List of top Questions asked in TS EAMCET

The four points whose position vectors are given by \( 2\bar{a}+3\bar{b}-\bar{c} \), \( \bar{a}-2\bar{b}+3\bar{c} \), \( 3\bar{a}+4\bar{b}-2\bar{c} \) and \( \bar{a}-6\bar{b}+6\bar{c} \) are

A, B, C, D are any four points. If E and F are mid points of AC and BD respectively, then \( \vec{AB}+\vec{CB}+\vec{CD}+\vec{AD} = \)

Consider the following statements:
Assertion (A): When \( x, y, z \) are positive numbers, then \[ \tan^{-1}\left( \sqrt{\frac{x(x+y+z)}{yz}} \right) + \tan^{-1}\left( \sqrt{\frac{y(x+y+z)}{xz}} \right) + \tan^{-1}\left( \sqrt{\frac{z(x+y+z)}{xy}} \right) = \pi \] Reason (R): \( \tan^{-1}a + \tan^{-1}b = \tan^{-1}\left( \frac{a+b}{1-ab} \right) \) if \( a>0 \) and \( b>0 \).

If \( e^{(\sinh^{-1} 2 + \cosh^{-1} \sqrt{6})} = a + (b+\sqrt{c})\sqrt{a} + b\sqrt{c} \), then \( a+b+c = \)

\( \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} = \)

If \( 3\sin(\alpha-\beta) = 5\cos(\alpha+\beta) \) and \( \alpha+\beta \neq \frac{\pi}{2} \), then \( \frac{\tan(\frac{\pi}{4}-\alpha)}{\tan(\frac{\pi}{4}-\beta)} = \)

If \( 5\sin\theta + 3\cos\left(\theta + \frac{\pi}{3}\right) + 3 \) lies between \( \alpha \) and \( \beta \) (including \( \alpha, \beta \) also), then \( (\alpha-\beta)(\alpha+\beta-6) = \)

When \( |x|>3 \), the coefficient of \( \frac{1}{x^n} \) in the expansion of \( x^{3/2} (3+x)^{1/2} \) is

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - Px^2 + Qx - R = 0 \) and \( (\alpha-2)^2, (\beta-2)^2, (\gamma-2)^2 \) are the roots of the equation \( x^3 - 5x^2 + 4x = 0 \), then the possible least value of \( P+Q+R \) is

The number of all common roots of the equation \( x^4 - 10x^3 + 37x^2 - 60x + 36 = 0 \) and the transformed equation of it obtained by increasing any two distinct roots of it by 1, keeping the other two roots fixed, is

If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order then the rank of the word STOM when counted from the rank of the word MOST, is

The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is

The number of non negative integral solutions of the equation \( x+y+z+t=10 \) when \( x \ge 2, z \ge 5 \) is

In Argand plane, no value of \( \sqrt[3]{1-i\sqrt{3}} \) lie in

If the equation \( x^2 - 3ax + a^2 - 2a - K = 0 \) has different real roots for every rational number \( a \), then \( K \) lies in the interval

\( \omega \) is a complex cube root of unity and \( Z \) is a complex number satisfying \( |Z-1| \le 2 \). The possible values of \( r \) such that \( |Z-1| \le 2 \) and \( |\omega Z - 1 - \omega^2| = r \) have no common solution are

If \( |Z|=2 \), \( Z_1 = \frac{Z}{2}e^{i\alpha} \) and \( \theta \) is the amp(Z), then \( \frac{Z_1^n - Z_1^{-n}}{Z_1^n + Z_1^{-n}} = \)

If \( l \) is the maximum value of \( -3x^2+4x+1 \) and \( m \) is the minimum value of \( 3x^2+4x+1 \), then the equation of the hyperbola having foci at \( (l,0), (7m,0) \) and eccentricity as 2 is

If \( A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\0 & 1 & 2 \end{bmatrix} \), then \( \text{tr}(A) - \text{tr}(B) = \)

If \( \left| \begin{matrix} 1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3 \end{matrix} \right| = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D+A = \)

A metal rod of area of cross-section \(3 \text{cm}^2\) is stretched along its length by applying a force of \(9 \times 10^4 \text{N}\). If the Young's modulus of the material of the rod is \(2 \times 10^{11} \text{Nm}^{-2}\), the energy stored per unit volume in the stretched rod is

Observe the following data (\(\Delta_i H_1\), \(\Delta_i H_2\) and \(\Delta_{eg}H\) represent the first, second ionisation enthalpies and electron gain enthalpy respectively).

Using the data identify the most reactive metal.

Match the following

The correct answer is

Monochromatic light of wavelength 6000 Å incidents on a small angled prism. If the angle of the prism is 6°, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48, then the angle of dispersion produced for this incident light is

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 $p =$