List of top Mathematics Questions

If the function $f(x)=x^{3}-kx$ is increasing for all real x, then:
Match List-I (Differential equations) with List-II (Order and Degree).
If A is a matrix of order $3\times4$ and B is a matrix such that AB and BA are both defined, then order of B is:
Area of the region bounded by the curves $x=y^{2},\; y=-1,\; y=2$ and y-axis is:
Evaluate \[ \int \frac{1+x+\sqrt{x+x^{2}}}{\sqrt{1+x}+\sqrt{x}}dx \]
Which of the following set of constraints represents the feasible region (shaded portion) in the figure given below?
Value of the determinant \(\begin{vmatrix} \log_{3}512 & \log_{4}3 \\ \log_{3}8 & \log_{4}9 \end{vmatrix}\) is:
General solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+3x^{2}e^{-y} \] is:
Matrix $A=[a_{ij}]_{3\times3}$ where } \[ a_{ij}= \begin{cases} i+j, & i \ne j \\ i-j, & i=j \end{cases} \] Find matrix $A$.
Particular solution of the differential equation \[ \frac{dy}{dx}+2y^{2}=0,\quad y(1)=1 \] is:
If \( y = \sqrt{x} + \frac{1}{\sqrt{x}} \), then \( 2x \frac{dy}{dx} \) is equal to
10 people went to a restaurant to have a meal as a group. Of these, 9 had already contributed Rs 400 each, while the 10th person had to give the entire additional amount required to honour the restaurant's bill. How much did this person pay if he had to pay Rs 900 more than the group's average?
The ratio of alcohol to water in two containers, A and B, is 5:3 and 1:3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litres of liquid, which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?
Rajan invests an amount of INR 15,860 in the names of his three sons Rohan, Sohan and Mohan in such a way that they get the same amount after two, three and four years respectively. If the rate of simple interest is 5% then the ratio of amounts invested among Rohan, Sohan and Mohan will be
Five years ago, A was three times as old as B. Now, A is twice as old as B. What is A's current age?
X,Y,W,Z jointly purchased an office space for Rs 84 lakhs. The amount contributed by Y, W and Z put together is three times of X. The amount contributed by X, W and Z put together is 320% of Y. Further, the amount contributed by W is 20% of X, Y and Z put together. What is the contribution of Z?
Suppose the price of liquefied petroleum gas (LPG) increases by 16%, by how much percentage should the consumption of LPG be reduced by the household in order to keep the expenditure on LPG at the same level? (Rounded to two decimals)
Kartik has three solid objects — a cone, a hemisphere, and a cylinder. All three have the same base radius and the same height. He completely immerses each solid in a bucket full of water. What is the ratio of the volumes of the cylinder: cone: hemisphere?
Consider the sequence: 72, 69, 66, ---. The numbers continue in the same pattern as long as they remain positive. What will be the maximum possible sum of the terms of this sequence?
In a school, 70 play only hockey, 100 play only football, 30 play both the games. 150 do not play anything at all. What is the percentage (rounded to two decimals) of hockey players to total students in the school?
A researcher found that 70% of people who own a cat also own a dog, but only 20% of dog owners also own a cat. If there are 1,001 dog owners, how many cat owners are there?
An examination consists of 160 questions. One mark is given for every correct option. If a 1/4 mark is deducted for each wrong option and a half mark is deducted for every unanswered question, the person scores 79. If half a mark is deducted for every wrong option and 1/4 mark is deducted for every unanswered question, the person scores 76. Find the number of correct answers he wrote?
The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is
Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?
Say 10600 is divided into positive quantities A, B, C, and D. Use the following information to find the value of D: If you remove A, the average of the other 3 numbers is 1000. If you remove B, the average of the other 3 numbers is 3220. If you remove C, the average of the other 3 numbers is 3180.