List of top Mathematics Questions

Match List-I and List-II

LIST I		LIST II
A.	No. of triangles formed using 5 points in a line and 3 points on parallel line is	I.	20
B.	No. of diagonals drawn using the vertices of an octagon	II.	10
C.	The no. of diagonals in a regular polygon of 100 sides is	III.	45
D.	A polygon with 35 diagonals has sides	IV.	4850

Choose the correct answer from the options given below:

A triangle with vertices (4, 0), (-1,-1), (3, 5) is

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:

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 f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]²+[g(x)]² and h(5)=11, then h(10) =

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

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

The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is

The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) is:

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

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

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

The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval

Given below are two statements
Statement I: Let G a finite group and H a subgroup of G. Then, the order of H is a divisor of the order of G. That is, |H| divides |G|
Statement II: Let a be an element in a finite group G. Then, O(a) divides |G|
In the light of the above statements, choose the most appropriate answer from the options given below

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?

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

The sequence is

Given below are two statements
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below

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

The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)

The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c₁ and c₂ are arbitrary constants)

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

Which one of the following statements is wrong.

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