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The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the following figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of Δ PQR if C is the origin?

Also calculate the areas of the triangles in these cases. What do you observe?

In an envelope there are some $5$ rupee notes and some $10$ rupee notes. Total amount of these notes together is $350$ rupees. Number of $5$ rupee notes are greater by $10$ than number of $10$ rupee notes. Then find the number of $5$ rupee and $10$ rupee notes.

In quadrilateral ABCD; angle D = ${90}^o$, BC = 38 cm and DC = 25 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 27 cm. Finthe the radius of the circle.

If a and b are the roots of the equation, $x^2$ – 6x + 1 = 0, then the value of $a^2$ + $b^2$ is​ __

Mass of two spheres is in the ratio 8:1. Assuming that both of them have the same density, find the ratio of their radii.

Question 106(iv)

The food table is given below information about 2 types of soup cream of tomato and sweet corn. Use these lables to answer the given questions. (all the serving are based on a 2000 calories diet.)

Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.

Classify the following numbers as rational or irrational:

$\left(i\right)\frac{22}{7}\left(ii\right)3.1416\left(iii\right)\pi \left(iv\right)3.\overline{142857}\left(v\right)\mathrm{5.636363...}\left(vi\right)\mathrm{2.040040004...}\left(viii\right)\mathrm{1.535335333....}\left(viii\right)\mathrm{3.121221222...}\left(ix\right)\sqrt{21}\left(x\right)\sqrt[3]{33}$

Solve the following quadratic equation by factorization.
$3x^2-14x-5=0$

Find and correct the errors in the statement: (z + 5)²
= z² + 25

Statements:
Some tests are exams.
No test is a question.
All questions are solutions.
Conclusions:
I. No question is an exam.
II. Some exams are tests.

Mr. Darshit purchases a bicycle for Rs 2298.24 which includes two successive discounts of 20% and 5% respectively on the marked price and then 8% sale tax on the remaining price. Find the marked price of the bicycle.

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing one mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

If the mean of $x$ and $\frac{1}{x}$ is M, the mean of $x^3$ and $\frac{1}{x^3}$ is _____.

If $\mu$ is the mean of a distribution, then $\sum f_i(y_i-\mu )$ is equal to

Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one tap takes 5 mintues more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

If $\sin \theta =\cos \theta$, $0⩽\theta ⩽{90}^{\circ }$
$\left(a\right){30}^{\circ }$
$\left(b\right){45}^{\circ }$
$\left(c\right){60}^{\circ }$
$\left(d\right){90}^{\circ }$

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 42 cm, find the area in $c{m}^2$ between the two consecutive ribs of the umbrella.

1. 140

A test paper contains 100 true - false questions. The number of questions with answer "true" was 59. Find the probability that a question’s answer is "false".

Plot the points A (1, 1), B (4, 7) and C (4, 10) on a graph paper. Connect A and B, and also A and C.

Which segment appears to have the steeper slope, AB or AC?

Justify your conclusion by calculating the slopes of AB and AC.

In the given figure, AB // EF // DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.
(i) Name the three pairs of similar triangles.
(ii) Find the lengths of EC and EF.

The observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of top of the chimney from her eyes is 45°. What is the height of the chimney?

In the given figure, PA and PB are two tangents drawn from an external point P. If $\angle APB={40}^{\circ }$, then $\angle PAB=$

Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

$\text{In the figure given below, point D divides}\text{AB in the ratio 3 : 5 and DE is parallel to}\text{BC. If AE = 4.8 cm, then find the}\text{length of AC(in cm).}$

1. 12.8