Find the next term of the series \(\sqrt { 2 } ,\sqrt { 8 } ,\sqrt { 18 } ,\sqrt { 32 } ....\)

In fig., PA and PB are tangents to the circle with centre O such that \(\angle APB={ 50 }^{ ° }\)  Write the measure of \(\angle OAB\) .

To divide the line segment AB in the ratio 2 : 3, a ray AX is drawn such that LBAX is acute, AX is then marked at equal intervals. Find minimum number of these marks

The centroid of triangle divides the median in the ratio ...........

Draw a circle of radius 4cm.  Take two points P and Q on one of its extended diameter each at a distance of 6 cm from its centre.  Draw tangents to the circle from these two points P and Q.

Draw a triangle ABC with \(AB=6cm,\ <A=60^o\) and \(<B=60^o\).  Then construct another triangle whose sides are \(4\over 5\) times the corresponding sides of \(\triangle ABC.\)

If A is a point on Y-axis, whose ordinate is 3 and B is a point (- 5, 2), then find the distance AB.

Write first four terms of the AP, when the first term a and the common difference d are given as follows: a = -2, d = 0

Find the ratio in which the line joining points (a + b, b + a) and (a - b, b - a) is divided by the point (a, b).

From a rectangular sheet of paper ABCD with AB=40cm and AD=28cm, a semicircular portion with BC as diameter is cut off.Find the area of the remaining paper.[Use \(\pi={22\over7}\)]

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60^o and angle of depression of the base of the hill as 30^o. Find the distance of the hill from the ship and height of the hill.

A card is drawn from a well shuffled deck of 52 cards.Find the probability of getting:
(i)A king of red colour
(ii)A face card
(iii)The queen of diamonds.

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

Construct triangle D'EF' \(\sim \) triangle DEF in which EF = 10 cm, DE = 5 cm and angle D = 60^o using a scale-factor \(\frac { 1 }{ 2 } \)

Find the median of the following data.

Find the sum of all three-digit natural numbers, which are multiples of 11.

Evaluate : sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}{2}\) sin² 90° - 2 cos² 90° + \(\frac{1}{24}\)

Find the mean of following data by direct method.

If one zero of polynomial 3x²-8x+2k+1 is seven times the other. Then find the zeroes and the value of k.

Solve the following pair of linear equations by the substitution and cross-multiplication methods.
8x+5y=9, 3x+2y=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?

Write the missing numbers is the following factorisation.
(i)       (ii)