List of top Mathematics Questions

If the sum of the coefficients in the expansion of \( (x + y)^n \) is 1024, then the value of the greatest coefficient in the expansion is:
If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:
Given \[ \frac{dy}{dx} \tan x = y \sec^2 x + \sin x, \quad {find the general solution:} \]
The area of the region bounded by the parabola \( (y - 2)^2 = (x - 1) \), the tangent to the parabola at the point \( (2, 3) \), and the X-axis is:
For each parabola \( y = x^2 + px + q \), meeting the coordinate axes at three distinct points, if circles are drawn through these points, then the family of circles must pass through:
If \( a_1, a_2, \ldots, a_n \) are in AP, then evaluate the following expression: \[ \frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \cdots + \frac{1}{\sqrt{a_n} + \sqrt{a_{n+1}}} \]
In the given figure, ABCD is a rectangle. AB is 3m and BC is 2m. It is given that CF is 1m. AF intersects CD at E, and it is known that BE is parallel to HG and GE is perpendicular to AB. Find the length of HG (in m).
ABCD is a rectangle. AB is 3m and BC is 2m.
A work was completed by three persons of equal ability, first one doing \( m \) hours for \( m \) days, second one doing \( n \) hours for \( n \) days (where \( m \) and \( n \) are integers) and third one doing 16 hours for 16 days. The work could have been completed in 29 days by the third person alone with his respective working hours. If all of them do the work together with their respective working hours, then they can complete it in about:
ABCD is an isosceles trapezium with angle \( A = 45^\circ \) and the length of one of the non-parallel sides is \( 10\sqrt{2} \). The area of triangle \( ABD \) is 200 sq. units. What is the sum of the lengths of the parallel sides?
In triangle ABC, two points P and Q are on AB and BC respectively such that \( \frac{AP}{BP} = 1 : 4 \) and \( \frac{BQ}{CQ} = 2 : 3 \). The ratio of areas of triangle BPQ and the quadrilateral PQCA is:
Metal A costs Rs. 8.40 per gm and metal B Rs. 0.21 per gm. In what proportion must these metals be mixed so that 1 gram of the mixture may be worth Rs. 5.67?
Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.
A man’s petrol bill in July is Rs. 200. In August, the price of petrol increases by 10% and his consumption is reduced by 10%. Find his petrol bill in August.
A motorcyclist covers 4 successive 4 km stretches at speeds of 20 kmph, 30 kmph, 40 kmph, and 50 kmph respectively. Find the average speed over the total distance.
If each of the dimensions of a rectangle is increased by 100%, then the area is increased by?
A square pyramid with a side of 10 cm has a volume of 400 cm\(^3\). Find the total surface area of the pyramid.
PBA and PDC are two secants. AD is the diameter of the circle with centre at O. \( \angle A=40° \), \( \angle P=20° \). Find the measure of \( \angle DBC \).
AD is the diameter of the circle with centre at O.
Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.
A student walks from his house at \( \frac{5}{2} \) km/h and reaches his school late by 6 minutes. Next day, he increases his speed by 1 km/h and reaches 6 minutes before school time. How far is the school from his house?
In \(\Delta ABC\), given \(AC = BC\) and \(DE\) is the diameter of the circle. \(AC\) and \(BC\) touch the circle at points \(M\) and \(N\), respectively. If \( \angle ADP = \angle BEQ = 100^\circ \), find \( \angle PRD \).
AC and BC touch the circle at M and N
The lengths of perpendiculars drawn from any point inside an equilateral triangle are \(a_1\), \(a_2\) and \(a_3\) respectively. Find the length of the side of the equilateral triangle.
In an isosceles triangle \( PQR \) with \( PQ = PR \), PT and PZ trisect \( QR \) such that \( QT = TZ = ZR \). If \( \angle TPZ = \angle PQR \) and the area of triangle \( PQR \) is equal to \( \frac{27\sqrt{7}}{4} \), then find \( PR \).
ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?
A square of perimeter 88 cm and a circle of perimeter 88 cm are given. Which figure has larger area and by how much?
ABCD is a rectangle as shown in the figure. AB = 8 cm and BC = 6 cm. BE is the perpendicular drawn from B to the diagonal AC. EF is the perpendicular drawn from E to AB. What is the length of BF?
ABCD is a rectangle