List of top Mathematics Questions asked in TS EAMCET

If \( \sinh^{-1}(-\sqrt{3}) + \cosh^{-1}(2) = K \), then \( \cosh K = \):
In triangle ABC, if \( a = 4, b = 3, c = 2 \), then \( 2(a - b \cos C)(a - c \sec B) = \):
If a circle passing through the point \((1,1)\) cuts the circles \(x^2 + y^2 + 4x - 5 = 0\) and \(x^2 + y^2 - 4x + 3 = 0\) orthogonally, then the center of that circle is:
If \( p \) and \( q \) are the real numbers such that the 7th term in the expansion of \( \left( \frac{5}{p^3} \cdot \frac{3q}{7} \right)^8 \) is 700, then \( 49p^2 = \):
If \( T_4 \) represents the 4th term in the expansion of \( \left( 5x + \frac{7}{x} \right)^{-\frac{3}{2}} \) and \( x \not\in \left[ \frac{\sqrt{7}}{5}, \frac{\sqrt{7}}{5} \right] \), then \( \left( x^3 \cdot \sqrt{5x} \right) T_4 = \):}
The pole of the line \(x - 5y - 7 = 0\) with respect to the circle \(S \equiv x^2 + y^2 - 2x - 2y + 1 = 0\) is \(P(a,b)\). If \(C\) is the centre of the circle \(S = 0\) then \(PC =\):
If \(P\left( \frac{\pi}{4} \right)\), \(Q\left( \frac{\pi}{3} \right)\) are two points on the circle \(x^2 + y^2 - 2x - 2y - 1 = 0\), then the slope of the tangent to this circle which is parallel to the chord \(PQ\) is:
The slope of one of the pair of lines \(2x^2 + hxy + 6y^2 = 0\) is three times the slope of the other line, \(h = ?\)
The power of a point \( (2,0) \) with respect to a circle \( S \) is \(-4\) and the length of the tangent drawn from the point \( (1,1) \) to \( S \) is \( 2 \). If the circle \( S \) passes through the point \( (-1,-1) \), then the radius of the circle \( S \) is:
The lengths of two equal sides of an isosceles triangle are given by \(L_1 = 2x + y - 3 = 0\) and \(L_2 = ax + by + c = 0\). If \(L_3 = x + 2y + 1 = 0\) is the third side of this triangle and \((5, 1)\) is a point on \(L_2\), then \(b^2/|ac|\) is:
(-2, -1), (2,5) are two vertices of a triangle and \( \left(2, \frac{5}{3} \right) \) is its orthocenter. If \( (m, n) \) is the third vertex of that triangle, then \( m+n = \):
A question paper has 3 parts A, B, C. Part A contains 7 questions, part B contains 5 questions and Part C contains 3 questions. If a candidate is allowed to answer not more than 4 questions from part A; not more than 3 questions from part B and not more than 2 questions from part C, then the number of ways in which a candidate can answer exactly 7 questions is:
If \( \tan A = -\frac{60}{11} \) and A does not lie in the 4th quadrant. \( \sec B = \frac{41}{9} \) and B does not lie in the 1st quadrant. If \( \csc A + \cot B = K \), then \( 24K = \):
If all the possible 3-digit numbers are formed using the digits 1, 3, 5, 7, 9 without repeating any digit, then the number of such 3-digit numbers which are divisible by 3 is:
If \( \tan A + \tan B + \cot A + \cot B = \tan A \tan B - \cot A \cot B \) and \( 0^\circ<A + B<270^\circ \), then \( A + B = \):
If the line \(L = x \cos \alpha + y \sin \alpha - p = 0\) represents a line perpendicular to the line \(x + y + 1 = 0\) and \(p\) is positive, \(a\) lies in the fourth quadrant and perpendicular distance from \(\left(\sqrt{2}, \sqrt{2}\right)\) to the line \(L = 0\) is 5 units, then find \(p\):
If \( \alpha, \beta \) are the real roots of the equation \( 12x^\frac{1}{3} - 25x^\frac{1}{6} + 12 = 0 \), if \( \alpha>\beta \), then \( 6\sqrt{\frac{\alpha}{\beta}} = \):
If \( \cos^2 84^\circ + \sin^2 126^\circ - \sin 84^\circ \cos 126^\circ = K \) and \( \cot A + \tan A = 2K \), then the possible values of \( \tan A \) are:
If the expression \( 7 + 6x - 3x^2 \) attains its extreme value \( \beta \) at \( x = \alpha \), then the sum of the squares of the roots of the equation \( x^2 + ax - \beta = 0 \) is:
The equation that is satisfied by the general solution of the equation \( 4 - 3 \cos \theta = 5 \sin \theta \cos \theta \) is:
All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is:
If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + 3x^2 - 10x - 24 = 0 \). If \( \alpha>\beta>\gamma \) and \( \alpha^3 + 3\beta^2 - 10\gamma - 24 = 11k \), then \( k = \):
If \( \alpha, \beta, \gamma \) are the roots of the equation \( 8x^3 - 42x^2 + 63x - 27 = 0 \), If \( \beta<\gamma<\alpha \) and \( \beta, \gamma, \alpha \) are in geometric progression, then the extreme value of the expression \( \gamma x^2 + 4\beta x + \alpha \) is:
In triangle ABC, if \( A = 45^\circ \), \( C = 75^\circ \), and \( R = \sqrt{2} \), then the value of \( r \) is:
P and Q are the points of trisection of the line segment AB. If the position vectors of A and B are \( 2\hat{i} - 5\hat{j} + 3\hat{k} \) and \( 4\hat{i} + \hat{j} - 6\hat{k} \) respectively, then the position vector of the point that divides PQ in the ratio 2:3 is: