List of top Questions asked in AP EAPCET

If \[ \vec{a} = \hat{i} + 3\hat{j} + 13\hat{k}, \quad \vec{b} = 2\hat{i} - 4\hat{j} + 3\hat{k} \] are two vectors, then the component vector of \(\vec{a}\) perpendicular to \(\vec{b}\) is

Let \[ \vec{a} = 2\hat{i} - 3\hat{j} - 5\hat{k}, \quad \vec{b} = 3\hat{i} + 2\hat{j} - 5\hat{k} \] be two vectors and \(\vec{r}\) be a vector in the plane of \(\vec{a} \text{ and } \vec{b}\). If \(\vec{r}\) is orthogonal to \(5\hat{i} - 2\hat{j} + 3\hat{k}\) and the magnitude of \(\vec{r}\) is \(\sqrt{94}\), then \(|\vec{r} \cdot \vec{b}|\) is

If \(x_1, x_2, \ldots, x_n\) are 'n' observations and \(\bar{x}\) is their mean. If \[ \sum_{i=1}^{n}(x_i - \bar{x})^2 \text{ is almost zero, then a true statement among the following is} \]

Let \(A\) and \(B\) be two independent events of a random experiment. If the probability that both \(A\) and \(B\) occur is \(\frac{1}{6}\) and the probability that neither of them occurs is \(\frac{1}{3}\), then the probability of occurrence of \(A\) is:

If \( \cos^3 x \sin 4x = \sum_{r=0}^n a_r \sin rx \ \forall x \in \mathbb{R} \), then \( a_3 + a_5 : a_1 + a_7 = \)

In \( \triangle ABC \), \( (\cot A + \cot B)(\cot B + \cot C)(\cot C + \cot A) = \)

If \( 2\sinh x = \cosh x \), then \( x = \)

In \(\triangle ABC\), if \(\cos A + \cos C = 4 \sin^2 \frac{B}{2}\), then the ratio between the perimeter of the triangle and \((a + c)\) is

In \(\triangle ABC\), if \(\angle A = 90^\circ\), then \((r_2 - r_1)(r_3 - r_1) = \)

In \(\triangle ABC\), if \(a, b, c\) are in arithmetic progression and \(C = 2A\), then \(a : c = \)

If \[ \frac{-x^2 + 6x + 1}{(x - 1)^2 (x^2 + 2)} = \frac{A}{x - 1} + \frac{B}{(x - 1)^2} + \frac{Cx - 3}{x^2 + 2}, \] then \(A + B + C =\) ?

The coefficient of \( x^3 \) in the expansion of \( (1 - 2x)^{\frac{1}{2}} (1 + 3x)^{\frac{1}{3}} \) is:

The number of arrangements of the letters of the word ARRANGEMENT in which two E’s do not occur adjacently is:

The number of words that can be formed using the letters of the word VOWEL such that vowels always remain together is:

The number of elements in the set \( \left\{ x \in \mathbb{N} : \binom{20 - 2x}{x - 3} \in \mathbb{N} \right\} \) is

\(\frac{\cot A}{1 - \tan A} + \frac{\tan A}{1 - \cot A} =\)

If \( \theta = \frac{\pi}{9} \), then \( 1 + 27 \tan^2 \theta - 33 \tan^4 \theta + \tan^6 \theta = \)

\( \cot 18^\circ \cdot \cot 36^\circ + 1 = \)

If \( x^2 + x - 6 \) is a factor of \( 2x^3 + x^2 + ax + b \), then \( 6a + 13b = \) ?

If \( c \) and \( d \) are the roots of \( x^2 + ax + b = 0 \), then a root of the equation} \[ x^2 + (4c + a)x + (b + 2ac + 4c^2) = 0 \] is:

If the equation \(x^4 + 7x^3 + 18x^2 + 20x + 8 = 0\) has a repeated root, then that repeated root is:

If the equation \(2x^3 + 5x^2 - 4x - 12 = 0\) has a repeated root, then the constant term of the quadratic equation whose roots are the distinct roots of the given equation is:

The greatest integer \( r \) such that \( 30^r \) divides \( 30! \) is:

A matrix whose elements \( a_{ij} \) are defined by \( a_{ij} = \frac{1}{3}|i - 5j|, \; i, j = 1, 2, 3 \) is

If \( P, Q \) and \( R \) are \( 3 \times 3 \) matrices such that} \[ P = \begin{bmatrix} 3x^2 + x + 3 & 2x^2 - x + 4 & 7x^2 + 8x + 5 \\ 5x^2 + 3x + 2 & 4x^2 - 2x - 1 & 7x^2 + 5x + 8 \\ 3x^2 + 2x + 5 & 4x^2 - x - 2 & 3x^2 + 8x + 7 \end{bmatrix} = Px^2 + Qx + R \] then det \( R = \) ?