List of top Water Science and Technology Questions on Mathematics asked in ICAR AIEEA (PG)

The derivative of x$^2$ cos x is _____________

What is the nature of the roots of the quadratic equation X$^2$--6X+9=0

The differential equation corresponding to \(y = e^{mx}\) by eliminating \(m\) is

Solve the differential equation
\[ \cos x \frac{dy}{dx} - \cos 2x = \cos 3x \]

Solve
\[ y e^{x/y} dx = (x e^{x/y} + y^2) dy, \quad y \neq 0 \]

The procedure adopted in the Gauss- Jordan method in solving linear simultaneous equation is that
A. It is required to assume initial approximate values of the variables
B. It reduces the given system of equation to an equivalent triangular system
C. It reduces the given system of equation to a diagonal matrix
D. The given matrix is factored into lower and upper triangular matrix
Choose the correct answer

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The polynomial equation \(x(x+1) + 8 = (x+2) \times (x-2)\) is a linear equation.
Reason R: There is only one variable.
In light of the above statements, choose the correct answer:

Given below are two statements
Statement I: A quadratic equation can have three distinct real roots.
Statement II: In quadratic equation \(ax^2 + bx + c = 0\), if \(b^2 - 4ac = 0\), then the quadratic equation has real and equal roots.
In the light of the above statements, choose the correct answer from the options given below:

The differentiation of the \(\sin(x^2 + 1)\) function with respect to \(x\), will be

What is the value of the determinant \(\begin{vmatrix} 1 & 2 1 & 3 \end{vmatrix}\)?

Which differential equation would be obtained, if the boundary layer transition from a boundary of zero thickness and the lateral inflow is zero in canal?

\(\frac{d}{dx}(\sec x) =\)

The arithmetic mean of the series \(1, 2, 4, 8, 16, \dots, 2^n\) is

The order and degree of the differential equation \(\frac{d^2 y}{dx^2} + \sqrt{x + \left(\frac{dy}{dx}\right)^3 = 0\) is}

\(\int_0^{\pi/2} \cos x \cdot e^{\sin x} \, dx\) is equal to

If \(f(\theta) = e^{\sin \theta\), then \(f'(\theta) = 0\) for which value of \(\theta\)}

If \(x^y = e^{x-y}\), \(\frac{dy}{dx} = ?\)

If x is real, the minimum value of \(f(x) = x^2 - 8x + 17\) would be