List of top Mathematics Questions

If $A = \begin{bmatrix} {1}&{-3}\\ {2}&{K} \\ \end{bmatrix}$ and $A^2-14A+10I=A$,then $K$ = is equal to :
The distance between the pair of parallel lines $ x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0$ is :
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.
A well 22.5 deep and of diameter 7m has to be dug out. Find the cost of plastering its inner curved surface at Rs 3 per sq metre.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cyclindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?
A circular grassy plot of land, 42 m in diameter, has a path 3.5 m wide running around it outside.The cost of gravelling the path at Rs 4 per square metre is
A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is
A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm that the level may be raised 20 cm in 5 hours?
An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe is
A metallic sheet is of rectangular shape with dimensions 48 cm \(\times\) 36 cm. From each one of its corners, a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box.
There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A room has 3 lamps. From a collection of 10 light bulbs of which 6 are not good, a person selects 3 at random and puts them in a socket. The probability that he will have light is
Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that atleast one of the selected persons will be a woman is
The probability that a certain electronic component fails when first used is 0.10. If it does not fail immediately, then the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is
In a certain laboratory, chemicals are identified by a colourcoding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique twocolour pair. If the order of colours in the pair doesn't matter, then what is the minimum number of differentcolours needed to code all the 20 chemicals with either a single colour or a unique pair of colours?
A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs X refuses to serve in a committee if Mr Y is its member, is
A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs 250 a quintal, the total monthly expenses of the family are Rs 1000 and when it is Rs 240 a quintal, the total monthly expenses are Rs 980. Find the total monthly expenses of the family when the cost of wheat is Rs 350 a quintal.
Speed of a speedboat when moving in the direction perpendicular to the direction of the current is 16 km/hr. Speed of the current is 3 km per hour. So the speed of the boat against the current will be (in km/hr)
Company C sells a line of 25 products with an average retail price of Rs 1,200. If none of these products sells for less than Rs 420 and exactly 10 of the products sell for less than Rs 1,000, then what is the greatest possible selling price of the most expensive product?
Profits of a business are distributed among three partners A, B and C in such a way that 4 times the amount received by A is equal to 6 times the amount received by B and 11 times the amount received by C. The ratio in which the three received the amount is
Population of a district is 2,96,000 of which 1,66,000 are males. \(50\%\) of the population is literate. If \(70\%\) males are literate, then the number of women who are literate, is
A shopkeeper marks up his goods to gain \(35\%\). But he allows \(10\%\) discount for cash payment. His profit on the cash transaction therefore, in percentage, is
A sink contains exactly 12 litres of water. If water is drained from the sink until it holds exactly 6 litres of water less than the quantity drained away, then how many litres of water were drained away?