List of top Mathematics Questions

If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
If the number of diagonals of a regular polygon is 35, then the number of sides of the polygon is
If \( x^6 = (\sqrt{3}-i)^5 \), then the product of all of its roots is
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
The points in the Argand plane represented by the complex numbers \(4\hat{i}+3\hat{j}\), \(6\hat{i}-2\hat{j}-3\hat{k}\) and \(\hat{i}-\hat{j}-3\hat{k}\) form
If the values \( x = \alpha, y = \beta, z = \gamma \) satisfy all the 3 equations \(x+2y+3z=4\), \(3x+y+z=3\) and \(x+3y+3z=2\), then \(3\alpha + \gamma = \)
If \( z = x+iy \) and \(x^2+y^2=1\), then \( \frac{1+x+iy}{1+x-iy} = \)
If \( \alpha \neq 0 \) and zero are the roots of the equation \( x^2 - 5kx + (6k^2-2k) = 0 \), then \( \alpha = \)
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:
Find the area (in square units) of the region bounded by the lines \( x=0 \), \( x=\frac{\pi}{2} \), and the curves \( f(x) = \sin x \), \( g(x) = \cos x \):
The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:
Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]
Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]
The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:
Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]
Evaluate the integral: \[ \int \frac{x^4-16x^2+2x+8}{x^3-4x^2+2}dx \]
Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]
Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]
If the lengths of the tangent, subtangent, normal, and subnormal for the curve \( y = x^2 + x - 1 \) at the point \( (1,1) \) are \( a, b, c, \) and \( d \) respectively, then their increasing order is:
Evaluate the integral: \[ I = \int_0^x \frac{t^2}{\sqrt{a^2 + t^2}} dt \]