If the length of the rectangle is one more than the twice its width, and the area of the rectangle is 300 square meter. What is the measure of the width of the rectangle?

How many terms of AP 54, 51, 48… are required to give a sum of 513

The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

In the figure, P divides AB internally in the ratio

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

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.

Find the sum of the first n positive integers

In the figure, QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find length of QR.

In drawing a triangle, if AB = 3 cm, BC = 2 cm and AC = 6 cm. What is the possibility that a triangle cannot be drawn.

The height of a tower is 10m.The height of its shadow when sun's altitude is 45⁰ , is ...........

x = -1 is a root of the quadratic equation \(3x^{2} - x - 4 = 0\) .

If \({T}_{an}=6n+5,\) then common difference is 6.

In the figure, PT is a tangent to the circle with centre O such hat OP is 4 cm and \(\angle OPT={ 30 }^{ \circ }\) , then length of tangent is 5 cm.

At least three parts are sufficient for construction of a triangle.

Two posts are 120m apart and the height of one is double that of the other.If from the middle point of the line joining their feet, an observer finds that the angular elevations of their tops to be complementary, then the height of the poles are \(30\sqrt{2}m\) and \(60\sqrt{2}m\)

The angle of depression of the top of a tower at a point 100m from the house is 45⁰ , then the height of the tower is

If the discriminant of \(3x^{2} + 2x\ +a = 0\) is double the discriminant of \(x^{2}-4x + 2 = 0\)  , then find the value of a.

In the given figure, AB, AC and PQ are tangents. If AB = 5 cm, then find the perimeter of \(\triangle \)APQ.

To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that \(\angle BAX\) is an acute angle then find the minimum number of such points marked at equal distances on the ray AX.

The tops of two poles of heights 16 m and 10 m are connected by a wire. If the wire makes an angle of \({ 30 }^{ ° }\)\(​​\)with the horizontal, then find the width of the river.

The denominator of a fraction its numerator by 3. If one is added to both numerator and denominator, the difference between the new and the original fraction is 1/24. Find the original fraction.

The angry Arjun carried some arrows for fighting with Bhesshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the rath driver of Bheeshm. width one arrow each he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconcious on an arrow bed. Find the total number of arrows Arjun had.

Solve the following quadratic equation for x :
x²-2ax-(4b²-a²)=0

Find the sum of the following AP: 0.6, 1.7, 2.8, ........, to 100 terms

Find the common difference of the A.P.  2, 2 + \(\sqrt{2}\) , 2 + 2\(\sqrt{2}\) , 2 + 3\(\sqrt{2}\),.......

Find the common difference of an AP, whose first term is \(\frac {1}{2}\) and 8th term is \(\frac {17}{6}.\)

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

C(0, r₁) and C(0, r₂) are two concentric circles, with r₁ > r₂.AB is a chord of C(0, r₁) touching C(0, r₂) at C, then the relation between AB, r₁ and r₂.

Define tangent to a circle.

Draw a pair of tangents to circle of radius 6cm which are inclined to each other at an angle of \(130^o\).

Draw an equilateral triangle ABC of side 6cm each.  Construct a \(\triangle PQR\) similar to triangle ABC, where each side of \(\triangle PQR\) is 8cm.

Draw a circle of radius 4 cm. Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from P.

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30^o . The angle of depression of the reflection of the cloud in the lake, at A is 60^o . Find the distance of the cloud from A.

An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

The shadow of tower standing on a level plane is found to be 50m longer when sun's elevation is 30^o than when it is 60^o. Find the height of the tower.

Using the quadratic formula, solve the quadratic equation.
\(\sqrt { 3 } { x }^{ 2 }+11x+6\sqrt { 3 } =0\)

If -4 is a root of the quadratic equation x²+px-4=0 and the equation 2x²+px+k=0 has equal roots, then find the value of k.

In an AP, given a = 2, d = 8, \({S}_{n}=90,\) find n and \({a}_{5}.\)

Examine that the list of numbers obtained from following situation, will be in the form of an AP. "Amount left with Sandeep (in RS) out of the total amount of RS.12000 which he had in the beginning, when he spends RS.500 in the beginning of every month."

At the point of contact the angle between radius and tangent to a circle is 90^o.

In \(\triangle ABC\),  AB = AC. If the interior circle of \(\triangle ABC\) touches the sides AB, BC and CA at D, E, F respectively. Prove that E bisects BC.

Construct a triangle PQR, such that QR = 5 cm, angle \(\angle\) Q = 60^o and PQ = 6 cm. Construct another triangle similar to triangle \(\Delta\)PQR, such that its sides are \(\frac { 3 }{ 5 } \)th of the corresponding sides of triangle \(\Delta\)PQR.

Draw an equilateral \(\Delta ABC\) of each side 4 cm.Construct a triangle similar to it and of scale factor \(\frac{3}{5}\).Is the new triangle also an equilateral?

The angle of elevation of an aeroplane from a point on the level ground is 60°. After 10 s of flight, the angle of elevation changes to 30°. If the aeroplane is flying horizontally at a height of 3000 m, then find the speed of the plane.

The angle of elevation of a jet fighter from a point A on the ground is \({ 60 }^{ ° }\). After a flight of 10 s, the angle of elevation charge to \({ 30 }^{ ° }\) .

If the jet is flying at a speed of 432 Km/h, then find the constant height at which the jet is flying.

Solve the following quadratic equations
\(x^{ 2 }-55x+750=0\)

Solve the following quadratic equation \(\sqrt { 3 } { x }^{ 2 }+11x+6\sqrt { 3 } =0\)

Find the sum of 10 terms of an AP: 50,46,42,... .

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that \(\angle DBC={ 120 }^{ \circ }\), prove that BC + CD = BO i.e., BO = 2BC.

If PQ is a tangent drawn from an external point P to a circle with centre O and QOR is a diameter where length of QOR is 8 cm such that \(\angle POR=120°\), then find OP and PQ.

Draw two tangents from the end points of the diameter of a circle of radius 4.0 cm. Are these tangents parallel?

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stones on the opposite sided of the aeroplane are found to be \(\alpha\) and \(\beta\), show that the height of the aeroplane is \(\frac { tan\alpha tan\beta }{ tan\alpha +tan\beta } \).

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its \(5\over12\).On walking 192m towards the tower, the tangent of the angle is found to be \(3\over4\) .Find the height of the tower.