The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equals to?
The price of a commodity is increased by 5% from 2010 to 2011, 8% from 2011 to 2012 and 77% from 2012 to 2013. What is the average price increase (approximate) from 2010 to 2013?
The sides of a triangular field are 41 m, 40 m and 9 m. The number of rose beds that can be prepared in the field if each rose bed, on an average, needs 900 square cm space is
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the speed of 10 km/hr and 11 km/hr respectively. What is the distance between them after 6 minutes?
ABCD is a parallelogram. P and R are the midpoints of DC and BC respectively. The line PR intersects the diagonal AC at Q. The distance CQ will be equal to
In the given figure A, B, C, D are four points on a circle. AC and BD intersect at point E such that \[\angle \,BEC=130{}^\circ \]and\[\angle \,ECD=20{}^\circ \]. Find the value of\[\angle \,BAC\].
A pole is bent at a point above the ground due to storm. Its top just touches the ground at a distance of \[10\sqrt{3}\]metres from its foot and makes an angle of \[30{}^\circ \] with the horizontal. Then the height (in metres) of the pole is
If \[{{x}_{i}}'s\] are the midpoints of the class intervals of a grouped data, \[{{f}_{i}}'s\] are the corresponding frequencies and \[\overline{x}\] is the mean, then what is \[\sum\limits_{{}}^{{}}{{{f}_{i}}({{x}_{i}}-\overline{x})}\] equal to?
Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass (in cm) is
The parallel sides of a field, which is in the shape of a trapezium, are 20 m and 41 m and the remaining two sides are 10 m and 17 m. Find the cost of levelling the field at the rate of Rs. 30 per sq.metre.
There are five players A, B, C, D and E in a group. One plays football, one plays tennis and one plays chess. A and D are maidens and play no game. No woman plays either chess or football. There is a married couple in the group of which E is husband. C's brother is B who is neither a chess player nor a tennis player. Who plays chess?
A family has a man, his wife, their four sons and their wives. The family of every son also has 3 sons and one daughter. Find out the total number of male members in the whole family.
A man walks 30 km towards East, then turning to right he walks 30 km further. Then turning to his left he again walks 20 km. Again turning to his left he walks 30 km. How far is he from his starting point?
The cost of manufacturing a car includes the cost of materials, labour and overheads. In 2014, the cost of these items was in the ratio of 5 : 4 : 3. In 2015, the cost of the material rose by 16%, the cost of the labour increased by 10% but the overheads were reduced by 8%. Find the increased percent in the price of the car.
A right circular cone is cut by two planes parallel to the base such that the height is divided into three equal parts. Find the ratio of volumes of the three parts of the cone.
In a class, there are 20 boys and 18 girls. The class teacher wants to choose one student as class representative. He writes the name of each student on flash cards and puts them into a bag and mixes them. A student picks one card from the bag. Find the probability that the name written on the card is the name of a girl.
If \[(a-2)\] is a factor of \[({{a}^{3}}+k{{a}^{2}}+ma+6)\] and leaves the remainder as 3 when it is divided by\[(a-3),\] then which one of the following options represents the value of k and m?
The HCF and LCM of two polynomials are \[(x+y)\] and \[(3{{x}^{5}}+5{{x}^{4}}y+2{{x}^{3}}{{y}^{2}}-3{{x}^{2}}{{y}^{3}}-5x{{y}^{4}}\] \[-2{{y}^{5}})\] respectively. If one of the polynomials is \[({{x}^{2}}-{{y}^{2}})\], then the other polynomial will be
1. Let D be a point on the side BC of a triangle ABC. If the area of the triangle ABD = area of triangle ACD, then for any point O on AD the area of triangle ABO = area of triangle ACO.
2. If G is the point of concurrence of the medians of a triangle ABC, then area of triangle ABG = area of triangle BCG = area of triangle ACG.
Three equal circles each of diameter d are drawn on a plane in such a way that each circle touches the other two circles. A big circle is drawn in such a manner that it touches each of the small circles internally. The area of the big circle is