List of top Mathematics Questions asked in AP ECET BSc Mathematics

\[ \frac{1}{D^{3}-3D^{2}+4}\,e^{2x}=\_ \]

\[ \frac{1}{D-a}X=\_ \]

If \[ \mathbf{F}=ax\mathbf{i}+by\mathbf{j}+cz\mathbf{k}, \] where \(a\), \(b\), and \(c\) are constants, and \(S\) is the surface of the unit sphere, then \[ \iint_{S}\mathbf{F}\cdot\mathbf{n}\,dS=\_ \]

If \[ \overline{a}\ \text{and}\ \overline{b} \] are constant vectors and \[ \overline{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}, \] then \[ \nabla\!\left(\overline{r}\cdot(\overline{a}\times\overline{b})\right)=\_ \]

\[ \lim_{x\to0}\frac{e^{\frac{1}{x}}}{e^{\frac{1}{x}}+1}=\,\_ \]

If $\alpha, \beta$ are vectors in an inner product space V, then

Let V be an inner product space and $S = \{\alpha_{1}, \alpha_{2}, \dots, \alpha_{m}\}$ be a finite subset of V. If S is an orthonormal set, then consider the following statements:
I: $||\alpha_{i}|| = 1$ for each $\alpha_{i} \in S$
II: $(\alpha_{i}, \alpha_{j}) = 0$ for $\alpha_{i}, \alpha_{j} \in S, i \neq j$.
Which of the following is correct?

The necessary condition to diagonalize a matrix is that

Which of the following matrices is NOT diagonalizable?

If $\alpha = (-1,0,1), \beta = (2,0,-2) \in V_{3}(R)$ an inner product space, then $||\alpha + \beta|| = $

The matrix $\left[\begin{matrix}1& 4\\ 3& 2\end{matrix}\right]$ is

For the vectors $u = (a,b), v = (c,d)$ in $C^{2}$ the inner product of $u$ and $v$ is defined by $\langle u,v \rangle = a\bar{c} + b\bar{d}$. If $u = (1+i, i), v = (i, 1-i)$ then $\langle u,v \rangle = $

For what values of a and b the following simultaneous equations have an infinite number of solutions? $x + y + z = 5, x + 3y + 3z = 9$, and $x + 2y + \alpha z = \beta$.

The determinant of a skew-symmetric matrix of odd order is

The equation $\left|\begin{matrix}2& 1& 1\\ 1& 1&-1\\ y& x^{2}& x\end{matrix}\right|=0$ represents a parabola passing through the points}

If A and B are square matrices of size $n \times n$, then which of the following statement is not true.

The characteristic equation associated with the matrix $\left[\begin{matrix}0& 0& 3\\ 1& 0& 2\\ 0& 1& 1\end{matrix}\right]$ is

Solution for the system of equations $4y + 3z = 8, 2x - z = 2$ and $3x + 2y = 5$ is

Let $T:R^{3}\rightarrow R^{3}$ be a linear transformation defined by $T(a,b,c)=(a+b-c, a+b+c, b-c)$. Then the matrix of $T$ with respect to the ordered basis $B = \{(0,1,0), (0,0,1), (1,0,0)\}$ is}

If $W=\{\left(\begin{matrix}x& y\\ z& 0\end{matrix}\right):x,y,z\in R\}$ is a subspace of the vector space $M_{2}$ of $2\times2$ matrices over the field of real numbers R, then $dimW=_$

If $T:R^{3}\rightarrow R^{2}$ be a linear transformation defined by $T(a,b,c)=(a+b+c,a-b-c)$, then which of the following is an element in the null space of T.

If T is a linear transformation from $R^{2}\rightarrow R^{2}$ defined by $T(1,-1)=(2,-4)$ and $T(1,1)=(0,2)$. Then $T(a,b)=$

Which of the following sets of vectors in $R^{2}$ are linearly independent over R.

The coordinates of (4,5,6) with respect to the basis set $e_{1}=(1,1,1), e_{2}=(-1,1,0), e_{3}=(1,0,-1)$ are}