List of top Mathematics Questions asked in AP EAPCET

If the difference between the mean and variance of a binomial variate is \( \dfrac{5}{9} \), then the probability of getting 2 successes for an event when the experiment is conducted 5 times is:

If the equations \( x = t^2 + t + 1, \quad y = t^2 - t + 1 \) represent a curve \( C \) with parameter \( t \), then the Cartesian equation of \( C \) is:

The value of the constant \( c \), so that \( P(x) = c\left(\dfrac{2}{3}\right)^x,\, x = 1,2,3,\ldots \) is the probability distribution function of a discrete random variable \( X \), is:

Two dice are rolled. If \( A \) denotes the event that the same number shows on each die and \( B \) denotes the event that the sum of the numbers on both dice is greater than 7, then \( P(A \mid B) \) and \( P(B \mid A) \) respectively are:

A box contains 5 white balls and 7 black balls. In how many ways can 3 balls be drawn from the box such that at least one black ball is included?}

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 \(x_1, x_2, \ldots, x_n\) 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 \[ \vec{a} = 2\hat{i} + \hat{j} - \hat{k} \quad \text{and} \quad \vec{b} = \hat{i} + 3\hat{j} - 5\hat{k} \] be two vectors, and \(\vec{r}\) be a vector along the vector \(3\vec{a} - 2\vec{b}\) such that \(|\vec{r}| = \sqrt{74}\). If the direction of \(\vec{r}\) is opposite to that of \(3\vec{a} - 2\vec{b}\), then \(\vec{r} =\)

If \(\vec{r}\) is the position vector of the centroid \(G\) of triangle \(ABC\) and \[ 2\hat{i} + \hat{j} - \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} - 4\hat{k} \] are respectively the position vectors of its vertices \(A\) and \(B\), then \[ AG^2 + BG^2 + CG^2 =\ ? \]

If \[ \vec{a} = -2\hat{i} + 9\hat{j} - 6\hat{k}, \quad \vec{b} = t\hat{i} - 2\hat{j} + 6\hat{k} \] are vectors such that \(|\vec{a} + \vec{b}| = 25\), then the sum of the values of \(t =\ ?\)

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

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 \(A + B + C =\) ?

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

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

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

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

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

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

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: