AP EAPCET 2021 - 20th August Morning Shift

The equation of the base of an equilateral triangle is \(x+y=2\) and one vertex is \((2,-1)\), then the length of the side of the triangle is

The equation of a straight line which passes through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to \((x \sec \theta+y \operatorname{cosec} \theta)=a\) is

The acute angle between lines \(6 x^2+11 x y-10 y^2=0\) is

If the lines, joining the origin to the points of intersection of the curve \(2 x^2-2 x y+3 y^2+2 x-y-1=0\) and the line \(x+2 y=k\), are at right angles, then \(k^2\) equals

The equation of bisector of the angle between the lines represented by \(3 x^2-5 x y+4 y^2=0\) is

If the bisectors of the pair of lines \(x^2-2 m x y-y^2=0\) is represented by \(x^2-2 n x y-y^2=0\), then

If the lines, \(\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}\) and \(\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}\) are coplanar, then \(\sin ^{-1}(\sin \lambda)+\cos ^{-1}(\cos \lambda)\) is equal to

The line passing through \((1,1,-1)\) and parallel to the vector \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) meets the line \(\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}\) at \(A\) and the plane \(2 x-y+2 z+7=0\) at \(B\). Then...

If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthocentre, centroid, circumcentre and incentre, then H + G + S + I is equal to

A(2, 3, 4), B(4, 5, 7), C(2, \(-\)6, 3) and D(4, \(-\)4, k) are four points. If the line AB is parallel to CD, then k is equal to

If the direction cosines of two lines are \(\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)\) and \(\left( {{5 \over {13}},{{12} \over {13}},0} \right)\), then identify the direction ratios of a line which is bisecting one o the angle ...

If \(\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)\), then \(\theta\) is equal to

What is the value of \(\cos \left(22 \frac{1}{2}\right)^{\circ}\) ?

If \(\cos \theta=-\sqrt{\frac{3}{2}}\) and \(\sin \alpha=\frac{-3}{5}\), where '\(\theta\)' does not lie in the third quadrant, then the value of \(\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}\) is equal to

If \(\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}\), then \(\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}\) is equal to

The sides of a triangle inscribed in a given circle subtend angles \(\alpha, \beta, \gamma\) at the center. The minimum value of the AM of \(\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)\) and $$\cos \left(\g...

The position vectors of the points \(A\) and \(B\) with respect to \(O\) are \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). The length of the internal bisector of...

Let \(\mathbf{u}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{v}=-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}\) and \(\mathbf{w}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). Then which of the following statement is t...

If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

Let \(\mathbf{a}=\hat{\mathbf{i}}\) and \(\mathbf{b}=\hat{\mathbf{j}}\), the point of intersection of the lines \(\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}\) and \(\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}\) ...

A 20 V AC is applied to a circuit consisting of
a resistor and a coil with negligible
resistance. If the voltage across the resistor is
12 V, the voltage across the coil is

The angular momentum of the orbital
electron is integral multiple of

Which of the following values is the correct order of nuclear density?

A 60 \(\mu\)F parallel plate capacitor whose plates
are separated by 6 mm is charged to 250 V,
and then the charging source is removed.
When a slab of dielectric constant 5 and
thickness 3 mm is placed between the plates,
find the change in...

A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 \(\times\) 10\(^7\) Nm\(^{-2}\). The area of cross-section from the wire is 10\(^{-6}\) m\(^{2}\). The maximum angular velocity with which it can be rota...

Five current carrying conductors meet at a
point P. What is the magnitude and direction
of the current in the fifth conductor?

The graph between the maximum speed \((v_{max})\) of a photoelectron and frequency \((\nu)\) of the incident radiation, in photoelectric effect is correctly represented by

The induced emf cannot be produced by

Assertion (A) When plane of coil is perpendicular to magnetic field, magnetic flux linked with the coil is minimum, but induced emf is zero.
Reason (R) \(\phi=n A B \cos \theta\) and \(e=\frac{d \phi}{d t}\)

The electric and the magnetic fields associated with an electromagnetic wave propagating along the \(z\)-axis, can be represented by

What is the electric flux for Gaussian surface \(A\) that encloses the charged particles in free space? [Given, \(q_1=-14 \mathrm{~nC}, q_2=78.85 \mathrm{~nC}, \left.q_3=-56 \mathrm{~nC}\right]\)

Two charges 8 \(\mu\)C each are placed at the corners A and B of an equilateral triangle of side 0.2 m in air. The electric potential at the third corner C is

A glass flask weighting 390 g, having internal
volume 500 cc just floats when half of it is
filled with water. Specific gravity of the glass
is

Water does not wet an oily glass because

The gravitational potential energy is maximum at

A geostationary satellite is taken to a new
orbit, such that its distance from centre of
the earth is doubled. Then, find the time
period of this satellite in the new orbit.

Boiling water is changing into steam. The specific heat of boiling water is

If the volume of a block of metal changes by \(0.12 \%\) when heated through \(20^{\circ} \mathrm{C}\), then find its coefficient of linear expansion.

Isothermal process is the graph between

For a monoatomic ideal gas is following the
cyclic process ABCA shown in the U versus p
plot, identify the incorrect option.

The pressure of a gas is proportional to

A book is lying on a table. What is the angle
between the normal reaction acting on the
book on the table and the weight of the
book?

A paramagnetic sample showing a net magnetisation of \(0.8 \mathrm{~A} \mathrm{~m}^{-1}\), when placed in an external magnetic field of strength \(0.8 \mathrm{~T}\), at a temperature \(5 \mathrm{~K}\). If the temperature is raised to $$20 \...

A boy throws a cricket ball from the
boundary to the wicket keeper. If the
frictional force due to air \((f_a )\) cannot be
ignored, the forces acting on the ball at the
position X are represented by

The displacement of a particle starting from rest at \(t=0\) is given by \(s=9 t^2-2 t^3\). The time in seconds at which the particle will attain zero velocity is

Two cars A and B are moving with a velocity
of 30 km/h in the same direction. They are
separated by 10 km. The speed of another car
C moving in the opposite direction, if it meets
these two cars at an interval of eight minutes
is

A wire of length \(L\) metre carrying a current \(I\) ampere is bent in the form of a circle. Magnitude of its magnetic moment is

What is the net force on the square coil?

A sphere and a hollow cylinder without
slipping, roll down two separate inclined
planes A and B, respectively. They cover same
distance in a given duration. If the angle of
inclination of plane A is 30\(^\circ\), then the angle
of inclinati...

Four spheres each of diameter \(2 a\) and mass \(m\) are placed in a way that their centers lie on the four corners of a square of side \(b\). Moment of inertia of the system about an axis along one of the sides of the square is