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How many diagonals are present in the given polygon?

From isosceles triangles are shown below. One angle of each is given. Find the other two angles of each.

The smallest number among $-\frac{2}{3}$,$-\frac{9}{6}$,$-\frac{5}{2}$ and $-\frac{3}{4}$ is .

There is a pathway around a rectangular building of length 50 m and breadth 45 m. The width of the pathway is 5 m. So the area of the pathway in sq m is:

At a constant temperature, the product PV of a given amount of gas is constant. This is:

To factorise $3y^2-y-4$, the coefficient of $y$ should be split into $a$ and $b$ such that

The accommodation in an apartment costs ₹ 42 lakh. After 6 months, there was a 10% price hike, the new cost is:

Solve:

$\frac{1}{18}+\frac{1}{18}$

Given a
parallelogram ABCD. Complete each statement along with the definition
or property used.

(i) AD = …

(ii) ∠DCB = …

(iii) OC = …

(iv) m∠DAB + m∠CDA
= …

Factorise each of the following:

$27–125a^3–135a+225a^2$ [3 MARKS]

Resolve into factors:

(i) (ii) ; (iii) ; (iv) .

Rational numbers are not closed under ________

Question 124

A hall has a capacity of 2704 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row.

Parallelogram with diagonals 6 centimetres and 7 centimetres; angle between them 70°.

Time intervals measured by a clock give the following readings : 1.25 s, 1. 24 s, 1.27 s, 1.21 s, 1.28 s What is the percentage relative error of the observation?

Construct a triangle XYZ in which XY = 7.8 cm, YZ = 4.5 cm and XZ = 9.5 cm.

What is rearrangement property ?

Question 8

Refer to Question 7, draw the frequency polygon representing the above data without drawing the histogram.

If $A,B,C$ are the vertices of a triangle whose position vectors are $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ and $G$ is the centroid of the $\Delta ABC,$ then $\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}$ is equal to

The greatest common divisor of x²-x-2, x²+x-6, 3x²-13x+14 is

State
whether True or False.

(a) All
rectangles are squares.

(b) All
rhombuses are parallelograms.

(c) All
squares are rhombuses and also rectangles.

(d) All
squares are not parallelograms.

(e) All
kites are rhombuses.

(f) All
rhombuses are kites.

(g) All
parallelograms are trapeziums.

(h) All
squares are trapeziums.

If two angles are supplementary, then their sum is _____.

In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $\angle DBC={55}^{\circ }$ and $\angle BAC={45}^{\circ }$, then $\angle BCD$ = ___ .

Factorise the following:

The perimeter and length of a rectangular hideout is given. The width of the hideout is ft.

There is a box which contains 4 red, 3 blue and 1 black identical balls. For each red ball withdrawn (without replacement), you have to put 1 blue and 1 black ball in the bag. For each blue ball withdrawn (without replacement), you have to put 2 blue and 1 red ball. If the first ball drawn is red, what will be the contents of the box just before withdrawing the second ball?

Shalini deposited ₹4,00,000 in a bank where she was promised an interest of 10%. She deposited it for a period of two years. Find the difference in the amount if the interest is calculated in a compounded manner to the amount interested in a simple manner.