List of top Questions asked in AP ECET BSc Mathematics

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.

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 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 $T(a,b)=$

Let $f(x)=2+3x^{2}, g(x)=1+2x^{2}$ be polynomials in the ring $Z_{4}$ under mod 4. Then, $deg\{f(x)g(x)\}=$

Which of the following polynomial is irreducible over $Z_{3}$, a field modulo 3?

Let $A=\left[\begin{matrix}1& 1& 1\\ 2& 2& 3\\ x& y& 2\end{matrix}\right]$ and let $V=\{(x,y,z)\in R^{3}:\det(A)=0\}$. Then the dimension of V equals}

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}

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

Invertible elements in the ring of integers are

The ring of integers (Z, +, $\cdot$) is

The ring of all $2 \times 2$ matrices over reals is

Let Z be the ring of integers and $f: Z \to 2Z$ defined by $f(n)=2n$, $\forall n \in Z$. Then f is

If f is monotonic in [a, b], then f is

For a Riemann integrability, the condition of continuity is

If the function $f(x)$ is bounded and integrable on $[a,b]$ such that $f(x) \ge 0$ $\forall x \in [a,b]$, $b \ge a$ then $\int_{a}^{b} f(x) dx$ is __}

If $f(x)=x,$ $x \in [0,3]$, and $P=\{0,1,2,3\}$ be a partition of [0,3], then $L(P,f)=$

Let $f(x)=\begin{cases}x^{p}cos\frac{1}{x},x\ne0\\ 0,x=0\end{cases}$ Then $f(x)$ is differentiable at $x=0$ if}

The function f is defined by $f(x)=\begin{cases}x^{2}+3x+a,& if~x\le1\\ bx+2,& if~x>1\end{cases}$ is derivable for every x. Then the value of a is}

The value of C of the Cauchy's mean value theorem for the function $f(x)=e^{x}$ and $g(x)=e^{-x}$ defined on $[a,b]$ is}

If $f(x+y)=f(x)+f(y)+x^{2}y+yx^{2},\forall x,y\in R,$ and $\lim_{x\to0}\frac{f(x)}{x}=1$. Then $f'(3)$ is equal to}

If for $x\ne0$ and $f(x)=x^{3}sin\frac{1}{x}, f(0)=0$ then $f(x)$ is}

The least upper bound of the set $\{\frac{3n+2}{2n+1}/n\in N\}$ where N is set of natural numbers is}

Which of the following is a convergent series?

The function $f(x)=(2)^{\frac{1}{x}}$ is not continuous at}