List of top Mathematics Questions

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
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.
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 ........
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 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:
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:
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?
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?
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 .......
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?
In 25 days, 30 men complete 15 projects. In how many days can 14 men complete 7 projects?
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 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?
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.

If the line x – 1 = 0 is a directrix of the hyperbola kx2 – y2 = 6, then the hyperbola passes through the point

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
\((2, a),−\frac{1}{2}<a<2 \)
then p is equal to _______.

If\(\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}\)is equal to 2n. m, where m is odd, then n + m is equal to ______.
Let R be a relation from the set \(\{1, 2, 3, ….., 60\}\) to itself such that \(R = \{(a, b) : b = pq,\) where \(p, q≥ 3\) are prime numbers\(\}\). Then, the number of elements in R is :
A cable network provider in a small town has 500 subscriber and he used to collect Rs. 300 per month from each subscriber. He proposes o increase the monthly charges and it is believed from the past experience that for every increase of Rs. 1, one subscriber will discontinue the service.
Based on the above information answer the following question:
What is the increase in the changes per subscriber that yields maximum revenue?

Let Q and R be two points on the line 
\(\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}\) at a distance \(\sqrt{26}\) 
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), 

\(y=12(1+sint)^2,0<t<\frac{π}{2}, \)

with the positive x-axis is π/3, then y0 is equal to

Let A and B be two events such that
 \(\begin{array}{l} P\left(B/A\right)\frac{2}{5},\ P\left(A/B\right)=\frac{1}{7}\ \text{and}\ P\left(A\cap B\right)=\frac{1}{9}.\end{array} Consider \begin{array}{l} \left(S1\right)P\left(A’\cup B\right)=\frac{5}{6},\end{array}\)
\(\begin{array}{l} \left(S2\right)P\left(A’\cap B’\right)=\frac{1}{18}.\end{array}\)Then
If the plane 2x + y – 5z = 0 is rotated about its line of intersection with the plane 3x – y + 4z – 7 = 0 by an angle of π/2, then the plane after the rotation passes through the point:
In an isosceles triangle ABC, the vertex A is \((6, 1)\) and the equation of the base BC is \(2x + y = 4\). Let the point B lie on the line \(x + 3y = 7\). If \((α, β)\) is the centroid of ΔABC, then \(15(α + β)\) is equal to :