List of top Mathematics Questions asked in TS EAMCET

The point of intersection of the line joining the points \( \bar{i} + 2\bar{j} + \bar{k} \), \( 2\bar{i} - \bar{j} - \bar{k} \) and the plane passing through the points \( \bar{i}, 2\bar{j}, 3\bar{k} \) is

The position vectors of two points A and B are \( \bar{i} + 2\bar{j} + 3\bar{k} \) and \( 7\bar{i} - \bar{k} \) respectively. The point P with position vector \( -2\bar{i} + 3\bar{j} + 5\bar{k} \) is on the line AB. If the point Q is the harmonic conjugate of P, then the sum of the scalar components of the position vector of Q is

Let the angles A, B, C of a triangle ABC be in arithmetic progression. If the exradii \( r_1, r_2, r_3 \) of triangle ABC satisfy the condition \( r_3^2 = r_1 r_2 + r_2 r_3 + r_3 r_1 \), then \( b = \)

If \( 2\tanh^{-1}x = \sinh^{-1}\left(\frac{4}{3}\right) \) then \( \cosh^{-1}\left(\frac{1}{x}\right) = \)

The general solution of the equation \( \sqrt{6 - 5\cos x + 7\sin^2 x} - \cos x = 0 \) also satisfies the equation

If \( A+B+C = 4S \) then \( \sin(2S-A) + \sin(2S-B) + \sin(2S-C) - \sin 2S = \)

The period of the function \( f(x) = \frac{2\sin\left(\frac{\pi x}{3}\right) \cos\left(\frac{2\pi x}{5}\right)}{3\tan\left(\frac{7\pi x}{2}\right) - 5\sec\left(\frac{5\pi x}{3}\right)} \) is

If \( \frac{x^3+3}{(x-3)^3} = a + \frac{b}{x-3} + \frac{c}{(x-3)^2} + \frac{d}{(x-3)^3} \), then \( (a+d)-(b+c) = \)

If the expression \( 5^{2n} - 48n + k \) is divisible by 24 for all \( n \in \mathbb{N} \), then the least positive integral value of k is

If the coefficient of \(3^{\text{rd}}\) term from the beginning in the expansion of \( \left(ax^2 - \frac{8}{bx}\right)^9 \) is equal to the coefficient of \(3^{\text{rd}}\) term from the end in the expansion of \( \left(ax - \frac{2}{bx^2}\right)^9 \) then the relation between \( a \) and \( b \) is

If all the letters of the word 'HANDLE' are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word 'HELAND' is

Number of triangles whose vertices are the points \( (x, y) \) in the XY-plane with integer coordinates satisfying \( 0 \le x \le 4 \) and \( 0 \le y \le 4 \) is

If the sum of two roots of the equation \( x^4 - 2x^3 + x^2 + 4x - 6 = 0 \) is zero then the sum of the squares of the other two roots is

If the roots of the equation \( 32x^3 - 48x^2 + 22x - 3 = 0 \) are in arithmetic progression, then the square of the common difference of the roots is

The number of integral values of 'a' for which the quadratic equation \( ax^2 + ax + 5 = 0 \) cannot have real roots is

\( \alpha, \beta \) are the roots of the equation \( \sin^2 x + b\sin x + c = 0 \). If \( \alpha + \beta = \frac{\pi}{2} \) then \( b^2 - 1 = \)

If \( \omega \) is a complex cube root of unity and \( x = \omega^2 - \omega + 2 \) then

If \( \Delta_r = \begin{vmatrix} 1 & 2 & r\\ 3r-2 & 3r-5 & 2 \\ 0 & 3 & 3r+1 \end{vmatrix} \) (inferred), then \( \sum_{r=1}^{33} \Delta_r' = \)
(Note: Based on the answer options, the question implies a telescoping sum resulting in 0.99, likely \( \sum \frac{3}{(3r-2)(3r+1)} \).)

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is

If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$

$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $

$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$

$\int \frac{\log x}{(1+x)^2}dx = $