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The total perimeter of a quadrilateral ABCD is 18 cm. The opposite sides are equal and parallel. The adjacent sides are 1 cm more than the other. One of the angles of the quadrilateral ABCD measures 60°. Construct the quadrilateral ABCD.

For the given histogram data set, what is the width of the bar graph? Given that 1kg is 2 units in the x axis.

$$\begin{array}{cccccc}Weights\left(Kg\right)& 40-45& 45-50& 50-55& 55-60& 60-65\\ No.ofPerson& 4& 12& 13& 6& 5\end{array}$$

There is a continuous growth in population of a village at the rate of $5\%$ per annum. If its present population is 9261, what it was 3 years ago?

Question 81 (ii)

Add :

$9ax+3by-cz,-5by+ax+3cz$

Factorise:
$16x^2-24x+9$

10.20$\%$ of Rs. 800 ? (a) Rs. 160 (b) Rs. 16 (c) Rs. 1600 (d) none of these

Find the value of ‘m‘ if $(-2{)}^2\times (-5{)}^3=50m$.

In the figure, the perimeter of the rhombuses NUTS and ARCH are 20 m and 28 m respectively. If the width of each isosceles trapezium is 11 m, then find the area of the shaded region.

PQ is a straight line. What is the value of y?

By following these steps of construction,

(i) Draw a line segment PQ = 11 cm

(ii) At P construct an angle of 60^o and at Q, an angle of 45^o.

(iii) Bisect these angles. Let the bisectors of these angles intersect at a point A.

(iv) Draw perpendicular bisectors DE of AP to intersect PQ at B and FG of AQ to intersect PQ at C.

(v). Join AB and AC. Triangle ABC has been obtained. In this ∆ABC,

Two equal chords AB and CD of a circle are such that the length of perpendicular OE on CD = 5 cm. If OF is the perpendicular on AB, then OF =

123 + 231 + 312 is divisible by:

Construct angle ABC = ${90}^{\circ }$. Draw BP, the bisector of angle ABC. State the measure of angle PBC.

A fan is listed at ₹1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to ₹1104 ?

In the given figure, ABCD is parallelogram.If $\angle A={75}^{\circ }$, then $\angle B$ is

Expand:
$(x+3)(x+5)(x+2)$

Find the HCF of $(x-2{)}^2$, $x^2-4$ and $x^2+x-6$.

There is a chessboard whose area is 576 square units. What is the length of the side of an individual check box?

A triangle can be drawn if two sides and $\_\_\_\_\_$ angle are given.

What is the value of (3³)³

If Sandy spent ₹ 400 on fencing and ₹ 500 on ploughing the land he had earlier (ABCD), find the cost of fencing per unit and cost of ploughing per square unit respectively.

Evaluate :

(i) $(2x-\frac{3}{5})(2x+\frac{3}{5})$

(ii) $(\frac{4}{7}a+\frac{3}{4}b)(\frac{4}{7}a-\frac{3}{4}b)$

(iii) $(6-5xy)(6+5xy)$

(iv) $(2a+\frac{1}{2a})(2a-\frac{1}{2a})$

(v) $(4x^2-5y^2)(4x^2+5y^2)$

(vi) $(1.6x+0.7y)(1.6x-0.7y)$

(vii) $(m+3)(m-3)(m^2+9)$

(viii) $(3x+4y)(3x-4y)(9x^2+16y^2)$

(ix) $(a+bc)(a-bc)(a^2+b^2{c}^2)$

(x) $203\times 197$

(xi) $20.8\times 19.2$

Question 9 (ii)
Solve the following pairs of equation
$\frac{x}{3}+\frac{y}{4}=4\frac{5x}{6}-\frac{y}{8}=4$

Question 9 (i)
Classify $\sqrt{23}$ as rational or irrational.

Tick $\left(✓\right)$ the correct answer in each of the following:
The sum of $(6a+4b-c+3),(2b-3c+4,(11b-7a+2c-1\left)\right)$ and $(2c-5a-6)$ is

(a) $(4a-6b+2)$
(b) $(-3a+14b-3c+2)$
(c) $(-6a+17)$
(d) $(-6a+6b+c-4)$

Solve the following equations and verify your answer :

$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$

In the given figure, $\angle BCA=\angle RPQ={15}^{\circ }$. Then $\angle PQR$ is

Question 62

In a pie chart, two central angles can be ${180}^{\circ }$.

For point symmetry, which of the options hold true?

If the sum of the two angles of a quadrilateral is ${180}^{\circ },$ What is the sum of the remaining two angles?

A cube A has side thrice as long as that of cube B ? What is the ratio of the volume of cube A to that of cube B?

Toshiba bought 100 hens for Rs. 8000 and sold 20 of these at a gain of $5\%$. At what gain percent she must sell the remaining hens so as to gain $20\%$ on the whole?

Question 112

Solve the following

On dividing Rs. 200 between A and B, such that twice of A's share is less than 3 times B's share by 200, what is B's share?

What is a regular polygon? State the name of a regular polygon of:
(i) 3 sides (ii) 4 sides (iii) 6 sides

In the given figure, AE and BC are equal and parallel. If the sides AB, CD and DE are equal and $\angle$BAE = 100°, then $\angle$AED is equal to

The pillars of an apartment are in a cylindrical shape. If each pillar has a circular base of radius 40 cm and height 20 m, then how much concrete would be required to build 7 such pillars?

Tina noticed juicy oranges in a shop and asked the shopkeeper for the price. He said each costs Rs x. She bought 3 of them. The coefficient of x is ___ after calculating the total amount spent by Rina and Tina if Rina had already spent Rs(6x + 4y).

Why does the sum of angle of triangle is 180^o and quadrilateral is 360^o

The reflection of point (-7, -9) through the origin gives us___

Look at the figure below:

To draw a line parallel to l through A, the first step will be:

Find the point on Cartesian plane where the line 5x - y = 10 intersect the x - axis.

A jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a marble from this jar is taken out randomly then the probability of getting a red marble is :