The sum of the areas of two squares is 640m². If the difference in their perimeters is 64m² find the sides of the two squares.

If a point P is 17 cm from the centre of a circle of radius 8 cm, then find the length of the tangent drawn to the circle from point P.

Find the distance between P(2,3) and Q(4,1).

What is the degree measure of the largest angle of a right triangle?

In nth term of an AP is (2n + 1), then find the sum of its first three terms.

Construct a quadrilateral ABCD, in which AB = 2.5 cm, BC = 3.5 cm, AC = 4.2 cm, CD = 3.5 cm and AD = 2.5 cm. Construct another quadrilateral AB' C'D' with diagonal AC' = 6.3 cm such that it is similar to quadrilateral ABCD.

If the probability of winning a game is 0.3, what is the probability of losing it?

Find the next term of AP \(\sqrt{2},\sqrt{8},\sqrt{18}.\)

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30^o , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60^o . Find the time taken by the car to reach the foot of the tower from this point.

If 'a' is the length of one of the sides of an equilateral triangle ABC, base BC lies on x-axis and vertex B is at the origin, find the coordinates of the vertices of the triangle ABC.

The ages of employees in a factory are as follows:

Find the median age of the employees. 

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.

An aeroplane, when 3000 m high, passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are \({ 60 }^{ ° }\)and \({ 45 }^{ ° }\), respectively, Find the vertical distance between the two aeroplanes.

A box contains 35blue, 25 white and 40 red marbles.If a marble is drawn at random from the box, find the probability that the drawn marble is:
(iWhite
(ii)Not blue
(iii)Neither white nor blue

Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

If the difference between the circumference and the radius of a circle is 37 crn, then using \(\pi =\frac { 22 }{ 7 } \)

The first term of an A.P. is -5 and the last term 45. If the sum of the terms of the A.P. is 120, then find the number of terms and the common difference.

Show that the points A(2, 4), B(-2, 3), C(-1, -1) and D(3, 0) form the square ABCD.

Find the area of the shaded region in figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle.

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

If the zeroes of the cubic polynomial x³-6x²+3x+10 are of the form a, a+b and a+2b for some real numbers a and b, then find the values of a and b.

Evaluate : \(\frac { \cos { { 45 }^{ ° } } }{ \sec { { 30 }^{ ° } } } +\frac { 1 }{ \sec { { 60 }^{ ° } } } \)

It is given that \(\triangle ABC\sim \triangle EDF\) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

If twice the area of a smaller square is subtracted from the area of larger square, the result is 14 \(cm^{2}\)  . However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 \(cm^{2}\) .  Determine the sides of two squares.

Find HCF of SI and 237 and express it as a linear combination of SI and 237 i.e., HCF (81, 237) = 81x + 237y for some x and y.

Draw the graph of the linear polynomial x + 5 and also find the zeros of the polynomial.

Solve the following pair of linear equations by the elimination method and the substitution method :
x + y = 5 and 2x - 3y = 4

A solid ball is exactly fitted inside the cubical box of side a. What is the volume of remaining space inside the cubical box?

Two posts are k metre apart and the height of one is double that of the other. If from the midpoint of the line segment joining their feet, an observer finds the angles of elevation of their tops to be complementary, then find the height of the shorted post.

How long will a man take to go once round a circular track of radius 4.2 m, if he runs at an average speed of 6 km/h?

If median of the number of patients attending a hospital is 36, then find the missing frequencies f₁ and f₂ in the following frequency distribution. When it is given that total number of days is 100.

The shadow of a tower, when the angle of elevation of the sun is 45⁰, is found to be 40 40m longer than when it is 60⁰.Find the height of the tower.

A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a
(i) triangle  (ii) square
(iii) square of blue colour  (iv) triangle of red colour