List of top Mathematics Questions

If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( x^2 \) is equal to
The value of \( k \) for which the system of equations \( x + ky + 3z = 0 \); \( 3x + ky + 2z = 0 \); \( 2x + 3y + 4z = 0 \) has a non-trivial solution is
Let \( A \) be a square matrix of order 3 and \( |A| \) denote the determinant of \( A \). If \( A = kB \), where \( k \) is a scalar, then \( |A| \) is equal to
On a shelf, 2 books of History, 3 books of Philosophy, and 5 books of Economics are to be arranged in such a way that the books of any subject are kept together. The number of ways this can be done is
A person bought 76 articles and sold 20 articles at 15% profit, 40 articles at 19% profit and remaining 16 articles at 25% profit and got a profit of Rs 6570 as a whole. The cost price of each article is:
The ratio between Rohit's and Vivek's age at present is 5:3. Vivek is 8 years younger than Rohit. The ratio of Rohit's age to Vivek's age after 5 years will be:
Three containers contain alcohol to water in the ratios 3:5, 1:3, and 1:1 respectively. If the solutions of the three containers are mixed in the volume ratio of 1:2:3, then what is the ratio of alcohol to water in the final solution?
Three fair dice are thrown simultaneously. What is the probability that the sum is 5?
The letters of the word CEBADA are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word CEBADA is

The value of the determinant where \( \omega \) is cube root of unity is \[ \begin{vmatrix} \omega^2 & \omega & \omega^2 \\ \omega^2 & \omega & \omega^2 \\ \omega^2 & \omega & \omega^2 \end{vmatrix} \]

If \( z = e^{i\theta} \), then which of the following complex numbers is of unit modulus?
For the matrix \( A = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \), the matrix \( A^{2n} \) has the form
For any positive integer \( n \), the value of \( 1 + 1! + 2.2! + 3.3! + \cdots + n.n! \) will be
If the straight line \( \frac{x}{p} - \frac{y}{q} = 1 \) touches the curve \( \left( \frac{x}{a} \right)^n - \left( \frac{y}{b} \right)^n = 1 \), then
If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a,b)$, then $2b =$
Differentiate \(\frac{\sin x}{\sqrt{\cos x}}\) with respect to x.
The solution of \[ x\frac{dy}{dx}+y=x^4 \] with \[ y(1)=\frac{6}{5} \] is
Which of the following is the solution of \[ p^2+p\left(\frac{y}{x}-\frac{x}{y}\right)-1=0, \] where \[ p=\frac{dy}{dx}\,? \]
General solution of \[ y=x\left(p+\sqrt{1+p^2}\right) \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]
Solution of \[ p^3y+2px-y=0 \] is \(____\), where \[ p=\frac{dy}{dx}. \]
General solution of \[ xp^2-yp+a=0, \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]
The complementary function of \[ (D-2)^2y=8e^{-x} \] is
\[ \frac{1}{(D-2)^2}x^2= \]
\[ e^{-x}\left(c_1\cos\sqrt{3}\,x+c_2\sin\sqrt{3}\,x\right)+c_3e^{2x} \] is the general solution of

The circulation of \(\vec{F}=y\hat{i}+z\hat{j}+x\hat{k}\) around the circle \(x^2+y^2=1,\ z=0\) is ____.