The roots of quadratic equation x² – 9 = 0 are

Which term of the A.P. 1, 4, 7 … is 88?

 PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR=120°, then ∠OPQ is

If four sides of a quadrilateral ABCD are tangential to a circle, then

Find AB in the given figure

One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son's age, Find their present ages.

What is the next term of an AP.\( \sqrt { 7 } ,\sqrt { 28 } ,\sqrt { 63 } ,.....?\)

The length of the tangents drawn from an external point to a circle are _____________

What is the ratio of division of the line segment AB by the point P from A?

The ................ is the line drawn from the eye of an observer to the point in the object viewed by the observer.

The sum of a real number x and its reciprocal from a quadratic equation.

\({a}_{30}-{a}_{20}\) of AP a, a + d, a + 2d, a + 3d, .... is 10 d.

In the given figure, incircle of MBC touches its sides at D, E and F. If perimeter of \(\triangle \) ABC = 24 cm, then AF + BD + CE = 12 cm.

In the given figure, if AP = 6 cm and BP = 8 cm, then m : n = 3 : 4.

Trigonometric ratios are same for the same angles.

The angle of elevation of the top of the tower from a point on the ground which is 30m away from foot of the tower is 30⁰.the height of the tower is.

Which constant should be added or subtracted to solve the quadratic equation \(4x^{2} - \sqrt {3 }x -5 = 0\) by the method of completing the square?

If \(\frac { 3+5+7+...\ to\ n\ terms }{ 5+8+11+...\ to\ 10\ terms } \)=7, then find the value of n.

In figure, a circle is inscribed in a quadrilateral ABCD touching the sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and , then find the length of CD
.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60° , it is required to draw tangents at end points of those two radii of the circle, then find the angle between them.

A tree is broken by the wind. The top struck the ground at an angle of  \({ 45 }^{ \circ }\)and it a distance 35m from the foot. Then the whole height of the tree before broken.

Find the value of m so that the quadratic mx(x-7)+49=0 has two equal roots.

Niharika's mother is 28 years older than her. Seven years ago, the product of their ages in years was 245. We would like to find Niharika's present age. Represent the given situation in the form of a quadratic equation. How one should care their parents in old age ?

Solve the following equation for x
\(4x^{ 2 }+4bx-(a^{ 2 }-b^{ 2 })\)

Find the sums given below: -5 + (-8) + (-11) + ..... + (-230)

If the 2^nd term of an A.P.is 8 and the 5^th term is 17, find its 19^th term.

Ho many terms of the A.P.18, 16, 14 ....be taken so tliat their sum is zero? 

The length of a tangent from a point A at distance 5cm from the centre of the circle is 4cm.Find the radius of the circle.

PAQ is a tangent to the circle with centre O at point A as shown in figure.If \(\angle OBA=35^0\), find the value of \(\angle BAQ \ and\ \angle ACB\)

In the given figure, AB is a chord of length 16 cm, of a circle of radius 10 cm. Tangents at A and B intersect at a point P. Find the length of tangent AP.

Draw a triangle ABC with sides BC = 6 cm, AB = 5 cm and (Then construct a triangle whose sides are \({3\over 2}\) of the corresponding sides of the triangle ABC.

Construct a \(\triangle ABC\) in which BC = 9 cm,  and \(AB=6cm.\) Then construct another triangle whose sides are \(2\over 3\) of the corresponding sides of \(\triangle ABC\).

Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3 : 5.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60^o with the wall, then find the height of the wall.

A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30^o . The peacock with the speed of 300 m/minute catches the serpent in 12 seconds. What is the height of the tree?

The hypotenuse of a right triangle is 4 times the smallest side.The third side is \(\sqrt{735}\) .Find the hypotenuse and the smallest side.

Find the roots of the following quadratic equation (if they exist) by the method of completing square \(25x^{2}-20x+4 = 0\) .

Find the roots of the quadratic equation \({x+3\over {x + 2}} = {3x - 7 \over {2x - 3 }} ; x \neq -\ 2 , {3 \over 2}.\)

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Two APs have two same common difference. The difference between their 100th terms is 111222333. What is the different between their millionth terms?

ABC is an isosceles triangle, in which AB=AC, circumscribed about a circle.Show that BC is bisected at the point of contact.

In the given figure, PT is tangent to the circle at T.If PA=4cm and AB=5cm find PT.

Draw an isosceles \(\triangle ABC\) in which \(BC=5.5cm\) and altitude AL = 3cm.  Then construct another triangle whose sides are \(3\over 4\) of the corresponding sides of \(\triangle ABC\).

Draw a right triangle with sides of length 5 cm and 4 cm making a right angle. Construct another triangle whose sides are \(\frac { 3 }{ 5 } \) times the corresponding sides of the first triangle.

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 60^o . Find the angle between the sunrays and the ground at the time of longer shadow.

A straight tree is broken due to thunderstorm. The broken part is bent in such a way that the peak of the tree touches the ground at an angle of 60\(°\)at a distance of \(2\sqrt { 3 } m\) Find the whole height of the tree.

In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

Twenty-seven years hence Sanjay's age will be the square of what it was 29 yr ago. Find his present age.

In the following APs, find the missing terms of the boxes. -,13,-,3

As a part of a campaign, a huge balloon with message of ''AWARENESS OF CANCER" was displayed from the terrace of a tall building. It was held by strings of length 8 m each and inclined at an angle of 60° at the point, where it was tied as shown in the figure.

(i) What is the length of AB?
(ii) If the perpendicular distance from the centre of the circle to the chord AB is 3 m, then, find the radius of the circle.
(iii) Which method should be apply to find the radius of circle?
(iv) What do you think of such campaign?

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that \(\angle POR=135°\), then find \(\angle OPB\).

Draw a right-angled triangle, in which the sides (other than the hypotenuse) are lengths 8 cm and 6 cm. Then, construct another triangle, whose sides are \(\frac { 3 }{ 4 } \)  times of the corresponding sides of  given triangle. Justify your construction.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is \(30°\) (see figure)

Two poles of equal heights are standing opposite to each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.