List of top Mathematics Questions

Vijay purchased two different kinds of alcohol. In the first mixture the ratio of alcohol to water is 3 : 4 and in the second mixture it is 5 : 6. If he mixes the two given mixtures and makes a third mixture of 18 litres in which the ratio of alcohol to water is 4 : 5, the quantity of the first mixture (whose ratio is 3 : 4) that is required to make 18 litres of the third kind of mixture is

Two companies A and B quote for a tender. On the tender opening day, A realises that the two quotes are in the ratio 7 : 4 and hence decreases its price during negotiations to make it Rs.1 lakh lower than B's quoted price. B then realises that the final quotes of the two were in the ratio 3 : 4. By how much did A decrease its price in order to win the bid?

There are a total of 43800 students in 4 schools of a city. Half the number of students of the first school, two-thirds of the second, three-fourth of the third and four-fifths of the fourth are all equal. What is the ratio of the number of students of A to D, if A, B, C and D be the first, second, third and fourth schools,respectively?

A bath can be filled by the cold water and hot water pipes in 10 minutes and 15 minutes respectively. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath should be full. Finding, however, that the waste pipe has been open, he then closes it. In exactly four minutes more the bath is full. In how much time would the waste pipe empty the full bath, if it alone is opened?

For the married couple living in Jammu, the probability that a husband will vote in an election is $ 0.5 $ and the probability that his wife will vote is $ 0.4 $ . The probability that the husband votes, given that his wife also votes is $ 0.7 $ . Then, the probability that husband and wife both will vote is

Solution of $e^\frac {dy}{dx} = x$ when $x = 1$ and $y = 0$ is

The sum of the series $ 5-\frac{10}{3}+\frac{20}{9}-\frac{40}{27}+.... $ is equal to

The sum $1\times 1! + 2 \times 2! + ... + 50 \times 50!$ equals

The value of the integral $ \int_{0}^{1}{x{{(1-x)}^{49}}\,dx} $ is equal to

If $ ^{m+n}P{{ }_{2}}=90 $ and $ ^{m-n}P{{ }_{2}}=30, $ then $ (m,n) $ is given by (where, m and n are positive integers)

If $ f(x)={{(1+x)}^{n}}, $ then the value of $ f(0)+f'(0)+\frac{f'\,'(0)}{2!}+.....+\frac{{{f}^{(n)}}(0)}{n!} $ is equal to

Let $ P(x,y) $ be a point on the curve $ {{y}^{2}}=4x $ at which the tangent is perpendicular to the line $ 2x+y=-2. $ Then, the coordinates of the point $P$ are

If the points $ (2a,\,a),\,(a,\,2a) $ and $ (a,\,\,a) $ form a triangle of area $ 32\text{ }sq $ units, then the centroid of the triangle is

Let \(f:R\to R\) be a function such that the third derivative of \(f(x)\) vanishes for all \(x\). If \(f(0)=1,\,f'(2)=4\) and \(f''(1)=2,\) then \(f(x)\) equals to

In the binomial expansion of $ {{(a-b)}^{n}},\,\,n\,\,\ge \,5, $ the sum of $5^{th}$ and $6^{th}$ term is zero. Then, $ \frac{a}{b} $ is equal to

If $ f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x), $ then the value of $ \int_{-1/2}^{1/2}{f(x)\,\,\,dx} $ equals to

The angle between the two lines $ \frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1} $ and $ \frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2} $ is

If $p :$ The earth is round, $q : 3 + 4 = 7 $ then $\left(\sim p\right)\vee\left(\sim q\right)$ is

If $\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9, $ where $x \in\left(0, \frac{\pi}{2}\right)$, then the value of $x$ is equal to

Let $A$ and $B$ be two mutually exclusive events such that $ P(A\cap {{B}^{c}})=0.25 $ and $ P({{A}^{c}}\cap B)=0.5 $ . Then, $ P\{(A\cup {{B}^{c}})\} $ is equal to

$\int\frac{1+log\,x}{\left(1+x\,log\,x\right)^{2}}dx$ is equal to

If one of the slopes of the pair of lines $ax^2 + 2hxy + by^2 = 0$ is $n$ times the other then

The last digit of number $7^{886}$ is

The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is