List of top Mathematics Questions

The set of all values of k for which
\((\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in R\)
, is the interval :
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
The remainder when \(3^{2022}\) is divided by 5 is :
Let
\(A = \{z \in C : 1 \leq |z-(1+i)| \leq 2\}\)
and
\(B = \{z \in A : |z-(1-i)| = 1\}\)
. Then, B :
\((p\wedge r)\Leftrightarrow(p\wedge(\sim q))\) is equivalent to \((\sim p)\) when \(r\) is
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.
N\(^2\) leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?
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?
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?
Four years ago, ages of A and B were respectively thrice and twice that of the age of C. If the total of their ages is 48, then the present age of B is.
A certain amount earns simple interest of Rs. 2,550 after 8 years. Had the rate of interest been 3% more, how much interest would it have earned?
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.
In 25 days, 30 men complete 15 projects. In how many days can 14 men complete 7 projects?
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 \( PR \).
The ratio of diameter to its height of a cylindrical pillar is 7 : 3. The volume of the pillar is 924 m\(^3\). Its curved surface area is .......
In the given figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that \( AE : EB = 1 : 2 \), and DF is perpendicular to MN such that \( NL : LM = 1 : 2 \). The length of DH in cm is:
AB and MN are two diameters
Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8, and 8 on division by 9?
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:
If each of the dimensions of a rectangle is increased by 100%, then the area is increased by?
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
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 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:
In a certain school, 25% of students are below 10 years of age. The number of students above 10 years of age is 3/5 of the number of students of 10 years of age, which is 75. What will be the total number of students in the school?
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.
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.