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

Find the distance of the point (-4, -7) from the y-axis.

What is the sum of five positive integers divisible by 6.

Two tangents making an angle of 60° between them are drawn to a circle of radius \(\sqrt{3}\) cm, then find the length of each tangent.

Draw a right triangle in which the sides containing the right angle are 5 cm and  4cm.  Construct a similar triangle whose sides are \(5\over 3\) times the sides of the given triangle.

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.

Find the fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3) B(6,7) and C(8,3).

Check whether 301 is a term of the list of numbers 5, 11, 17, 23,......

If the point A(0,2) is equidistant from the points B(3,p) and C(p,5), find p. Also find the length of AB.

The shaded area, in the figure between the circumference of two concentric circles is 346.5 cm² . The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point 'A' on the ground is 60^o and the angle of depression of the point 'A' from the top of the tower is 45^o . Find the height of the tower. \((\sqrt { 3 } =1.73)\)  

A box contain 100red cards, 200 yellow cards and 50blue cards.If a card is drawn at random from the box, the find the probability that it will be:
(i)A blue card
(ii)Not a yellow card
(iii)Neither yellow nor a blue card.

AB is a diameter of a circle and AC is its chord such that \(\angle BAC=30°\). If the tangent at C intersects AB extended at D, then prove that BC=BD.

Draw a circle of radius 2.8 cm. From an external point P, draw tangents to the circle without using the centre of the circle

The ages of employees in a factory are as follows:

Find the median age of the employees. 

The sum of first n, 2n and 3n terms of an AP are S₁, S₂ and S₃, respectively. Prove that S₃=3(S₂-S₁).

Prove that \(\cot ^{ 2 }{ A } \left[ \frac { \sec { A } -1 }{ 1+\sin { A } } \right] +\sec ^{ 2 }{ A } \left[ \frac { \sin { A } -1 }{ 1+\sec { A } } \right] =0\)

To find out the concentration of SO₂ in the air (in parts per million, i.e, ppm), the data was collected for 30 localities in a certain city and its presented below:

Find the mean concentration of SO₂ in the air.

Find the zeroes of the following quadratic polynomials and verify the relationship betwee the zeros and its coefficients.
(i) x²-2x-8
(ii) 4s²-4s+1
(iii) 6x²-3-7x
(iv) 4u²+8u
(v) t²-15
(vi) 3x²-x-4

Form the pair of linear equations in the following problems and find their solutions graphically:
10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Two sets of English and Social Science Books containing 336 and 96 books respectively in a library, have to be stacked in such a way that all the books are stored topicwise and the height of each stack is the same. Assuming that the books are of the same thickness, determine the total number of stacks. What are the characteristics of library?
[Number of stacks = \(\frac { 336+96 }{ HCF\left( 336,96 \right) } \)]