List of top Mathematics Questions

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y -11 = 0$ is
If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$, then the equation of the circle is
The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$, is
The radius of the circle with the polar equation $r^2 - 8r( \sqrt{3} \, \cos \, \theta + \sin \, \theta) + 15 = 0$ is
In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to
A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is
Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?
Rahul started a business with a capital of Rs 8,000. After six months, Sanjay joined him with an investment of some capital. If at the end of the year each of them gets equal amount as profit, how much did Sanjay invest in the business?
A manufacturer of a certain item can sell all he can produce at the selling price of Rs 60 each. It costs him Rs 40 in materials and labour to produce each item and he has overhead expenses of Rs 3000 per week in order to operate that plant. The number of units he should produce and sell in order to make a profit of at least Rs 1000 per week is
At a college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, 80% pass the tests and of the incapable, 25% pass the tests. Given that 40% of the candidates are really capable, then the proportion of capable college students is about
In an examination, there were 2000 candidates, out of which 900 candidates were boys and the rest were girls. If 32% of the boys and 38% of the girls passed, then the total percentage of failed candidates is
From the salary of an officer, 10% is deducted as house rent, 15% of the rest he spends on children's education and 10% of the balance he spends on clothes. After this expenditure he is left with Rs 1377. His salary is
If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before.
A monthly return railway ticket costs 25 per cent more than a single ticket. A week's extension can be had for the former by paying 5 per cent of the monthly ticket's cost. If the money paid for the monthly ticket (with extension) is Rs 84, the price of the single ticket is
A papaya tree was planted 2 years ago. It increases at the rate of 20% every year. If at present, the height of the tree is 540 cm, what was its height when the tree was planted?
The ratio between the number of passengers travelling by I and II class between the two railway stations is 1: 50, whereas the ratio of I and II class fares between the same stations is 3: 1. If on a particular day, Rs 1325 revenue collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
A and B enter into a partnership with Rs. 50,000 and Rs. 60,000 respectively. C joins them after x months contributing Rs 70,000 and B leaves x months before the end of the year. If they share the profit in the ratio of 20: 18: 21, then find the value of x.
A person travels 285 km in 6 hrs in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hr. In the second part of the journey, he travels by train at the speed of 55 km per hr. How much distance did he travel by train?
Two persons are walking in the same direction at rates 3 km/ hr and 6 km/hr. A train comes running from behind and passes them in 9 and 10 seconds. The speed of the train is
A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 450. Then which of the following statements is correct?
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 600 and when he walks 40 metres away from the tree the angle of elevation becomes 300. The breadth of the river is
Rampur is 100 km from Sitapur. At 3 pm Bharat Express leaves Rampur for Sitapur and travels at a constant speed of 30 km/ h. One hour later, Laxman Mail leaves Sitapur for Rampur and travels at a constant speed of 40 kmph'. Each train makes one stop only at a station 10 km from its starting point and remains there for 15 min. Which train is nearer to Rampur when they meet?
A car starts running with the initial speed of 40 kmph, with its speed increasing every hour by 5 kmph. How many hours will it take to cover a distance of 385 km?
There are two taps to fill a tank while a third to empty it. When the third tap is closed, they can fill the tank in 10 minutes and 12 minutes, respectively. If all the three taps be opened, the tank is filled in 15 minutes. If the first two taps are closed, in what time can the third tap empty the tank when it is full?
Two taps can fill a tank in 20 minutes and 30 minutes respectively. There is an outlet tap at exactly half level of that rectangular tank which can pump out 50 litres of water per minute. If the outlet tap is open, then it takes 24 minutes to fill an empty tank. What is the volume of the tank?