The solution of x² + 4x + 4 = 0 is

The 8^th term of 117, 104, 91, 78, …….is.....

In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is

In drawing triangle ABC, it is given that AB = 3 cm, BC = 2 cm and AC = 6 cm. It is not possible to draw the triangle as:

The figure shows the observation of point C from point A. The angle of depression from A is:

If p(x) is quadratic polynomial, then p(x) = 0 is called a .............. equation.

In an A.P. the common difference is always ...........

If angle between two radii of a circle is 130°. The angle between the tangents at the ends of the radii is _______________

In order to divide a line segment internally in the ratio m : n, both m and n are ________________

A tower stands vertically on the ground.From a point on the ground, which is 100m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60⁰, then the height of the tower is .........

The equation \((x+2)^{ 2 }=0\) has real roots.

The sum of first 4 terms and sum of first 13 terms of the A.P. 24, 21, 18, .......... is 78.

The common point of a tangent to a circle with circle is called point of contact.

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

From the figure, height h is 173.2m

A player sitting on the top of a tower of height 40m observes the angle of depression of a ball lying on the ground as 60⁰.The distance between the foot of the tower and ball is

Find the discriminant of quadratic equation \(x^{ 2 }+4x-1\)

The n^th term of an A.P. cannot be n²+1. Justify your answer.

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 \(\angle POR=110^0\)Find \(\angle OPQ.\)

Find the ratio in which A divides the line segment PQ

Find the angle of elevation of the top of 15 m high tower at a point 15 m away from the base of the tower.

Is x=-4 a solution of the equation 2x²+5x-12=0

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

Out of a group of children, \({7\over 2}\) times the square root of the number are creative, the two remaining ones are visionary. What is the total number of children ? How many persons in the group are creative?
Write one-one characteristics each of creativity and vision.

Interior angles of a polygon are in AP. If the smallest angle is 120^o and common difference is 5^o, find the number of sides of the polygon.

Find the missing term of the A.P. 2, ......, 24, 35

The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

In figure, there are two concentric circles, with centre O and of radii 5cm and 3cm. From an external point P, tangents PA are drawn to these circles. If AP = 12cm, find the length of BP.

A circle is inscribed in a \(\Delta ABC\) having sides 16cm, 20cm and 24 cm as shown in figure.Find AD, BE and CF.

In figure, a circle is inscribed in a triangle PQR with PQ = 10cm, QR = 8 cm and PR = 12 cm. Find the lengths QM, RN and PL.

Draw a circle of radius 4 cm. From a point 12 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Write the two concepts used for justification in division of a line segment .

Draw a circle of radius 5 cm. Take a point P on it. Without using the centre of the circle, draw a tangent to the circle at point P.

A boy flying a kite has let out 60 m of string. If the angle of elevation of the kite is 60^o , calculate the height of the kite above the ground.

Find the angle of elevation of the sun when the shadow of a pole h metres high is \(\sqrt{3}\) h metres long

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.

The sum of the reciprocals of Anjali's age 3yr ago and 5yr from now is \(\frac{1}{3}\) . Find the present age of Anjali.

For what value of k, the roots of the quadratic equation kx(x - 2 \(\sqrt { 5 } \) ) + 10 = 0 are equal ?

How many terms are there in the sequence 3,6,9,12,...,111?

How many multiples of 4 lie between 11 and 266?

In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.

If a line which is perpendicular to the radius of the circle through the point of contact. What will you call that line?

Draw a triangle DEF with EF = 5 cm and DE = DF = 4 cm. Construct another triangle similar to given triangle, such that its sides are \(\frac { 6 }{ 7 } \) th of the sides of triangle DEF.

Draw a circle of radius 3.5 cm. Take a point T outside the circle at a distance of 7 cm from the centre and construct a pair of tangents from this point T to the circle.

The top of a broken tree has its top touching the ground (shown in the following figure) at a distance of 10 m from the bottom. If the angle made by the broken part with ground is 30°, then find the length of the broken part.

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.

Is it possible to design a rectangular mangrove whose perimeter is 38 m and area is \(84 \ m^{2}\) ?  Find its length and breadth.

Write the discriminant of the following
(i) 3x²-4x+7=0
(ii) \(\sqrt { 3 } { x }^{ 2 }-2\sqrt { 2 } x-2\sqrt { 3 } =0\)
(iii) 2x²+3x+m=0
(iv) x²+x+7=0
(v) (4x-3)²+20x=11
(vi) a²x²+8abx+4b²=0

If \({a}_{1},{a}_{2},{a}_{3},...,{a}_{n}\)  are in AP, where \({a}_{i}>0\) then find the value of \(\frac { 1 }{ \sqrt { { a }_{ 1 } } +\sqrt { { a }_{ 2 } } } +\frac { 1 }{ \sqrt { { a }_{ 2 } } +\sqrt { { a }_{ 3 } } } +...+\frac { 1 }{ \sqrt { { a }_{ n-1 } } +\sqrt { { a }_{ n } } } \)

In the adjoining figure, a right angled ΔABC, circumscribes a circle of radius r. If AB and BCare of lengths 8 cm and 6 cm respectively, then find the value of r.

In the given figure, PT and PM are two tangents to the circle with centre O. If OT = 6 cm and OP = 10 cm. then find the length of PT and PM.

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle sides are \(\frac { 3 }{ 4 } \) times the corresponding sides of the isosceles triangle.

If the shadow of a tower 30m long, when the sun's elevation is 30⁰.What is the length of the shadow, when sun's elevation is 60⁰ ?

The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is \(\sqrt { st } \) .