List of top Mathematics Questions

If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

Consider the linear mapping F: R² →R² defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R²: E= {e₁, e₂} = {(1, 0), (0, 1)} and S = {u₁, u₂} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:

If λ₁,λ₂,λ₃ are the given values of the matrix \(\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\), then λ₁²+λ₂²+λ₃² is equal to

The dimension of the general solution space W of the homogeneous system
x₁+2x₂-3x₃+2x₄-4x₅=0
2x₁+4x₂-5x₃+x₄-6x₅ = 0
5x₁+10x₂-13x₃+4x₄-16x₅= 0

If A=\(\begin{bmatrix} 1 & 2 & 0 & -1\\   2 & 6 & -3 & -3\\  3 & 10 & -6 & -5 \end{bmatrix}\), then which one of the following is true?

If income of A is 20% more than that of B, then income of B is how much percent less than that of A?

The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x₁+3x₂+4x₃+5x₄ = 6

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

If \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is

If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is

if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are three non-coplanar vectors, then \((\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]\) equal to

If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to

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

Which one of the following is wrong?

If P(x) is a polynomial of degree 10 with leading coefficient as 11 and having (x-1), (x-2), (x-3),...(x-10) as factor, then the coefficient of x⁹ in P(x) is

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

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

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

Which one of the following is not correct?

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

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)² + .... then f(z) 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

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

The area of region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 is