List of top Mathematics Questions asked in TS EAMCET

Given \( \cos B - \sin A = \frac{\sqrt{3}+1}{4\sqrt{2}} \) and \( 2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}} \), calculate \( \cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} \):
When the origin is shifted to the point \( (2,b) \) by translation of axes, the coordinates of the point \( (4,4) \) have changed to \( (6,8) \). When the origin is shifted to \( (a,b) \) by translation of axes, if the transformed equation of \( x^2 + 4xy + y^2 = 0 \) is \( X^2 + 2HXY + Y^2 + 2GX + 2FY + C = 0 \), then \( 2H(G + F) = \) ?
If \( y = \frac{\tan x \cos^{-1}x}{\sqrt{1 - x^2}} \), then the value of \( \frac{dy}{dx} \) when \( x = 0 \) is:
If \(m\cos(\alpha + \beta) - n\cos(\alpha - \beta) = m\cos(\alpha - \beta) + n\cos(\alpha + \beta)\), then \(\tan \alpha \tan \beta\) is:
The centroid of a variable triangle ABC is at the distance of 5 units from the origin. If A = (2,3) and B = (3,2), then the locus of C is:

If

\[ \cosh^{-1}\left(\frac{5}{3}\right) + \sinh^{-1}\left(\frac{3}{4}\right) = k, \]

then \( e^k \) is:

A circle passes through the points \( (2, 0) \) and \( (1, 2) \). If the power of the point \( (0, 2) \) with respect to this circle is 4, then the radius of the circle is
The general solution of the differential equation $$ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. $$ 
If \( 3^{2n+2} - 8n - 9 \) is divisible by \( 2^p \) \(\forall n \in \mathbb{N}\), then the maximum value of \( p \) is
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):
A circle passing through the points \( (1, 1) \) and \( (2, 0) \) touches the line \( 3x - y - 1 = 0 \). If the equation of this circle is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then a possible value of \( g \) is
The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:
If A and B are arbitrary constants, then the differential equation having \[ y = Ae^{-x} + B \cos x \] as its general solution is:
If \( (1,1), (-2,2), (2,-2) \) are 3 points on a circle \( S \), then the perpendicular distance from the center of the circle \( S \) to the line \( 3x - 4y + 1 = 0 \) is:
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 combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intersection of the lines \[ x + 2y - 3 = 0 \quad \text{and} \quad 2x - y - 1 = 0 \] is: \
The common solution set of the inequalities \[ x^2 - 4x \leq 12 \quad \text{and} \quad x^2 - 2x \geq 15 \] taken together is:
S' is the focus of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1, (b<5) \) lying on the negative X-axis and \( P(\theta) \) is a point on this ellipse. If the distance between the foci of this ellipse is 8 and \( S'P = 7 \), then \( \theta \) is:
If \( Q \) and \( R \) are the images of the point \( P(2,3) \) with respect to the lines \( x - y + 2 = 0 \) and \( 2x + y - 2 = 0 \) respectively, then \( Q \) and \( R \) lie on
If \(2 \tan^2 \theta - 4 \sec \theta + 3 = 0\), then \(2 \sec \theta\) is:
A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is:
If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 is:
If \( \alpha, \beta \) are the real roots of the equation \( x^2 + ax + b = 0 \). If \( \alpha + \beta = \frac{1}{2} \) and \( \alpha^3 + \beta^3 = \frac{37}{8} \), then \( {a}-{\frac{1}{b}} =\)
If \( A(1, -2), B(-2, 3), C(-1, -3) \) are the vertices of a triangle ABC. \( L_1 \) is the perpendicular drawn from \( A \) to \( BC \) and \( L_2 \) is the perpendicular bisector of \( AB \). If \( (l, m) \) is the point of intersection of \( L_1 \) and \( L_2 \), then \( 26m - 3 = \)
The sum of all the 4-digit numbers formed by taking all the digits from 0, 3, 6, 9 without repetition is: