List of top Mathematics Questions

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 &  3\\ 2 & 7\end{bmatrix}\)
Find out the degree of the differential equation \(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)
For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?
A box of dimensions 25cm x 30cm x 45cm is to be painted. A container which contains colour has a capacity to paint 1075cm2. How many containers are required to paint the box completely?
The average age of three boys is 22 years. Eight times the age of the youngest of them is 3 times the sum of the ages of the other two boys. Find the age of the eldest of them if he is 8 years older to the youngest of them.
The length of a rectangular plot is 30 m more than its breadth. If the cost of fencing the plot @ 25 per meter is Rs. 5000, what is the length of the plot in m?

Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Then the inradius of the triangle ABC is

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number pair?
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)
Three containers have their volumes in the ratio 3:4:5. They are full of mixture of milk and water in the ratio 4:1, 3:1 and 5:2 respectively. The mixtures from all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is:
The difference between simple interest and compound interest on a certain sum at 5% per annum for 2 years is ₹25. What is the sum invested?
Ayan borrowed Rs. 50,000 from Ayush on 25th April, 2022 at 12% p.a. simple interest. Ayan cleared his debt on 18th September, 2022. How much interest is paid by Ayan?
If the rate of annual simple interest is \(11\frac{1}{2}\%\) , then how much money need to be deposited 2 to have ₹ 8,906 in total after 4 years?
The produce of a square field when sold at the rate of Rs. 1.50 per 100 sq. meters fetches Rs. 1350. What will be the cost of putting a fence all-round the field at the rate of 50 paise per meter?
Let M=(aij), i,j∈{1,2,3}, be the 3×3 matrix such that aij=1 if j+1 is divisible by i,otherwise aij=0. Then which of the following statements is(are) true? 
Let S be the set of all twice differentiable functions f from R to R such that \(\frac{d^2f}{dx^2}(x)>0\) for all x∈(-1,1). For f∈S, let Xf be the number of points x∈(-1,1) for which f(x)=x.Then which of the following statements is(are) true? 

Let the position vectors of the points P, Q, R and S be
\(\vec{a}=\hat{i}+2\hat{j}-5\hat{k}\), \(\vec{b}=3\hat{i}+6\hat{j}+3\hat{k}\), \(\vec{c}=\frac{17}{5}\hat{i}+\frac{16}{5}\hat{j}+7\hat{k}\) and \(\vec{d}=2\hat{i}+\hat{j}+\hat{k}\)
respectively. Then which of the following statements is true?

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are the same. If the probability of a random toss resulting in a head is \(\frac{1}{3}\), then the probability that the experiment stops with the head is
The speeds of A and B are in the ratio 3:4. A takes 20 minutes more than B to reach the destination. In what time does A reach the distination?
A window is in the form of a rectangle surmounted by a semicircle. Perimeter of the window is 4.6m and height of the rectangular portion is 0.5m, then find the radius of the semicircular portion. (Take \(\pi=\frac{22}{7}\))
A vegetable vendor buys 100kg tomatoes at the rate of Rs18 and spent Rs120 as cartage. He sells 80Kg tomatoes at Rs25/kg and 16kg tomatoes at Rs20/kg. Remaining tomatoes got rotten and could not be sold. Find his profit percentage (correct to one decimal place)
The average of 5 consecutive positive integers starting with m is n. What is the average of 6 consecutive positive integers starting with (m+2)?
Jayant invested a sum of Rs. 65,000 in two schemes and received Rs.7275 as interest after 2 years. In scheme I simple interest is payable at 6% per annum and in scheme II compound interest is payable at 5% per annum Find the ratio of sums he invested in scheme I and scheme II.
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time taken to fill the tank?
Which of the following is a relative measure of dispersion?