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

If \(f,g\) are bounded functions defined on \([a,b]\) and let \(P\) be any partition of \([a,b]\), then which of the following is NOT TRUE?
Which of the following statement is NOT CORRECT?
Let \(R=\{0,1,2,3\}\), under addition and multiplication modulo \(4\) is
The number of ideals in the ring \(\mathbb{Z}_{37}\) is
The characteristic of the ring \((\mathbb{Z}_6,+_6,\times_6)\) is
If \(f(x)=\sin\left(\dfrac{1}{x}\right)\), then \(f(x)\) is _ _ _ _ in \((0,2\pi]\).
Which of the following function is continuous but not uniformly continuous on the real line?
If \(f(x+y)=f(x)f(y),\ \forall x,y\), suppose \(f(3)=3\) and \(f'(0)=11\), then \(f'(3)=\)
The value of \(C\) of Rolle's theorem for the function \(f(x)=\sin x\) in \([0,\pi]\) is
If \(f(x)=1\) when \(x\in Q\) and \(f(x)=-1\) when \(x\in R-Q\), then
If \(f:[a,b]\to R\) is Riemann integrable, then
The values of infimum and supremum of the set \(S=\{x\in \mathbb{R}:x^3\leq x\}\) are
\(\displaystyle \lim_{n\to \infty}\frac{2^{n+1}+3^{n+1}}{2^n+3^n}=\)
The function \(f(x)=x|x|\) is
The function \(f(x)=|x+2|\) is not differentiable at a point
The radius of the sphere whose centre is \((4,4,-2)\) and which passes through origin is
If a plane passes through a fixed point \((a,b,c)\) and cuts the axes in \(A,B,C\), then the locus of the centre of the sphere \(OABC\) is
The equation of the sphere passing through \((1,0,0),(0,1,0),(0,0,1)\) and has its centre on the plane \(x+y+z=6\) is
The angle of intersection of the two spheres \(x^2+y^2+z^2+6y+2z+8=0\) and \(x^2+y^2+z^2+6x+8y+4z+20=0\) is
The distance between the planes \(2x+y+2z=8\) and \(4x+2y+4z+5=0\) is
The equation of the plane which is parallel to \(x+3y+5z+1=0\) and \(5\) units from the origin is
A plane which bisects the angle between the two given planes \(x+2y+2z-2=0\) and \(2x-y+2z-4=0\), passes through the point
The radical plane of the spheres \(x^2+y^2+z^2+4x-2y+2z+6=0\) and \(x^2+y^2+z^2+2x-4y-2z+6=0\) is
The equation of a plane containing the line of intersection of the planes \(2x-y-4=0\) and \(y+2z-4=0\), and passing through the point \((1,1,0)\), is
If \(f(2)=2\hat i-\hat j+2\hat k\) and \(f(3)=4\hat i-2\hat j+3\hat k\), then the value of \(\int_2^3\left(f\cdot\dfrac{df}{dt}\right)dt\) is