List of top Mathematics Questions

If the circles $x ^2 + y ^2 =9$ and $x^2 + y^ 2 + 2\alpha x + 2y +1 = 0$ touch each other internally, then $\alpha$ =
A point P moves so that the sum of its distances from $ (-ae,\,0) $ and $ (ae,\,0) $ is $ 2a $ . Then the locus of P is
If $ {{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}} $ denotes the binomial coefficients in the expansion of $ {{(1+x)}^{n}}, $ then $ {{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1} $ is equal to
Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is
If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|
Probability of getting positive integral roots of the equation x$^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is
The center and radius of the sphere $x^2 + y^2 + z^2 + 3x - 4z + 1 = 0$ are
The simplified expression of sin ($tan^{-1} x$), for any real number $x$ is given by
If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6} $ and $P(A \cap B) = \frac{1}{3}$, then $P(A)$ is equal to (Here, $E$ is the complement of the event $E$)
If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to
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
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
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.
Two men undertake to do a piece of work for Rs. 1,400. First man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should money be divided?
Two men undertake to do a piece of work for Rs 600. One alone could do it in 6 days and the other in 8 days. With the assistance of a boy they finish it in 3 days. Boy's share should be