List of top Questions asked in AP ECET BSc Mathematics

If $\phi = 2x^{3}y^{2}z^{4}$ then $\nabla^{2}\phi = $

If $f$ and $F$ are scalar and vector functions respectively, then which of the following is Not Correct?

For a vector $\overline{A}$, which of the following statement is NOT TRUE?

Consider the group homomorphism $f: (Z, +) \to (G = \{i^n : n \in Z\}, \cdot)$ defined by $f(n) = i^n, \forall n \in Z$. Then, $Ker f = $

Choose the WRONG statement

Let H be a subgroup of a group G, where $O(H) = m$ and $O(G) = n$. Then, for any $a \in G$, $O(aH) = $

A noncyclic group among the following is

Consider the following statements:
A. Every finite cyclic group of order n is isomorphic to the group $(Z_n, +_n)$.
B. Every infinite cyclic group is isomorphic to the group (Z, +).
Which of the following statement is TRUE?

The intersection of the subgroups 2Z, 3Z and 5Z, i.e., $2Z \cap 3Z \cap 5Z$ of (Z, +) is

The permutations $f = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 4 & 8 & 2 & 5 & 1 & 3 & 7 & 6 \end{pmatrix}, g = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 5 & 1 & 2 & 8 & 7 & 4 & 3 & 6 \end{pmatrix}$ of $S_8$ are respectively}

The highest power of 3 contained in 100! is

In the group $(R-\{-1\}, *)$ where $*$ is defined by $a*b = a+b+ab, \forall a,b \in R-\{-1\}$, inverse of the element 2 is}

Solution of $\frac{dx}{yz} = \frac{dy}{zx} = \frac{dz}{xy}$ is}

On the set of integers Z, the operation defined as following is not a binary operation.

Particular integral of $(D^{2} + D)y = x^{2} + 2x + 4$ is}

Particular integral of $y'' + y = \cosh 3x$ is

The complementary function of $y'' - 3y' + 2y = e^{3x}$ is}

Particular integral of $\frac{1}{(D - 2)^{2}} e^{2x} = $

The differential equation corresponding to the general solution $y = c_{1} + (c_{2}x + c_{3})e^{2x}$ is}

The general solution of $x^{4}p^{2} = y + px$, $p = \frac{dy}{dx}$ is}

The solution of $y = 2px + 4yp^{2}$ is}

The general solution of $xp^{2} - 2yp + ax = 0$ is where $p = \frac{dy}{dx}$.

The general solution of $4xp^{2} = (3x - a)^{2}$, $p = \frac{dy}{dx}$, is}

Solution of $\frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} + 29y = 0$, $y(0) = 0$ is}

Particular solution of $y'' + y = \cos x$ is