List of top Mathematics Questions

Let the locus of the centre (α, β), β> 0, of the circle which touches the circle x2 +(y – 1)2 = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:
The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point Q(k1, k2), then k1 + k2 is equal to :
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 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.
If \( a_1, a_2, \ldots, a_n \) are in AP, then evaluate the following expression: \[ \frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \cdots + \frac{1}{\sqrt{a_n} + \sqrt{a_{n+1}}} \]
The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11:37. What will be the rate of interest?
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:
A household wants to diversify his investment and invest Rs. 24,000 as a part of it at the rate of 10% per annum. But due to some pressing needs, he has to withdraw the entire money after 3 years, for a lower rate of interest. If he gets Rs. 6,640 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is:
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?
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.
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 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?
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?
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.
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
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.
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?
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