List of top Questions asked in Telangana State Engineering Agriculture & Medical CET- 2024

The numerically greatest term in the expansion of (3x - 16y)15 when x = 2⁄3 and y = 3⁄2 is ?

A body P is projected at an angle of 30° with the horizontal and another body Q is projected at angle of 30° with the vertical. If the ratio of the horizontal ranges of the bodies P and Q is 1:2, then the ratio of the maximum heights reached by the bodies P and Q is
If the coefficients of three consecutive terms in the expansion of (1 + x)23 are in arithmetic progression, then those terms are ?
Two point charges -10 µC and +5 µC are situated on the X-axis at \( x = 0 \) and \( x = \sqrt{2} \, \text{m} \). The point along the X-axis where the electric field becomes zero is.
The general solution of the differential equation \[ \frac{dy}{dx} + \frac{\sin(2x + y)}{\cos x} + 2 = 0 \] is:

If \( A = \begin{pmatrix} 9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2 \end{pmatrix} \) and

\[ A^T A^{-2} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

then

\[ \sum_{1 \leq i \leq 3} \sum_{1 \leq j \leq 3} a_{ij} \]

is:

The hybridisation of the central atom of \( BF_3 \), \( SnCl_2 \), \( HgCl_2 \), respectively is?
Given a square matrix \(A\) where \(A^2 + I = 2A\), find \(A^9\).

The potential difference \( V \) across the filament of the bulb shown in the given Wheatstone bridge varies as \( V = i(2i + 1) \), where \( i \) is the current in ampere through the filament of the bulb. The emf of the battery (\( V_a \)) so that the bridge becomes balanced 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 \( (2,3) \) is the focus and \( x - y + 3 = 0 \) is the directrix of a parabola, then the equation of the tangent drawn at the vertex of the parabola is:
Identify the pair of elements in which the difference in atomic radii is maximum.
A body is projected from the ground at an angle of \( \tan^{-1}\sqrt{7} \) with the horizontal. At half of the maximum height, the speed of the body is \( n \) times the speed of projection. The value of \( n \) 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:
If the ratio of the perpendicular distances of a variable point \( P(x,y,z) \) from the X-axis and from the YZ-plane is 2:3, then the equation of the locus of \( P \) is:
At T(K), \(K_c\) for the reaction AO\(_2\)(g) + BO\(_2\)(g) \(\rightleftharpoons\) AO\(_3\)(g) + BO(g) is 16. One mole each of reactants and products are taken in a 1L flask and heated to T(K), and equilibrium is established. What is the equilibrium concentration of BO (in mol L\(^{-1}\))?
A long straight rod of diameter 4 mm carries a steady current \( i \). The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is.
Three capacitors of capacitances 10 \(\mu\)F, 5 \(\mu\)F and 20 \(\mu\)F are connected in series with a 14 V dc supply. The charge on 5 \(\mu\)F capacitor 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 \( 24K = \):
The maximum horizontal range of a ball projected from the ground is 32 m. If the ball is thrown with the same speed horizontally from the top of a tower of height 25 m, the maximum horizontal distance covered by the ball is: (Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \)) \vspace{0.5cm}
If \(2\,\tan^{-1}x = 3\,\sin^{-1}x\) and \(x \neq 0\), then \(8x^2 +1 =\;?\)
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 \( 2H(G + F) = \) ?
UUU, CCC, AAA, GGG are the codons codes for the following amino acids respectively:
The equations \(2x^2 + ax - 2 = 0\) and \(x^2 + x + 2a = 0\) have exactly one common root. If \(a \neq 0\), then one of the roots of the equation \(ax^2 - 4x - 2a = 0\) is:
The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets at least 3 gold coins is