List of top Mathematics Questions asked in AP ECET Agricultural Engg

The eccentricity of the ellipse \[ 16x^2+7y^2=112 \] is

If \((2,0)\) is the vertex and \(y\)-axis is the directrix of a parabola, then its focus is

The equation of the parabola with focus \((2,0)\) and vertex \((1,0)\) is

If length of the tangent is \(8\) cm and the distance between the center of the circle and the external point is \(11\) cm, then the area of the circle is

The length of the tangent from the point \((5,1)\) to the circle \[ x^2+y^2+6x-4y-3=0 \] is

In a circle with center \(O\), a \(6\) cm long chord is at a distance \(4\) cm from the center. Then the length of diameter is

Modulus of the complex number \[ \frac{(1+i)^{10}}{(2i-4)^4} \] is equal to

The real part of \[ \frac{1+2i}{(2-i)^2} \] is

If \(\sin\theta-\cos\theta=\frac{4}{5}\), then the value of \(\sin\theta+\cos\theta\) is

The value of \[ \cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17} \] is

The general solution of the equation \(\tan^2x=1\) is

If \(\sin 5x+\sin 3x+\sin x=0\), then the value of \(x\) other than zero lying between \(0\leq x\leq \frac{\pi}{2}\) is

The maximum value of \(3\cos\theta+4\sin\theta\) is

\[ \sin^6\theta+\cos^6\theta+3\sin^2\theta\cos^2\theta= \]

For real \(x\) and if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is

If \[ 5\sin\theta=4, \] then the value of \[ \frac{\cosec\theta-\cot\theta}{\cosec\theta+\cot\theta} \] is

If \[ \cos\theta \cosec\theta=-1 \] and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)

If \[ \sin\theta=\frac{3}{5}, \] then \(\cos\theta=\)

If \[ \frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}, \] then the values of \((A,B,C)\) are

If \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1}+\frac{B}{x+3}, \] then \(A+B=\)

If the matrix \(A\) is of order \(3 \times 3\) and the system of equations \(AX=B\) has a unique solution, what can be concluded about the determinant of \(A\)?

If \[ A=\begin{bmatrix} a & b \\ c & d \end{bmatrix} \] and the determinant of \(A\) is \(5\), then determinant of the matrix \(2A\) is

\[ \int_{-a}^{a}|x|\,dx= \]

If \[ A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \quad \text{and} \quad B=\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}, \] then \((AB)^T=\)

If \[ A=\begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix} \quad \text{and} \quad A^{-1}=\begin{bmatrix} -2 & 1.5 \\ 1 & -0.5 \end{bmatrix}, \] then the value of \(x\) is