List of top Questions asked in AP EAPCET

If \(A(\cos \alpha, \sin \alpha)\), \(B(\sin \alpha, -\cos \alpha)\), and \(C(1, 2)\) are the vertices of \(\triangle ABC\), then find the locus of its centroid.
If the axes are translated to the orthocentre of the triangle formed by points \(A(7,5), B(-5,-7), C(7,-7)\), then the coordinates of the incentre of the triangle in the new system are?
Line \(L_1\) passes through the points \(\mathbf{i} + \mathbf{j}\) and \(\mathbf{k} - \mathbf{i}\). Line \(L_2\) passes through the point \(\mathbf{j} + 2\mathbf{k}\) and is parallel to the vector \(\mathbf{i} + \mathbf{j} + \mathbf{k}\). If \(\mathbf{x}i + \mathbf{y}j + \mathbf{z}k\) is the point of intersection of the lines \(L_1\) and \(L_2\), then find \((y - x) =\)
A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house gets at most one sample. The probability that no two consecutive houses get one sample is:
A and B are two independent events of a random experiment and \(P(A)>P(B)\). If the probability that both A and B occur is \(\frac{1}{6}\) and neither of them occurs is \(\frac{1}{3}\), then the probability of the occurrence of B is:
Evaluate: \(\tanh^{-1}\left(\frac{1}{3}\right) + \coth^{-1}(3) =\)
In \(\triangle ABC\), if the line joining the circumcentre and incentre is parallel to \(BC\), then find \( \cos B + \cos C \).
In a triangle \(ABC\), if \(r_1 : r_2 = 3 : 4\) and \(r_1 : r_3 = 2 : 3\), then find the ratio \(a : b : c\).
Let \(\mathbf{a} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}\) and \(\mathbf{b} = 6\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) be two vectors. If \[ |\mathbf{a} \times \mathbf{b}|^2 + |\mathbf{a} . \mathbf{b}|^2 = f(x,y)(x+y) - 46 = 0, \] then what does this represent?
Evaluate: \(\tan\left(2\tan^{-1}\left(-\frac{1}{3}\right) + \tan^{-1}\left(\frac{1}{7}\right)\right) =\)
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
Assertion (A): $S_3 = 55 \times 2^9$
Reason (R): $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$
If \[ \frac{2x^4 - 3x^2 + 4}{(x^2 + 1)(x^2 + 2)} = a + \frac{px + q}{x^2 + 1} + \frac{mx + n}{x^2 + 2}, \] then $\frac{n}{q} =$
Evaluate \[ (4 \cos^2 \frac{\pi}{20} - 1)(4 \cos^2 \frac{3\pi}{20} - 1)(4 \cos^2 \frac{5\pi}{20} - 1)(4 \cos^2 \frac{7\pi}{20} - 1)(4 \cos^2 \frac{9\pi}{20} - 1). \]
If A and B are the values such that $(A + B)$ and $(A - B)$ are not odd multiples of $\frac{\pi}{2}$ and $2\tan(A+B) = 3 \tan(A-B)$, then $\sin A \cos A =$
If $\cos 80^\circ + \cos 40^\circ - \cos 20^\circ = k$, then $\frac{4k}{3} =$
If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
Evaluate \[ \frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + .s \text{ up to } 24 \text{ terms}. \]
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$
If the values of $x, y,$ and $z$ satisfy the equations \[ 2x - 3y + 2z + 15 = 0,
3x + y - z + 2 = 0,
x - 3y - 3z + 8 = 0 \] simultaneously are $\alpha, \beta,$ and $\gamma$ respectively, then