Check whether the following are quadratic equations: x²-3x+5=(x+5)²

If the equation \(px^{ 2 }+4x-3=0\) has real roots, then find the value of p

If the first term of an A.P. is -5 and the common difference is 2, then find the sum of the first 6 terms.

If the numbers n-2, 4n-1 and 5n+2 are in A.P., find the value of n..

From a point Q, the length of tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm, then find the radius of circle.

In the given figure, AB is a chord of circle and AOC is diameter such that angle ACB = \({ 55 }^{ \circ }\). If  AT is a tangent to the circle at point A, then find angle BAT.

The height of a tower is 30 m. Calculate the length of its shadow made on the level ground when the sun's altitude is 60^o . 

Find the probability of getting a perfect square number from the numbers 1 to 10.

If P(E)=0.15, then find P(not E).

Find the distance between the points (0, 5) and (-5, 0).

Find the radius of the circle whose endpoints of diameter are (24, 1) and (2, 23).

The area of circle is numerically equal to twice its circumference.  Find the diameter of the circle.

A bucket is in the form of a frustum of a cone whose radii of bottom and top are 7 cm and 28 cm respectively. If the capacity of the bucket is 21560 cm³, find the whole surface area of the bucket.

Find the ratio of the volumes of two cones with equal heights and ratio of their radii as 1 : 3.

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.

Find a quadratic polynomial with zeroes \(3+\sqrt { 2 } \) and \(3-\sqrt { 2 } \) .

Find cosec 30° and cos 60° geometrically.

Find the mean of the following frequency distribution:

A speed of a boat in still water is 11km/hour. It can go 12km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.

Find the roots of the equation \(2x^{ 2 }+x-4=0\) by the method of completing the squares.

How many three-digit numbers are divisible by 11?

The sum of first n terms of an A.P.is given by S_n = 3n² - 4n. Determine the A.P.and the 12^th term.

If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is perpendicular bisector of AB.

A circle is inscribed in a ΔBC having sides AB=8 cm, BC = 10 cm and CA  = 12 cm as shown in figure. Find AD, BE and CF

Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then draw another triangle whose sides are \(\frac { 4 }{ 5 } \) of the corresponding sides of first triangle.

150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped the second day, four more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

In the given figure, ABC is a triangle in which \(\angle ABC>{ 90 }^{ ° }\) and \(AD\bot CB\) produced. Prove that AC² = AB² + BC² + 2 BC . BD

In \(\triangle\) ABC, AD is a median and 0 is any point on AD. BO and CO on producing meet AC and AB at E and F respectively. Now AD is produced to X such that OD = DX as shown in figure.
Prove that:
(i) EF II BC
(ii) AO : AX = AF : AB

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
\({ (\sin { A } +cosecA) }^{ 2 }+{ (\cos { A } +\sec { A } ) }^{ 2 }=7+\tan ^{ 2 }{ A } +\cot ^{ 2 }{ A } \)

The median of the following data is 525.Find the values of x and y if the total frequency is 100.