List of top Mathematics Questions

Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x₇} where x₇ denotes multiplication moduls 7?

The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is

If α and β are the roots of a quadratic equation x²+αx + β=0 where β≠0, then what is the value of α + β?

The value of \(\int\limits_C \frac{\sin\pi z^2+\cos\pi z^2}{(z-1)(z-2)}dz\), where C is the circle |z|=3 is

If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)

The solution of (x² -√2y) dx + (y² - √2x) dy = 0 is given by

With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:

The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c₁ and c₂ are arbitrary constants)

The function f(z) defined by \(f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}\)then which one of the following is true?

Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number

In a group G, if a⁵ = e, aba^-1 = b² for a, b ∈ G then o(b) is equal to:

The order of 16 in \((\mathbb{Z}_{24}, +_{24})\) is:

The minimum distance of the point (3, 4, 12) from the sphere x² + y² + z² = 1 is

If \(u=cos^{-1}\frac{x+y}{\sqrt{x}+\sqrt{y}}\), then the value of \(x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}\) is

The integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}\)is

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

The tangent to the hyperbola x²-y² = 3 are parallel to the straight line 2x + y +8=0 points are

The number of common tangents that can be drawn to the circle x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0 is

If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then

The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

Let \(F: R^4 → R^3\) be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals

Let f: R→R such that f(1) =3 and f'(1) = 6. Then \(\lim\limits_{x\rightarrow0}\left(\frac{f(1+x)}{f(1)}\right)^{1/x}\)equals

Let f : Z→ \(Z_2\), be a homomorphism of groups defined by
\(f(a) =   \begin{cases}    0,  & \quad \text{if } a \text{ is even}\\     1,  & \quad \text{if } a \text{ is odd}   \end{cases}\)

then Kerf is : 

The area of the region bounded by the curve x²=4y and the straight line x = 4y - 2 is

The equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0