AP EAPCET 2021 - 20th August Evening Shift

The distance of the point \((1,2)\) from the line \(x+y+5=0\) measured along the line parallel to \(3 x-y=7\) is equal to

Find the equation of a line which passes through \(\left(2 \cos ^3(\theta), 2 \sin ^3(\theta)\right)\) and is perpendicular to the line \(x \cos (\theta)-y \sin (\theta)=2 \cos (2 \theta)\).

The value of \(p\) for which the equation \(x^2+p x y+y^2-5 x-7 y+6=0\) represents a pair of straight lines is

If one of the line represented by \(-a x^2+2 h x y+b y^2=0\) passes through \((2,3)\) and the other passes through \((4,5)\), then \(a+2 h+b\) equals

If the lines represented by the equation \(2 x^2-p x y+2 y^2=0\) are real, then the value of \(p\) lies in the interval

The equation of the plane passing through \(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\) and parallel to the vectors \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and $$\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf...

The direction cosines of the line joining the points \((-2,4,-5)\) and \((1,2,3)\) are

The points (2, 3, 4), (\(-\)1, \(-\)2, 1) and (5, 8, 7) are

The sum of intercepts of the plane \(4 x+3 y+2 z=2\) on the coordinate axes is

Let \(\theta\) be an angle in the standard position such that the point \((-5,12)\) lies on its terminal side, then

If \(\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32}=2^m \operatorname{cosec} \frac{\pi}{n}\), then \(m+n\) is equal to

If \(A+B+C=\frac{3 \pi}{2}\), then \(\cos 2 A+\cos 2 B+\cos 2 C\) is equal to

\(\sinh (x+y) \cosh (x-y)\) is equal to

If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=x \hat{\mathbf{i}}+(x-2) \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and if the vector $$\mathbf{...

Let \(u=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(v=3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}\). Consider three points \(P, Q\) and \(R\) having the position vectors $$\left(\frac{5}{2}\right) \hat{\mathbf{i}}-2 \hat{\mathbf{j}} ;\left(\frac{...

The point of intersection of the lines joining points \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(-\hat{\mathbf{i}}, 2 \hat{\mathbf{i}}\) is

The value of \(\frac{(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2}{2(\mathbf{a})^2(\mathbf{b})^2}\) is

Let \(\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}\) if \(\mathbf{d}\) is a unit vector such $$\mathbf{a} \cdot \mathbf{b}=0=[\mathbf{b} \mat...

Let \(u\) and \(v\) be two non-zero vectors in \(R^3\) with the intermediate angle \(45^{\circ}\). Then \(|\mathbf{u} \times \mathbf{v}|\) is equal to

Given, \(\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=\mathbf{b}_1+\mathbf{b}_2\) where \(\mathbf{b}_1\) is parallel to \(\mathbf{a}\) and $$\mathbf{b}_...

The shortest wavelength of X-rays emitted from an X-ray tube depends upon ........... .

The wavelength of the first spectral line of
the Lyman series of hydrogen spectrum is

Which of the following nuclear reactions is
possible?

A ball of mass 3 kg, moving with a speed of
100 ms\(^{-1}\), strikes a wall at an angle 60\(^\circ\)
(as shown in figure). The ball rebounds at
the same speed and remains in contact with
the wall for 0.2 s, the force exerted by the
ball on ...

The conductivity of a conductor decreases
with temperature because, on heating

If a photocell is illuminated with a radiation of 1240 \(\mathop A\limits^o\), the stopping potential is found to be 8V. Then, the work-function of the emitter and the threshold wavelength are

An AC generator consists of a coil of 100 turns and is of cross-sectional area \(3 \mathrm{~m}^2\). It is rotating at a constant angular speed of \(60 \mathrm{~rads}^{-1}\) in a uniform magnetic field of \(0.04 \mathrm{~T}\). Resistance of ...

