List of top Mathematics Questions

The length of the shortest distance between the lines $\vec{r}=3\hat{i}+5\hat{j}+7\hat{k}+\lambda(\hat{i}-2\hat{j}+\hat{k})$ and $\vec{r} = -\hat{i}-\hat{j}-\hat{k}+\mu (7\hat{i}-6\hat{j}+\hat{k})$ is
If x = -9 is a root of A = $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{vmatrix}$ = 0, then other two root are
The values of $\alpha$ for which the system of equation x + y + z = 1, x + 2y + 4z = $\alpha$, x + 4y + 10z = $\alpha^2$ is consistent are given by
An equilateral triangle is inscribed in the parabola y$^2$ = 4x one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is
Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist
If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is
The value of the integral $\int\limits_{0}^{\frac{\pi}{2}} log \left(tan\,x\right)dx=$
The particular integral of $\frac{d^2y}{dx^2}+2y=x^2$is
The distance between the pair of parallel lines $ x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0$ is :
A company received two shipments of ball bearings. In the first shipment, 1 per cent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 percent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, then how many ball bearings were there in the first shipment?
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?
A school has 4 sections of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of the school in that examination is 71.8. Find the ratio of the number of boys to the number of girls that appeared in the examination.
At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is \(\frac{5}{12}\). On walking 192 metres towards the tower, the tangent of the angle of elevation is \(\frac{3}{4}\). The height of the tower is
Students of a class are made to stand in rows. If 4 students are extra in each row, then there would be 2 rows less. If 4 students are less in each row, then there would be 4 more rows. The number of students in the class is
A club consists of members whose ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 years, then the number of members in the club are
A chemist has 10 litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many litres of water must he add?
A can do \(50\%\) more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours?
A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/hr from the usual speed. Find its usual speed.