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In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. Calculate the sizes of :

(i) $\angle$ AOB,

(ii) $\angle$ ACB,

(iii) $\angle$ ABC.

If A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

The radius of the base of a circular cylinder is halved and height is doubled. Find the percentage change in the volume.

If (a^{​​​​​​2} + b^{​​​​​​2})³ = (a^{​​​​​​3} + b^{​​​​​​3})² then find the value of (a/b) + (b/a)

$\frac{cos{70}^{\circ }}{sin{20}^{\circ }}+\frac{cos{59}^{\circ }}{sin{31}^{\circ }}-8si{n}^2{30}^{\circ }=$

$x+\frac{1}{x}=3then{x}^6+\frac{1}{x^6}=$

What must be added to $3x^3+x^2$ - 22x + 9 so that the result is exactly divisible by $3x^2$ + 7x - 6 ?

A park, in shape of a quadrilateral ABCD has $\angle C={90}^0$, AB= 9m, BC= 12m, CD= 5m and AD = 8m. How much area does it occupy?

Question 110

Find the value of $\frac{(0.2\times 0.14)+(0.5\times 0.91)}{(0.1\times 0.2)}.$

If $n$ is a natural number, then $\sqrt{n}$ is

In the given figure, ABC is a triangle, right-angled at B. BCDE is a square on the side BC and ACFG is a square on AC. Then,

In the given figure, PR is a tangent to the unit circle. Find the length of tangent PR.

The sum of the coefficients of the polynomial p(x)=(3x-2^17(x+1)^4 is:

16

-1

10

Please explain.

If c and d are the midpoints of AB and AC respectively then prove that AD=1/4 AB.

Ram got a set square which is also similar to a triangle in which two vertices of the set square were marked as ${45}^0$ each. Find the third angle.

Choose the correct statements.

Draw an equilateral triangle of side 5 cm and its circumscribed circle. Find the length of the radius.

Among : √17- √12 and √11-√6 which is greater and how?

In the given $\Delta$ ABC, M and N are mid-points of AB and AC respectively. D is any point on the base BC. Which of the following relationships will always hold true?

What do you mean by the included angle/side of a triangle? What is the difference between ASA and AAS criteria for congruency of traingles

Insert 16 rational numbers between 2.1 and 2.2 .

If I draw two circles of radius 3cm and 5cm with common centre and draw a line AB such that it is a chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

In figure , if OA = OB, OD= OC then ∆AOD ≅ ∆BOC by congruence rule:

Two concentric circles are of radii 25 cm and 24 cm .The length of the chord of the larger circle which touches the smaller circle is

In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Now, what is the probability that the drawn ticket bears a prime number?

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is

In an isosceles right angled triangle, the measures of the acute angles are

The quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a

A sector of a circle of radius 10.5 cm subtends an angle of 45° at the centre of the circle as in adjoining figure. Find the perimeter of sector.

p/q is a rational number, so p and q must be

The diameter of a cylinder of volume 6160 cu cm and height 10 cm is ... cm.

In triangle PQR, PQ + QR …… PR

In the given figure, angle OAC is 35^o, angle ADC is

p³+ q³ = ?

A parallelogram and rectangle are on the same base and between the same parallel lines. Then perimeter of rectangle is:

Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find the following products:
$(2a^2+9)(2a^2+5)$

1.P (x) is equal to ax , a is not equal to 0

Given the circle having two chords intersecting at A. Find the length of x

Question 58

The factorisation of $2x+4y$ is ___

Question 78

Draw an angle of ${65}^{\circ }$ and draw an angle equal to this angle using ruler and compass.

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

In a frequency polygon plot why do we add extra class interval with frequency zero, one before and one after the given class intervals?

The options show circle centered at O. Certain parts of the circle have been shaded. Which of the following options represent the sector of the circle?