List of top Mathematics Questions

If \(\frac{dy}{dx}\) = y+7 and y(0) = 0, then the value of y(1) is?
Let $A$ be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a If $P(A)=\frac{11}{36}$, then a is equal to _____
The remainder when $(11)^{1011}+(1011)^{11}$ is divided by $9$ is

In a given data set mean of 40 observations is 50 and standard deviation is 12. Two readings which were 20 and 25, were mistakenly taken as 40 and 45. Find correct variance of data set

$\displaystyle\lim _{x \rightarrow 0} \frac{48}{x^4} \int_0^x \frac{ t ^3}{ t ^6+1} d t$ is equal to
The coefficient of $x^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is______
The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to
The value of the sum of 10 term of the series
\(S_{10}=\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...\)
A person walks from his house to his office at a speed of x1 km/hr and returns by the same route at a speed of x2 km/hr. What is his average speed ?
Let y = y(x), y>0, be a solution curve of the differential equation (1 + x2) dy=y (x–y)dx. If y(0)=1 and y(2√2) , = b then
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?
Let $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then
Find the number of integral values of x which satisfy the inequality x2–10x+19<6. 
 
A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :
Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)
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?
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:
Let $z_1=2+3 i$ and $z_2=3+4 i$ The set $S=\left\{z \in C:\left|z-z_1\right|^2-\left|z-z_2\right|^2=\left|z_1-z_2\right|^2\right\}$ represents a
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 mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?

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 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 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 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?