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An equilateral triangle ABC is inscribed in a circle of radius 12 cm, which is centered at O, as shown below. Calculate the length of the sides of this triangle.

Given $\overrightarrow{A}=0.3\hat{i}+0.4\hat{j}+c\hat{k}$. Calculate the value of c if A is a unit vector.

Question 56

In which of the following figures,

a) Perpendicular bisector is shown?

b) Bisector is shown?

c) only bisector is shown?

d) Only perpendicular is shown?

$\text{In the given figure,}BAD||EF,\angle AEF={55}^{\circ }and\angle ACB={25}^{\circ },find\angle ABC.$

The three angles of a quadrilateral are ${54}^{\circ },{76}^{\circ }$ and ${108}^{\circ }$. Find the value of fourth angle.

. If a, b, c are three unit vectors such that $a\times (b\times c)=\frac{1}{2}$b then the angles between a, b and a, c are

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$? $[Assume\pi =\frac{22}{7}]$

Question 107

Metallic discs of radius 0.75 cm and thickness 0.2 cm are melted to obtain 508.68 $c{m}^3$ of metal. Find the number of disc melted. (Use $\pi =3.14$)

1. 9488

Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. [4 MARKS]

The sum of total surface area of a hemisphere of radius $r$ and the total surface area of a sphere of radius $\frac{r}{2}$ is

A, B, C, D are 4 non collinear points in a plane such that $\angle$ACB = $\angle$ADB, then how many circle(s) can be drawn passing through all 4 points?

The value of ${\left({\left(\frac{3}{2}\right)}^{-1}\right)}^{-2}$ is

In $\Delta PQR$, MN||QR and MN divides the triangle into two park of equal areas. $\frac{QM}{PQ}=??$

In the given figure, O is the centre of a circle. Then $\angle OAB=?$

(a) ${50}^{\circ }$

(b) ${60}^{\circ }$

(c) ${55}^{\circ }$

(d) ${65}^{\circ }$

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that

[Hint: From A and C, draw perpendiculars to BD]

Find the area of the shaded part in the figure given below. (Take $\pi$ = $\frac{22}{7}$)

(Note: All the dimensions are in cm.)

Can two intersecting lines be parallel to a common line?

A cubic polynomial whose zeroes are α, β and γ such that α + β + γ = 4, αβ + βγ + γα = 1 and αβγ = – 6 can be

Two points on the circumference of the circle result in the formation of two arcs. The arc of greater length is called __ arc.

If the point P(a, 2) is equidistant from the points A(8, -2) and B(2, -2), then a = ___

If equals are added to equals, the wholes ___.

ADC is a right angled isosceles $△$ with right angle at D. What should be the area of $△$ AFE?

1. 8

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

(i) Draw a bar graph to represent the polling results.

(ii) Which political party won the maximum number of seats?

In figure, the value of x is:

In the parallelogram given below, point $P$ is the mid point of side $DA$.Which among the following statement follows?

Question 42(ii)
At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the second player wins a prize if the first has won?

In the given figure, ΔABC is isosceles triangle with $AB=ACand\angle ABC={40}^{\circ }$. The difference of $\angle BDCand\angle BEC$ is equal to

If the three sides of a triangle are 11m, 15m and 6m.What is the semi perimeter of the triangle?