List of top Mathematics Questions asked in MAT

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?
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
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?
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?
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.
A square pyramid with a side of 10 cm has a volume of 400 cm\(^3\). Find the total surface area of the pyramid.
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 \(\Delta ABC\), 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.
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?
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
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 \( PR \).
A square of perimeter 88 cm and a circle of perimeter 88 cm are given. Which figure has larger area and by how much?
Two times a two-digit number is 9 times the number obtained by reversing the digits and sum of the digits is 9. The number is ........
Ram sold 10 acres of land to Mani and Dinesh who paid him the total amount in the ratio of 2 : 3. Mani invested a further Rs.3 lakh in the land for the purpose of planting coconut and lemon trees in the ratio of 4 : 1. These trees were planted on equal areas of land. There were a total of 200 lemon trees. The sale price of one coconut was Rs.10 in 2019. The crop took 7 years to mature and when the crop was reaped in 2019, the total revenue generated was 50% of the total initial amount put in by Mani and Dinesh together. The revenue generated from the coconut and lemon trees was in the ratio of 5 : 4 and it was shared equally by Mani and Dinesh as the initial amount spent by them was equal.
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?
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?
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If tap A is open all the time and tap B and tap C are open for one hour each alternately, the tank will be filled in:
The ratio of the number of boys and girls in a college is 5 : 4, if the percentage decrease in the number of boys is 30% and the percentage increase in the number of girls is 5%. The new ratio will be:
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs.5,100 more. The sum is ........
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 .......