List of top Questions asked in AP ECET BSc Mathematics- 2025

Choose the correct option to arrange the words in the jumbled sentence to make it meaningful.

\[ \text{A comic story / to the students / was told / by our new teacher.} \]
\[ \text{A \_ \_ \_ \_ B \_ \_ \_ \_ C \_ \_ \_ \_ D} \]
Choose the correct option to arrange the words in the jumbled sentence to make it meaningful.

\[ \text{Rose flowers / are plucking / the children / in the garden.} \]
\[ \text{A \_ \_ \_ \_ B \_ \_ \_ \_ C \_ \_ \_ \_ D} \]
Choose the correct option to arrange the words in the jumbled sentence to make it meaningful.

\[ \text{The young man / by the committee / was selected / for scoring 100 runs.} \]
\[ \text{A \_ \_ \_ \_ B \_ \_ \_ \_ C \_ \_ \_ \_ D} \]
Choose the correct option to arrange the words in the jumbled sentence to make it meaningful.

\[ \text{By all the people / is always / respected / an honest man.} \]
\[ \text{A \_ \_ \_ \_ B \_ \_ \_ \_ C \_ \_ \_ \_ D} \]
The solution of \[ x\frac{dy}{dx}+y=x^4 \] with \[ y(1)=\frac{6}{5} \] is
Which of the following is the solution of \[ p^2+p\left(\frac{y}{x}-\frac{x}{y}\right)-1=0, \] where \[ p=\frac{dy}{dx}\,? \]
General solution of \[ y=x\left(p+\sqrt{1+p^2}\right) \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]
Solution of \[ p^3y+2px-y=0 \] is \(____\), where \[ p=\frac{dy}{dx}. \]
General solution of \[ xp^2-yp+a=0, \] is \( \_\_\_\_ \), where \[ p=\frac{dy}{dx}. \]
The complementary function of \[ (D-2)^2y=8e^{-x} \] is
\[ \frac{1}{(D-2)^2}x^2= \]
\[ e^{-x}\left(c_1\cos\sqrt{3}\,x+c_2\sin\sqrt{3}\,x\right)+c_3e^{2x} \] is the general solution of

The circulation of \(\vec{F}=y\hat{i}+z\hat{j}+x\hat{k}\) around the circle \(x^2+y^2=1,\ z=0\) is ____.

If the plane \(x-2y-2z=k\) touches the sphere \(x^2+y^2+z^2-2x+4y-6z+5=0\), then the value of \(k\) is ____.

Let \(S_n=\displaystyle\sum_{k=1}^{n}\frac{n}{n^2+k}\), for \(n\in N\). Then the sequence \(\{S_n\}\) is ____.

The series \(\displaystyle\sum_{n=0}^{\infty}(2x)^n\) converges if ____.

The polynomial \(x^2+9\) is reducible over ____.

If \(W\) is a subspace of \(V^3\), where \[ W=\{(a,b,c)\mid a+b+c=0\}, \] then \(\dim W=\)

Let \(T:\mathbb{R}^3\to\mathbb{R}^3\) be defined by \(T(a,b,c)=(-a-b,a-b,0)\), then ____.

If \(T:\mathbb{R}^2\to\mathbb{R}^2\) is a linear transformation defined by \[ T(x,y)=(x,0), \] then the matrix of \(T\) relative to the basis \[ B=\{(0,1),(1,0)\} \] is \(____\).

If \[ P= \begin{pmatrix} 1 & a & b\\ 0 & 2 & c\\ 0 & 0 & 1 \end{pmatrix}, \quad a,b,c\in\mathbb{Z}, \] then \(P\) is diagonalizable iff ____.

What is missing in the blank below?

\[ \text{ABD},\ \text{EFH},\ \_ \_ \_ \_,\ \text{MNP},\ \text{QRT} \]
What is missing in the blank below?

\[ 50:65::290:\ \_ \_ \_ \_ \]
What is missing in the blank below?

\[ V,\ S,\ P,\ M,\ \_ \_ \_ \_ \]
What is missing in the blank below?

\[ \text{AEF}:\text{BIJ}::\ \_ \_ \_ \_ :\text{QUV} \]