List of top Questions asked in ICAR AIEEA (PG)- 2021

Which of the following is a method to solve simple non-linear equations by numerical method

If the interval of differencing being unity and $\Delta$ be the forward difference operator, then for constants $a$ and $b$, the value of $\Delta (ab^x)$ is given by

The solution of the differential equation $\frac{dy}{dt} = ky$, $k > 0$ is given by}

A particular integral of the differential equation $\frac{d^2 y}{dx^2} + 3 \frac{dy}{dx} + 4y = 3x + 2$ is given by}

The solution of the initial value problem $\frac{dy}{dx} = -6xy \ ; \quad y(0) = 7$ is given by}

The general solution of $\frac{d^2 y}{dx^2} - \frac{dy}{dx} - 6y = 0$ is given by}

If $\beta(m, n)$, $\Gamma(m)$ and $\Gamma(n)$ for $m > 0, n > 0$ represents beta and gamma functions respectively, then which one of the following is correct?

The necessary and sufficient condition for the differential equation, $M(x, y) dx + N(x, y) dy = 0$ to be exact is given by

If $z = 3x^2 y^3$, $x = t^4$ and $y = t^2$, then using chain rule $\frac{dz}{dt}$ is given by}

The value of $\int (x^2 + 1)^{50} \cdot 2x \, dx$ is given by}

The value of $\int_0^2 x(x^2 + 1)^3 \, dx$ is given by

The value of $\int \frac{\cos x}{\sin^2 x} \, dx$ is given by}

The value of $\iint_R y^2 x \, dy \, dx$ over the rectangle, $R = \{(x, y) : -3 \le x \le 2, 0 \le y \le 1\}$ is given by}

Expansion of $f(x) = \log (1+x)$ by Taylor series is :

For the equation $yz - \ln(z) = x + y$, where $z$ is a function of two independent variables $x$ and $y$ and the partial derivatives exist. The value of $\frac{\partial z}{\partial x}$ is given by}

If the equation $f(x, y) = C$ defines $y$ implicitly as a differentiable function of $x$, and if $\frac{\partial f}{\partial y} \neq 0$, then $\frac{dy}{dx}$ is equal to}

If $z = x^4 \sin(xy^3)$, then the value of $\frac{\partial z}{\partial x}$ at the point (0, 0) is given by}

The curvature of a circle of radius 'a' is

A line $y = L$ is called a horizontal asymptote of the graph of a function $f(x)$ if

The derivative of $f(x) = x^{\sin x}$ is}

Consider the hyperbola $\frac{x^2}{(\cos \theta)^2} - \frac{y^2}{(\sin \theta)^2} = 1$. If $\theta$ changes, which of the following remains constant?}

A line $p x + q y + r = 0$ touches the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Then which of the following statements is true:

The equation of a normal to the parabola $y^2 = 4 x$, which passes through the point (9, 6) is :

The number of common tangents to the circles $x^2 + y^2 - 6x - 14y + 48 = 0$ and $x^2 + y^2 = 6x$ is :

The series $\sum_{n=1}^{\infty} \frac{x^n}{n+1}$ is :