List of top Mathematics Questions asked in AP ECET BSc Mathematics

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

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

For a Riemann integrability, the condition of continuity is

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

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

Invertible elements in the ring of integers are

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

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}

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 __}

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

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

Which of the following is a convergent series?

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

The equation of the plane passing through the midpoint of the line joining the points (1,2,3) and (3,4,5) and perpendicular to it is

Consider the planes: $P_{1}: 3x + 15y + 21z = 9$, $P_{2}: x - 3y - z = 5$, $P_{3}: 2x + 10y + 14z = 5$. Which of the following is TRUE?

The direction ratios of the line $x - y + z - 5 = 0 = x - 3y - 6$ are

If the line $\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$ intersect the curve $xy = c^{2}$ in XY-plane than $c = $

Radius of the circle $x^{2} + y^{2} + z^{2} = 169, x - 2y + 2z = 15$ is}

A non-empty sub-set of real numbers which is bounded below has