Assertion (A) Magnetic flux is a vector quantity.
Reason (R) Value of magnetic flux can be positive negative or zero.

Two charges \(10 ~\mu \mathrm{C}\) and \(-10 ~\mu \mathrm{C}\) are placed at points \(A\) and \(B\) separated by a distance of \(10 \mathrm{~cm}\). Find the electric field at a point \(P\) on the perpendicular bisector of \(A B\), at a dist...

When a number of charged liquid drops
coalesce, which of the following quantity
does not change?

What is the angle between maximum value of potential gradient and equipotential surface?

What causes the free surface of a liquid to
have minimum area?

Assertion (A) The upper surface of the wing of an aeroplane is made convex and the lower surface is made concave.
Reason (R) The air currents at the top have smaller velocity and thus less pressure at the bottom than at the top.

If the Earth stops rotating in its orbit about
the sun, there will be variation in the weight
of our bodies at

At what depth below surface of the Earth, the acceleration due to gravity will be half of its value that at \(1600 \mathrm{~km}\) above the surface of the Earth?

A glass vessel of volume \(V_o\) is completely filled with a liquid and its temperature is raised by \(\Delta T\). What volume of the liquid will flow over, if the coefficient of linear expansion of glass is \(\alpha_g\) and coefficient of ...

A Carnot engine whose heat sink is at 27\(^\circ\)C
has an efficiency of 40%. By how much
should its source temperature be changed, so
as to increase its efficiency to 60%?

A diatomic gas is heated at constant
pressure, what fraction of the heat energy is
used to increase the internal energy?

An ideal gas is taken from state-1 to state- 2 through optional path \(A, B, C\) and \(D\) as shown in the \(p\) - \(V\) diagram. Let \(Q, W\) and \(U\) represent the heat supplied, work done and change in internal energy respectively, then...

When the temperature of an ideal gas is increased from 27\(^\circ\)C to 127\(^\circ\)C. Calculate the percentage increase in its \(v_{rms}\).

A 30 kg slab B rests on a frictionless floor as
shown in the figure. A 10 kg block A rests on
top of the slab B. The coefficients of static
and kinetic friction between the block A and
the slab B are 0.60 and 0.40, respectively.
When block ...

A hiker stands on the edge of a cliff \(490 \mathrm{~m}\) above the ground and throws a stone horizontally with an initial speed of \(15 \mathrm{~ms}^{-1}\). The speed with which it hits the ground is

Two paper screens \(A\) and \(B\) are separated by \(150 \mathrm{~m}\). A bullet pierces \(A\) and than \(B\). The hole in \(B\) is \(15 \mathrm{~cm}\) below the hole in \(A\). If the bullet is travelling horizontally at the time of hitting...

An object is moving with a uniform
acceleration which is parallel to its
instantaneous direction of motion. The
displacement-velocity graph of this object is

Torque required to hold a small circular coil of 10 turns, area of \(2 \times 10^{-4} \mathrm{~m}^2\) area of carrying 0.5 A current in the middle of a long solenoid of \(10^3\) turns per metre carrying \(3 \mathrm{~A}\) current, with its a...

Two concentric coils each of radius equal to \(4 \pi ~\mathrm{cm}\) are placed at right angles to each other. If \(10 \mathrm{~A}\) and \(24 \mathrm{~A}\) are the currents flowing through the coils respectively, then the magnetic induction ...

Assertion (A) The focal length of lens does
not change when red light is replaced by blue
light.
Reason (R) The focal length of lens does not
depend on colour of light used.

As solid sphere of mass \(M\) and radius \(R\) spins about an axis passing through its centre making \(600 \mathrm{~rpm}\). Its kinetic energy of rotation is

Two fly wheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^2\) and \(20.0 \mathrm{~kg}-\mathrm{m}^2\), respectively. Wheel...

The output current versus time curve of a
rectifier is shown in the figure. The average
value of output current in this case is ........... .