List of top Mathematics Questions asked in AP EAMCET

If \(I_{n}=\int_{0}^{\pi/4}\tan^{n}x~dx,\) then \(I_{13}+I_{11}=\)
If the eleventh term in the binomial expansion of \( (x + a)^n \) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is:
The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
If \( \alpha \) and \( \beta \) are two distinct negative roots of the equation \( x^5 - 5x^3 + 5x^2 - 1 = 0 \), then the equation of least degree with integer coefficients having \( \sqrt{-\alpha} \) and \( \sqrt{-\beta} \) as its roots is:
The length of the tangent drawn at the point \( P \left( \frac{\pi}{4} \right) \) on the curve \( x^{2/3} + y^{2/3} = 2^{2/3} \) is:
If \( |\mathbf{\bar{f}}| = 10\), \( |\mathbf{\bar{g}}| = 14\) and \( |\mathbf{\bar{f}} - \mathbf{\bar{g}}| = 15\), then \( |\mathbf{\bar{f}} + \mathbf{\bar{g}}| =\)
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + 3x^2 - 10x - 24 = 0. \] If \( \alpha(\beta + \gamma), \beta(\gamma + \alpha) \), and \( \gamma(\alpha + \beta) \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then find the value of \( q \).
If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:
P is a point on \( x + y + 5 = 0 \), whose perpendicular distance from \( 2x + 3y + 3 = 0 \) is \( \sqrt{13} \), then the coordinates of P are:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = 2\hat{i} + \hat{j} + \hat{k} \) are two vectors and \( \vec{c} \) is a unit vector lying in the plane of \( \vec{a} \) and \( \vec{b} \), and if \( \vec{c} \) is perpendicular to \( \vec{b} \), then \( \vec{c} \cdot (\hat{i} + 2\hat{k}) = \):
If the points having the position vectors \( \mathbf{r}_1 = -i + 4j - 4k\), \( \mathbf{r}_2 = 3i + 2j - 5k\), \( \mathbf{r}_3 = -3i + 8j - 5k\) and \( -3i + 2j + \lambda k\) are coplanar, then \(\lambda = \)
In \(\triangle ABC\), \(bc - r_2 r_3 = \)
For \( a \in \mathbb{R} \setminus \{0\} \), if \( a \cos x + a \sin x + a = 2K + 1 \) has a solution, then \( K \) lies in the interval:
If the chord of the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) having \((1,1)\) as its middle point is \( x + \alpha y = \beta \), then:

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is \(\frac{29\pi}{4}\) sq. units, then |a| =

If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
5 boys and 6 girls are arranged in all possible ways. Let \(X\) denote the number of linear arrangements in which no two boys sit together, and \(Y\) denote the number of linear arrangements in which no two girls sit together. If \(Z\) denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then \(X:Y:Z\) = ?
If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are position vectors of 4 points such that \( 2\vec{a} + 3\vec{b} + 5\vec{c} - 10\vec{d} = 0 \), then the ratio in which the line joining \( \vec{c} \) divides the line segment joining \( \vec{a} \) and \( \vec{b} \) is:

If the curves $$ 2x^2 + ky^2 = 30 \quad \text{and} \quad 3y^2 = 28x $$ cut each other orthogonally, then \( k = \) 

Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
Find the sum of the sequence: \( 2 + 3 + 5 + 6 + 8 + 9 + \dots + 2n \) terms.
When an unfair dice is thrown, the probability of getting a number \( k \) on it is \( P(X = k) = k^2 P \), where \( k = 1, 2, 3, 4, 5, 6 \) and \( X \) is the random variable denoting a number on the dice. Then, the mean of \( X \) is:
The length of the subnormal at any point on the curve \( y = \left(\frac{x}{2024}\right)^k \) is constant if the value of \( k \) is:
If the roots of the equation \[ Z^3 + iZ^2 + 2i = 0 \] are the vertices of a triangle ABC, then that triangle ABC is:
Parametric equations of the circle \( 2x^2 + 2y^2 = 9 \) are: