AP EAPCET 2021 - 19th August Evening Shift

The angle between the lines represented by \(\cos \theta(\cos \theta+1) x^2-\left(2 \cos \theta+\sin ^2 \theta\right) x y+(1-\cos \theta) y^2=0\) is

\(X\) intercept of the plane containing the line of intersection of the planes \(x-2 y+z+2=0\) and \(3 x-y-z+1=0\) and also passing through \((1,1,1)\) is

Let \(L_1\) (resp, \(L_2\) ) be the line passing through \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\) (resp. \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}})\) and parallel to \(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) (...

If the points (2, 4, \(-\)1), (3, 6, \(-\)1) and (4, 5, \(-\)1) are three consecutive vertices of a parallelogram,
then its fourth vertex is

\(A(-1,2-3), B(5,0,-6)\) and \(C(0,4,-1)\) are the vertices of a \(\triangle A B C\). The direction cosines of internal bisector of \(\angle B A C\) are

If the projections of the line segment AB on xy, yz and zx planes are \(\sqrt{15},\sqrt{46},7\) respectively, then the projection of AB on Y-axis is

Find the equation of the plane passing through the point \((2,1,3)\) and perpendicular to the planes \(x-2 y+2 z+3=0\) and \(3 x-2 y+4 z-4=0\).

If \(\theta \in[0,2 \pi]\) and \(\cos 2 \theta=\cos \theta+\sin \theta\), then the sum of all values of \(\theta\) satisfying the equation is

In a \(\triangle A B C\), if \(3 \sin A+4 \cos B=6\) and \(4 \sin B+3 \cos A=1\), then \(\sin (A+B)\) is equal to

\(\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha\) is equal to

If \(f(x)=\frac{\cot x}{1+\cot x}\) and \(\alpha+\beta=\frac{5 \pi}{4}\), then the value of \(f(\alpha) f(\beta)\) is equal to

In \(\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3\), then \(\tan \frac{C}{8}\) is equal to

Mean of the values \(\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y\) is

When the coordinate axes are rotated through an angle 135\(\Upsilon\), the coordinates of a point \(P\) in the new system are known to be \((4,-3)\). Then find the coordinates of \(P\) in the original system.

The maximum value of \(f(x)=\sin (x)\) in the interval \(\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]\) is

Which of the following vector is equally inclined with the coordinate axes?

If \(\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), and \(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are position vectors of \(A, B\) and \(C\) respectively an...

If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|} < 0\) and \(|\mathbf{a} \cdot \mathbf{b}|=|\mathbf{a} \times \mathbf{b}|\) then the angle between the vectors $$\m...

Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three-unit vectors and \(\mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cdot \mathbf{c}=0\). If the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\). Then $$[\mathbf{a b c}]^...

Let \(x\) and \(y\) are real numbers. If \(\mathbf{a}=(\sin x) \hat{\mathbf{i}}+(\sin y) \hat{\mathbf{j}}\) and \(\mathbf{b}=(\cos x) \hat{\mathbf{i}}+(\cos y) \hat{\mathbf{j}}\), then \(|\mathbf{a} \times \mathbf{b}|\) is

A bulb of resistance \(280 \Omega\) is supplied with a 200 V AC supply. What is the peak current?

The ionisation potential of hydrogen atom is
13.6 V. How much energy need to be
supplied to ionise the hydrogen atom in the
first excited state?

Which of the following statement is correct?

Four capacitors with capacitances \(C_1=l \propto \mathrm{F}, C_2=1.5 \propto \mathrm{F}, C_3=2.5 \propto \mathrm{F}\) and \(C_4=0.5 \propto \mathrm{F}\) are connected as shown and are connected to a \(30 \mathrm{~V}\) source. The potential...

A 500 kg car takes a round turn of radius
50 m with a velocity of 36 km/h. The
centripetal force acting on the car is

A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius \(8.0 \mathrm{~m}\), with minimum speed of \(5 \sqrt{5} \mathrm{~ms}^{-1}\). The minimum value of coefficient of...

In a potentiometer of 10 wires, the balance
point is obtained on the 6th wire. To shift the
balance point to 8th wire, we should

The length of germanium rod is \(0.925 \mathrm{~cm}\) and its area of cross-section is \(1 \mathrm{~mm}^2\). If for germanium $$n_i=2.5 \times 10^{19} \mathrm{~m}^{-3}, \propto_n=0.19 \mathrm{~m}^2 / \mathrm{V}-\mathrm{s}, \propto_e=0.39 \m...

The de-Broglie wavelength associated with a
proton under the influence of an electric
potential of 100 V is

Young's modulus of a wire is \(2 \times 10^{11} \mathrm{Nm}^{-2}\). If an external stretching force of \(2 \times 10^{11} \mathrm{~N}\) is applied to a wire of length \(L\). The final length of the wire is (cross-section = unity)

A solenoid of length \(60 \mathrm{~cm}\) with 15 turns per \(\mathrm{cm}\) and area of cross-section \(4 \times 10^{-3} \mathrm{~m}^2\) completely surrounds another co-axial solenoid of same length and area of cross-section $$2 \times 10^{-...

The magnetic field of a plane electromagnetic wave is given by \(B=(400 \propto \mathrm{T})\sin \left[\left(4.0 \times 10^{15} \mathrm{~s}^{-1}\right)\left(t-\frac{x}{c}\right)\right]\). Average energy density corresponding to the electric ...

In an amplitude modulated signal, the maximum amplitude is \(15 \mathrm{~V}\) and minimum amplitude is \(5 \mathrm{~V}\). The amplitude of modulating wave will be

Gauss's law helps in

Charge on the outer sphere is \(q\) and the inner sphere is grounded. The charge on the inner sphere is \(q^{\prime}\), for \(\left(r_2 > r_1\right)\). Then,

Identify the incorrect statement regarding Reynold's number \(\left(R_e\right)\).

The distance through which one has to dig
the Earth from its surface, so as to reach the
point where the acceleration due to gravity is
reduced by 40% of that at the surface of the
Earth, is (radius of Earth is 6400 km)

Infinite number of masses each of 3kg are
placed along a straight line at the distances
of 1 m, 2m, 4m, 8m, ...... from a point O on
the same line. If G is the universal gravitational constant, then the magnitude of
gravitational field inte...

Expansion during heating

Match the following.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg t...

Which of the following is not a reversible
process?

Which one of the graphs below best
illustrates the relationship between internal
energy U of an ideal gas and temperature T of
the gas in K?

A refrigerator with coefficient of
performance 0.25 releases 250 J of heat to a
hot reservoir. The work done on the working
substance is

A vessel has 6 g of oxygen at pressure p and
temperature 400 K. A small hole is made in
it, so that oxygen leaks out. How much
oxygen leaks out if the final pressure is p/2
and temperature is 300 K?

Two blocks \(A\) and \(B\) of masses \(4 \mathrm{~kg}\) and \(6 \mathrm{~kg}\) are as shown in the figure. A horizontal force of \(12 \mathrm{~N}\) is required to make \(A\) slip over \(B\). Find the maximum horizontal force \(F_B\) that ca...

A particle of mass m is projected with a
velocity u making an angle \(\theta\) with the
horizontal. The magnitude of angular
momentum of the projectile about the point
of projection when the particle is at its
maximum height is

An object travelling at a speed of 36 km/h
comes to rest in a distance of 200 m after the
brakes were applied. The retardation
produced by the brakes is

A ball is projected upwards. Its acceleration
at the highest point is

In a co-axial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero

The magnetic field, of a given length of wire
for single turn coil, at its centre is B, then its
value for two turns coil for the same wire is