List of top Mathematics Questions

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin.Find vertices of the triangle.

Draw a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2). Also, find its area.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8^th set of letter is mailed.

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

Find the 20th term of the series 2×4+4×6+6×8+ ... + n terms.

Find the equation of the hyperbola satisfying the give conditions: Foci (0, \(±\sqrt{10}\)), passing through (2, 3)

Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), \(e = \frac{4}{3}\)

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12.

Find the equation of the hyperbola satisfying the give conditions: Foci (\(± 3\sqrt5, 0\)), the latus rectum is of length 8.

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(49y^ 2 - 16x ^2 = 784\)

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(5y^ 2 - 9x^ 2 = 36\)

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that \(a : b =\sqrt{ (m + √m^2 - n^2) }: (m -\sqrt{ √m^2 - n^2)}.\)

Solve the given inequality for real x: \(x+\frac x2+\frac x3<11\).

Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x)

Suppose f(x) ={ a+bx, x\(<\)1 4, x=1 b-ax x\(>\)1 and if lim x \(\rightarrow\)1 f(x) = f(1), what are possible values of a and b?