List of top Questions asked in TS EAMCET- 2024

A body is thrown vertically upwards with a velocity of 35 ms−1 from the ground.The ratio of the speeds of the body at times 3 s and 4 s of its motion is:

After the decay of a single \( \beta^- \) particle, the parent and daughter nuclei are?
The region in the output voltage versus input voltage graph where a transistor can be used as an amplifier is?
If the locus of the centroid of the triangle with vertices \( A(a,0) \), \( B(\cos t, a\sin t) \) and \( C(\sin t, -b\cos t) \) (\( t \) is a parameter) is given by \[ 9x^2 + 9y^2 - 6x = 49, \] then the area of the triangle formed by the line \[ \frac{x}{a} + \frac{y}{b} = 1 \] with the coordinate axes is: \

A rectangle is formed by the lines \[ x = 4, \quad x = -2, \quad y = 5, \quad y = -2 \] and a circle is drawn through the vertices of this rectangle. The pole of the line \[ y + 2 = 0 \] with respect to this circle is: 

S = (-1,1) is the focus, \( 2x - 3y + 1 = 0 \) is the directrix corresponding to S and \( \frac{1}{2} \) is the eccentricity of an ellipse. If \( (a,b) \) is the centre of the ellipse, then \( 3a + 2b \) is:

If \( 0 \leq x \leq \frac{\pi}{2} \), then \[ \lim\limits_{x \to a} \frac{2\cos x - 1}{2\cos x - 1} \] Options: 

If all the numbers which are greater than 6000 and less than 10000 are formed with the digits \( 3,5,6,7,8 \) without repetition of the digits, then the difference between the number of odd numbers and the number of even numbers among them is:
If \( Z_1, Z_2, Z_3 \) are three complex numbers with unit modulus such that \[ |Z_1 - Z_2|^2 + |Z_1 - Z_3|^2 = 4 \] then \[ Z_1 Z_2 + \overline{Z_1} Z_2 + Z_1 Z_3 + \overline{Z_1} Z_3 = \]
If \( Z_1 = \sqrt{3} + i\sqrt{3} \) and \( Z_2 = \sqrt{3} + i \), and \[ \left( \frac{Z_1}{Z_2} \right)^{50} = x + iy, \] then the point \( (x,y) \) lies in:

Given below are two statements, one is labelled as Assertion (A) and the other one labelled as Reason (R).
Assertion (A): \[ 1 + \frac{2.1}{3.2} + \frac{2.5.1}{3.6.4} + \frac{2.5.8.1}{3.6.9.8} + \dots \infty = \sqrt{4} \] Reason (R): \[ |x| <1, \quad (1 - x)^{-1} = 1 + nx + \frac{n(n+1)}{1.2} x^2 + \frac{n(n+1)(n+2)}{1.2.3} x^3 + \dots \] 

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 \( \tan A + \tan B + \cot A + \cot B = \tan A \tan B - \cot A \cot B \) and \( 0^\circ<A + B<270^\circ \), then \( A + B = \):
If \( \alpha, \beta, \gamma \) 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:
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 \( 49p^2 = \):
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:
The position vector of the point of intersection of the line joining the points \( \mathbf{i} - \mathbf{j} + \mathbf{k} \) and the line joining the points \( 2\mathbf{i} + \mathbf{j} - 6\mathbf{k} \), \( 3\mathbf{i} - \mathbf{j} - 7\mathbf{k} \) is:
If \( \mathbf{a} = 4\hat{i} + 5\hat{j} - 3\hat{k} \) and \( \mathbf{b} = 6\hat{i} - 2\hat{j} - 2\hat{k} \) are two vectors, then the magnitude of the component of \( \mathbf{b} \) parallel to \( \mathbf{a} \) is:
If \( a, b, c \) are the intercepts made on X, Y, Z-axes respectively by the plane passing through the points \( (1, 0, -2) \), \( (3, -1, 2) \), and \( (0, -3, 4) \), then \( 3a + 4b + 7c = \)?
Identify the complex ion with electronic configuration \( t_{2g}^{3} e_{g}^{2} \).
A circular coil of area 200 cm\(^2\) and 50 turns is rotating about its vertical diameter with an angular speed of 40 rad/s in a uniform horizontal magnetic field of magnitude \(2 \times 10^{-2} \, \text{T}\). The maximum emf induced in the coil is.
The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is 100 Hz. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is:
Cellulose is a polysaccharide and is made of:
The pair of molecules/ions with same geometry but central atoms in different states of hybridization is:
Two points A and B on the axis of a circular current loop are at distances of 4 cm and \( 3\sqrt{3} \) cm from the center of the loop. If the ratio of the induced magnetic fields at points A and B is 216:125, the radius of the loop is: