List of practice Questions

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.
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 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 \(\Delta ABC\), 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?
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.
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:
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 .......
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:
A bag contains 4 black, 6 yellow, and 8 red balls. Three balls are drawn at random from the bag. The probability that all of them are yellow is .......
In 25 days, 30 men complete 15 projects. In how many days can 14 men complete 7 projects?
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.
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?
In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
Various terms of a series are given with one term missing as shown by (?). Choose the missing term. \[ \text{QPO, SRQ, UTS, WVU, (?)} \]
Various terms of a series are given with one term missing as shown by (?). Choose the missing term.\[ 19, 2, 38, 3, 114, 4, (?) \]
Various terms of a series are given with one term missing as shown by (?). Choose the missing term.\[ YES, WFD, UHG, SKI, (?) \]
Various terms of a series are given with one term missing as shown by (?). Choose the missing term.\[ AZ, CX, FU, (?) \]
Various terms of a series are given with one term missing as shown by (?). Choose the missing term.\[ 225, 7Y7, 14X9, 23W11, 34V13, (?) \]
An application was received by inward clerk in the afternoon of a week day. Next day, he forwarded it to the table of the senior clerk, who was on leave that day. The senior clerk put up the application to the desk officer next day in the evening. The desk officer studied the application and disposed off the matter on the same day, i.e. Friday. The application was received by the inward clerk on.