List of top Questions asked in TS EAMCET

The work to be done to produce a strain of \(10^{-3}\) in a steel wire of mass 2.96 kg and density 7.4 gcm\(^{-3}\) is (Young's modulus of steel = \(2 \times 10^{11}\) Nm\(^{-2}\))

A body projected at certain angle (\(\neq 90^\circ\)) from the ground crosses a point in its path at a time of 2.3 s and from there it reaches the ground after a time of 5.7 s. The maximum height reached by the body is (Acceleration due to gravity = 10 ms\(^{-2}\))

A thin uniform wire of mass 'm' and linear density '\(\rho\)' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is

A circular path of radius 75 m is banked at an angle of \(\tan^{-1}(0.2)\). If the coefficient of static friction between the tyres of the car and the circular path is 0.1, then the maximum permissible speed of the car to avoid slipping is

\( \int_0^{\pi/2} \sqrt{\tan x} \, dx = \)

The differential equation corresponding to the family of ellipses \( \frac{x^2}{a^2} + \frac{y^2}{4} = 1 \), where 'a' is an arbitrary constant is

In an experiment, the coefficient of viscosity (in mPa s) of a liquid was determined as 2.62, 2.68, 2.58, 2.57, 2.54 and 2.55. The mean absolute error in the determination of the coefficient of viscosity of the liquid is

\( \int \frac{1}{(x+2)\sqrt{x^2+x+2}} dx = \)

If \( \int x^3 \sin(3x) dx = \frac{1}{27} [f(x)\cos(3x) + g(x)\sin(3x)] + c \) then f(1)+g(1)=

\( \int_{-1}^{5} \frac{1}{\sqrt{20+x-x^2}} dx = \)

\( \int \frac{x+\cos x}{1-\sin x} dx = \)

A rod of length 41 m with an end A on the floor and another end B on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of 3 ft/min. When the end B is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in ft/min)

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is 45°, then the approximate error in its volume is (in cu. cm)

If \( y = x^{\log x} + (\log x)^x, x>1 \) then \( (\frac{dy}{dx})_{x=e} = \)

The real valued function \( f(x) = \frac{x^2}{2} - \log(x^2+x+1) \) is

If the curves \(y^2=12x-3\) and \(y^2=12-kx\) cut each other orthogonally then the length of the sub tangent at (1,b) on the curve \(y^2=12-kx\) is

If the angle between the planes ax-y+3z=2a and 3x+ay+z=3a is \( \frac{\pi}{3} \) then the direction ratios of the line perpendicular to the plane (a+2)x+(a-4)y+2az=a are

If \( y = \tan^2(\cos^{-1}\sqrt{\frac{1+x^2}{2}}) \), then \( \frac{dy}{dx} = \)

If [x] is the greatest integer function and \( f(x) = \begin{cases} \frac{2[x]-x}{|x|} & x \neq 0 \\ 1 & x=0 \end{cases} \) is a real valued function, then f is

Let e be the eccentricity of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). If a=5, b=4 and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is \(lx+my=27\), then l+m=

The equation of the locus of a point whose distance from XY-plane is twice its distance from Z-axis is

If the latus rectum through one of the foci of a hyperbola \( \frac{x^2}{9} - \frac{y^2}{b^2} = 1 \) subtends a right angle at the farther vertex of the hyperbola, then \(b^2 = \)

If L(p,q), q>3 is one end of the latus rectum of the parabola \((y-2)^2 = 3(x-1)\) then the equation of the tangent at L to this parabola is

If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \( \cos\alpha + \cos^2\beta = \)

If P is any point on the ellipse \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \) and S, S' are its foci, then the maximum area (in sq. units) of \(\Delta SPS' = \)