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Question 3
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC=BD. Prove that PQRS is a rhombus.

Thinking Process

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Check which of the following are solutions of the equation $2x-y=6$ and which are not: (i) $(3,0)$ (ii) $(0,6)$ (iii) $(2,-2)$ (iv) $(\sqrt{3},0)$ (v) $(\frac{1}{2},-5)$

The sum of the two angles in a triangle is ${95}^{\circ }$ and their difference is ${25}^{\circ }$. Then which of the following are true?

In the figure, AB = AC and DB = DC, find the ratio $\angle ABD:\angle ACD.$

Factorize:

$7(x-2y{)}^2-25(x-2y)+12$

For the triangle below, which option correctly gives an arrangement of its sides in ascending order of their lengths?

If (x-a) is factor of $x^3+ax+a+1$. Which of the following is true?

Now in each of the following, find the quotient and remainder on dividing p(x) by q(x) and write then in the form p(x) = u(x) q(x) + v(x).

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Question 5

Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer

The perimeter of a triangular field is 540 m, and its sides are in the ratio 25:17:12. Find the area of the field. Also, find the cost of ploughing the field at Rs. 40 per 100 $m^2$.

In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.

What could be the measure of $x$ and $y$ if ABCD is a parallelogram?

Question 67

For all rational numbers x and y, $x\times y=y\times x$

If the sum of all the edges of a cube is 36 cm, then the volume $\left(inc{m}^3\right)$ of that cube is

Q39. Meghana and Bobbby are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meghana finishes ahead of Bobbby?

If a line intersects sides AB and AC of a $△ABC$ at D and E respectively and is parallel to BC, then $\frac{AD}{AB}$ = $\frac{AE}{x}$ Then $x$ is

Question 2 (iv)

Find : ${125}^{\frac{-1}{3}}$

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

So I can't get the sum solved by you in which is in the horizontal step linear equation but our school teachers have given me horizontal step

Find the sum of the deviations of the variate values 3,4,6,7,8,14 from their mean.

Factorise:
$9-a^2+2ab-b^2$

In a year, Seema earns Rs 1, 50, 000 and saves Rs 50, 000. Find the
ratio of

(a) Money
that Seema earns to the money she saves.

(b) Money
that she saves to the money she spends.

Question 38

State whether the given statement is True or False.

Two line segments may intersect at two points.

In the given figure, AP = AQ and the right angles are shown. Which of the following statements can certainly be stated?

In a ||gm ABCD, if $\angle A=(2x+25{)}^{\circ }$ and $\angle B=(3x-5{)}^{\circ }$, find the value of x and the measure of each angle of the parallelogram.