List of top Mathematics Questions

If A is symmetric real valued matrix of dimension 2022, then eigenvalues of A are

A solar photovoltaic system feeds power to a motor of 1hp at the shaft. The motor has an efficiency of 85%. Each module has 40 multi crestline Silicone solar cells arranged in 9x5 matrix? The cell is 130 mm×130 mm and the cell efficiency is 13%. Calculate the number of photovoltaic modules required, assuming global radiation incident to the panel as 1kW/m²

The line integral of function \(F = yz\hat{i}\), in the counter clockwise direction, along the circle x² + y² = 1 at z = 1 is

Which property is true for convolution integral?
A.$ h_1(t)*h_2(t)=h_2(t)*h_1(t) $
B. $[h_1(t)+h_2(t)]* h_3(t) = h_1(t)* h_3 (t) +h_2 (t) * h_3(t)$
C. $[h_!(t)+h_2(t)]*h_3(t) = h_1(t)h_3(t)+h_2(t)h_3(t) $
D. $h_1(t)*h_2(t)=h_2(t)h_1(t) $
Choose the correct answer from the options given below.

The value of \(∫_0^{2\pi} sin^{2}nxdx\), where \(n∈I\), is:

What is the volume of a 6m deep tank having rectangular shaped top 6mx4m and bottom 4mx2m (compound through the use of prismoidal formula)

A, B, C and D entered into a partnership. 'A' contributed one-third of the capital, 'B' contributed one-fourth, 'C' contributed one-fifth and 'D' contributed the rest. All four of them agreed to share profit in the ratio of their capital. What is the share of 'D' when total profit is ₹6000?

The system matrix of a linear time invariant continuous time system is given by \(A= \begin{bmatrix} 0 & 1 \\ -4 & -5 \end{bmatrix}\)
What are the roots of characteristics equation.

A cone of height at 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is:

The bus admittance matrix of a power system is given as.
1     2                3
\( 1\\2\\3 \begin{bmatrix}-j50 &+j10 &+j5\\+j10&-j30&+j10\\+j5&+j10&-j25\end{bmatrix}\)
The impedance of line between bus 2 and bus 3 will be equal to____

For Matrix \(A = \begin{vmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1  \end {vmatrix}\), the sum and differences of maximum & minimum 1 eight value of Matrix are 4 and 8, then the eigen values for the Matrix A are. 

$ \begin{vmatrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1=d  \end{vmatrix} $ is equal to

Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The state transition matrix represents the free response of the system.
Reason R: The state transition matrix satisfies the homogeneous state equation
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A): The numeric differences in the forecast of demand and actual demand is known as forecast error (e).
Reasons (R): Mean Absolute Deviation \((MAD) = \frac{Σ|e|}{n}\).
In the light of the above statements, choose the most appropriate answer from the options given below:

The mathematical statement regarding Divergence theorem which is true:

The area of surface of solid generated by the revolution of line segment y = 2x from x = 0 to x = 2 about x-axis is equal to:

Let f (x) be defined on [0, 3] by \(f(x) =   \begin{cases}     x,\text{if x is a rational number}       \\  3-x\text{, if x is an irrational number}   \end{cases}\) Then f(x) is continuous in the interval at:

Let f: G→H be a group homomorphism from group G into group H with kernel K. If the order of G, H and K are 50, 25 and 10 respectively then the order of f(G) is

The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are

If the cost function and revenue of x unit of an item are given by C(x)=25x²-x and R(x)=4x. Then the number of item to be produced to have maximum profit is,

For the two positive numbers \(a, b\), if \(a, b\) and \(\frac{1}{18}\) are in a geometric progression, while \(\frac{1}{a}, 10\) and \(\frac{1}{b}\) are in an arithmetic progression, then \(16 a+12 b\) is equal to

Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to

The integral \(16 \int\limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\)  is equal to