The roots of quadratic equation x² – 9 = 0 are

Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011

In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

Given a triangle with side AB = 8 cm. To get a line segment AB’ = 3/4 of AB, it is required to divide the line segment AB in the ratio:

Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?

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.

In the given figure, find \(\angle QSR\).

The sum of any two sides of a triangle is always _____________ than the third side.

The length of the shadow of a tree 10 high, when the sun's elevation is 30⁰ , is ..........

(x - 2) (x + 1) = (x - 1) (x + 3) represent a quadratic equation. 

If a, b, c are in A.P., then b is called the arithmetic mean of a and c.

The common point of a tangent and a circle is called point of contact.

Infinite tangents can be drawn from a point lying inside the circle.

If height of a tower and the distance of the point of observation from its foot, both are increased by 20%, then angle of elevation of its remains unchanged

A boy flying a kite has let out 60m of string if the angle of elevation of the kite is 60⁰ , then the height of the kite above the ground is

Write the nature of roots of the quadratic equation 9x²-6x-2=0

If 7 times the 7th term of A.P. is equal to 11 times the 11th term, then find the 18th term.

In fig., AP = 2 cm, BQ = 3 cm and RC = 4 cm, then find the perimeter of \(\triangle ABC\).

Construct a \(\Delta ABC\) with sides AB = 4 cm, BC = 5 cm and CA = 7cm. Then, construct a triangle to it whose sides are \(\frac { 5 }{ 7 } \)  times of the corresponding sides of the given triangle. First, we draw a ray BX such that \(\angle CBX\) is an acute angle and X lies on the opposite side of A with respect to Be. Then, locate points B₂ , B₂ , B ₃, ... on BX at equal distances. What is the next step to join?

A circus artist is climbing on a 10 m long rope which is tightly stretched and tied from the top of a vertical pole to the ground. If the angle made by the rope with the ground level is 45°, then find the height of pole.

Find two consecutive positive integers, sum of whose squares in 365.

Find the nature of the roots of the quadratic equation \(4\sqrt{5} x^{2} + 7x - 3\sqrt{5} = 0\) .

Find a positive number which when decreased by 20 is equal to 69 times its reciprocal.

Find the number of terms in each of the following APs.
7, 13, 19,...., 205

The sum of n terms of two APs are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 25th terms.

Find the sum of the series: (a - b)² + (a² + b²) + (a + b)² +......+ {(a + b)² + 6ab}.

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B.Prove that \(\angle AOB=90^0\)

 Angle between two tangents PQ and PR from point P to a circle with centre O, is right angle. If the radius of the circle is 4cm, then find the length of each tangent.

If the sides of a parallelogram touch a circle, prove that the parallelogram is a rhombus.

To construct a triangle similar to given triangle \(\Delta\)ABC with its sides \(\frac { 7 }{ 3 } \) of the corresponding sides of triangle \(\Delta\)ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁, B₂,...B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C' is drawn parallel to B₃C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.

Determine a point P on a line segment AB of length 6.5 cm, such that AP : PB = 4 : 3.

PQ is a line segment of length 6.4 cm. Geometrically, obtain point R on PQ such that \(\frac { QR }{ PQ } =\frac { 5 }{ 8 } \)

The length of the string between a kite and a point on the ground is 90 m. The string makes an angle of 60^o with the level ground. Assuming that there is no slack in the string, find the height of the kite.

A circus artist is climbing a 20m long rope, which is tightly stretched and from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30^o.

the angle of elevation of a cloud from a point h m above the surface of a lake is \(\theta\) and the angle of depression of its reflection in the lake is \(\phi\).Prove that the height of the clouds above the lake is:
\(h(tan\phi+tan\theta)\over tan\phi-tan\theta\)

Find the value of p, when px²+\(\left( \sqrt { 3 } -\sqrt { 2 } \right) x-1\)=0 and x=\(\frac { 1 }{ \sqrt { 3 } } \)

Find the value of k for which the distance between (9,2) and (3, k) is 10 units.

In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

The 13^th term of an A.P.is four times its 3^rd term. If the fifth term is 16, then find the sum of its first ten terms.

In the given figure, PQ and PR are tangents from point P to the circle, with centre O. N is a point on the circle. Prove that: PL + LN = PM + MN.

Two concentric circles are of radii 10 cm and 8 cm. RP and RQ are tangents to the two circles from R. If the length of RP is 24 cm, find the length of RQ.

Construct a triangle similar to given triangle ABC with AB = 4 cm, BC = 6 cm and CA = 7.5 cm, such that each of its sides are equal to \(\frac { 5 }{ 3 } \) rd  of the corresponding sides of triangle ABC.

Draw a circle of diameter 6 cm with centre O. Draw a diameter POQ. Through P or Q draw a tangent to the circle.

From a window (60 metres high above the ground) of a house in street the angles of elevation and depression of the top and the foot of another house on opposite side of street are 60^o and 45^o respectively. Show that the height of the opposite house is \(60(1+\sqrt { 3 } )\) metres.

The angle of elevation of the top of a tower from the bottom of a tree is 60° and the angle of elevation of the top of tree from the foot of the tower is 30°. If the tower is 50 m tall, then what is the height of the tree?

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in maths and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.

Find the difference of the roots of equation x²-7x-9=0

Jobanpreet applied for a teaching job and got selected. She has been offered the job with a starting monthly salary of Rs.12500 with an annual increment of Rs.1250. Find her salary after 15 years of service. Also, find the total amount received by Jobanpreet in 15 years.

The radius of the incircle of a triangle is 6 cm and the segments into which one side is divided by the point of contact are 9 cm and 12 cm. Determine the other two sides of the triangle.

PA and PB are two tangents from an exterior point P to a circle of radius 5 cm. If length of the chord AB is 8 cm, then find the length of the tangent.

Draw two equal circles with centres A and B and distance between A and B is 6 cm. Construct a pair of tangents from centres A and B to each other. Measure the lengths of the tangents. What type of 31. figure is enclosed by these four tangents?

A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30^o. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45^o. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. [given \(\sqrt2\) = 1414]

From the top of a hill the angles of depression of two consecutive kilometre stones east are found to be 30^o and 60^o . Find the height of the hill.