List of top Questions asked in TS EAMCET

If \(\vec{a},\,\vec{b},\,\vec{c}\) are non-coplanar vectors. If the three points \[ \lambda \vec{a} - 2\vec{b} + \vec{c},\quad 2 \vec{a} + \lambda\vec{b} - 2\vec{c},\quad 4\vec{a} + 7\vec{b} - 8\vec{c} \] are collinear, then \(\lambda = \,?\)
In a triangle ABC, if \( r_1 = 6 \), \( r_2 = 9 \), \( r_3 = 18 \), then \( \cos A \) is:

A pendulum clock loses 10.8 seconds a day when the temperature is \( 38^\circ C \) and gains 10.8 seconds a day when the temperature is \( 18^\circ C \). The coefficient of linear expansion of the metal of the pendulum clock is:

At 300 K, the vapour pressure of toluene and benzene are 3.63 kPa and 9.7 kPa, respectively. What is the composition of vapour in equilibrium with the solution containing 0.4 mole fraction of toluene?
If \( A(1, 2, -3) \), \( B(2, 3, -1) \), and \( C(3, 1, 1) \) are the vertices of triangle \( \Delta ABC \), then find \( \left| \frac{\cos A}{\cos B} \right|.\)

The correct order of boiling points of hydrogen halides is: 

If \( (p, q) \) is the center of the circle which cuts the three circles \( x^2 + y^2 - 2x - 4y + 4 = 0 \), \( x^2 + y^2 + 2x - 4y + 1 = 0 \), and \( x^2 + y^2 - 4x - 2y - 11 = 0 \) orthogonally, then find \( p + q \).
If the probability distribution of a random variable \( X \) is as follows, then the variance of \( X \) is: \[ X = x \quad 2 \quad 3 \quad 5 \quad 9 \] \[ P(X = x) = k \quad 2k \quad 3k^2 \quad k^2 \]

In a triangle \(ABC\), if

\[ (a - b)^2 \cos^2 \frac{C}{2} + (a + b)^2 \sin^2 \frac{C}{2} = a^2 + b^2, \]

then \( \cos A \) is:

Evaluate the expression: \[ \cos^{-1} \frac{3}{5} + \sin^{-1} \frac{5}{13} + \tan^{-1} \frac{16}{63} \]
If 4 letters are selected at random from the letters of the word PROBABILITY, compute the probability that at least one letter is repeated in the selection.
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 \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:
The end of a latus rectum of the ellipse \(3x^2 + 4y^2 = 12\) is lying in the third quadrant. If the normal drawn at \(L_1\) to this ellipse intersects the ellipse again at the point \(P(a,b)\), then find the value of \(a\):
The equations of the directrices of the ellipse \(9x^2 + 4y^2 - 18x - 16y - 11 = 0\) are:

Match the following substances with their respective equivalent weights: 

The major product 'Y' in the given sequence of reactions is:

If two linear antennas having lengths in the ratio 2:3 are emitting radiations of wavelengths in the ratio 8:9, then the ratio of effective powers radiated by them are in the ratio:
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 \(p\):
The sum of two roots of the equation \(x^4 - x^3 - 16x^2 + 4x + 48 = 0\) is zero. If \(\alpha, \beta, \gamma, \delta\) are the roots of this equation, then \(\alpha^4 + \beta^4 + \gamma^4 + \delta^4\) is:
Given the two parabolas: \[ S = y^2 - 4ax = 0, \quad S' = y^2 + ax = 0 \] where \( P(t) \) is a point on the parabola \( S' = 0 \). If \( A \) and \( B \) are the feet of the perpendiculars from \( P \) to the coordinate axes and \( AB \) is a tangent to the parabola \( S = 0 \) at the point \( Q(t_1) \), then the value of \( t_1 \) is:
An aircraft executes a horizontal loop of radius 9 km at a constant speed of 540 km/h. The wings of the aircraft are banked at an angle of
If the direction ratios of two lines are \( (3,0,2) \) and \( (0,2,k) \), and \( \theta \) is the angle between them, and if \( |\cos \theta| = \frac{6}{13} \), then \( k = \)
A(1, -2, 1) and B(2, -1, 2) are the end points of a line segment. If \(D(\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from \(C(1, 2, 3)\) to AB, then \(\alpha^2 + \beta^2 + \gamma^2 =\)
An organic compound containing phosphorus on oxidation with \( Na_2O_2 \) gives a compound \( X \). When \( X \) is boiled with \( HNO_3 \) and treated with a reagent, it gives a yellow precipitate \( Y \). Identify \( X \) and \( Y \).