC. If AD = 6 cm, AB = 24 cm and DE = 5 cm, then BC = ____ cm.

Three consecutive natural numbers are added and their sum is divided by 3. What is the remainder obtained?

If two chords AB and CD intersect internally at P and if PA = 5, PB = 4, PD = 2, then PC =

What will be the first class interval, if the fifth class interval is $60-65$, the fourth class interval is $55-60$ and the total number of classes is limited to five.

1 + $ta{n}^{2}A$ = $se{c}^{2}A$ is valid for which of the following ranges

Prove that x + 1 is a factor of xⁿ − 1 for every odd number n.

The table given below shows the weekly expenditures on food of some households in a locality.

$\begin{array}{cc}Weeklyexpenditure(inRs.)& Numberofhouseholds\\ 100-200& 5\\ 200-300& 6\\ 300-400& 11\\ 400-500& 13\\ 500-600& 5\\ 600-700& 4\\ 700-800& 3\\ 800-900& 2\end{array}$

Draw a 'less than type ogive' and a 'more than type ogive' for this distribution.

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. [4 MARKS]

Question 10
Prove that $\sqrt{3}+\sqrt{5}$ is irrational.

Which of the following list of numbers forms an AP?

(i) 4, 4 + $\sqrt{3}$ , 4 + 2$\sqrt{3}$, 4 + 3$\sqrt{3}$, 4 + 4$\sqrt{3}$



(ii) 0.3, 0.33, 0.333, 0.3333, 0.33333



(iii) $\frac{3}{5}$, $\frac{6}{5}$ , $\frac{9}{5}$ , $\frac{12}{5}$ , 3



(iv) -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$

Solution

Maximum no. of terms in a linear polynomial is