AP EAPCET 2021 - 19th August Morning Shift

the sum of the squares of the intercepts made the line \(5x-2y=10\) on the coordinate axes equals

For three consecutive odd integers \(a \cdot b\) and \(c\), if the variable line \(a x+b y+c=0\) always passes through the point \((\alpha, \beta)\), the value of \(\alpha^2+\beta^2\) equals

If \(2x+3y+4=0\) is the perpendicular bisector of the line segment joining the points A(1, 2) and B(\(\alpha,\beta\)), then the value of \(13\alpha+13\beta\) equals

The equation of the pair of straight lines perpendicular to the pair \(2 x^2+3 x y+2 y^2+10 x+5 y=0\) and passing though the origin is

If the centroid of the triangle formed by the lines \(2 y^2+5 x y-3 x^2=0\) and \(x+y=k\) is \(\left(\frac{1}{18}, \frac{11}{18}\right)\), then the value of \(k\) equals

If \(m_1\) and \(m_2,\left(m_1>m_2\right)\) are the slopes of the lines represented by \(5 x^2-8 x y+3 y^2=0\), then \(m_1: m_2\) equals

If the slope of one of the lines represented by \(a x^2+2 h x y+b y^2=0\) is the square of the other then, \(\left|\frac{a+b}{h}+\frac{8 h^2}{a b}\right|\) is equal to

The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, \(-\)4) is

The direction cosines of a line which makes
equal angles with the coordinate axes are

Let \(O\) be the origin and \(P\) be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{O P}\) are \((1,-2,-2)\), then the coordinates of \(P\) are

The value of \(x\) satisfying the equation \(3 \operatorname{cosec} x=4 \sin x\) are

\(\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)\) is equal to

If \(\sin \alpha - \cos \alpha = m\) and \(\sin 2\alpha = n - {m^2}\), where \(- \sqrt 2 \le m \le \sqrt 2\), then n is equal to

If \(\sinh u=\tan \theta\), then \(\cosh u\) is equal to

A vector makes equal angles \(\alpha\) with \(X\) and \(Y\)-axis, and \(90 \Upsilon\) with \(Z\)-axis. Then, \(\alpha\) is equal to
(c) 45Yand 135Y
(d) $90 \mathrm{Y}$

Angle made by the position vector of the point (5, \(-\)4, \(-\)3) with the positive direction of X-axis is

If the volume of the parallelopiped formed by the vectors \(\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+a \hat{\mathbf{k}}\) and \(a \hat{\mathbf{i}}+\hat{\mathbf{k}}\) becomes minimum, then \(a\) is equal to

If \(\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}\) and \(\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}}{2}\), then angle between \(\mathbf{a}+\mathbf{b}\) and \(\mathbf{a}-\mathbf{b}\) is

Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(\mathbf{c}=7 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}\), then the area of parallel...

If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(|\mathbf{a}|=2, |\mathbf{b}|=3\) and \(\mathbf{a}+t \mathbf{b}\) and \(\mathbf{a}-t \mathbf{b}\) are perpendicular, where \(t\) is a positive scalar, then

A resonant frequency of a current is \(f\). If the
capacitance is made four times the initial
value, then the resonant frequency will
become

Potential energy between a proton and an electron is given by \(U=\frac{K e^2}{3 R^3}\), then radius of Bohr's orbit can be given by

In the given circuit, if the potential
difference between A and B is 80 V, then the
equivalent capacitance between A and B and
the charge on 10 \(\propto\) F capacitor respectively,
are

A metal ball of mass 2 kg moving with a
velocity of 36 km/h has a head on collision
with a stationary ball of mass 3 kg. After the
collision, if both balls move together, then
the loss in kinetic energy due to collision is

A particle of mass m, moving with a velocity
v makes an elastic collision in one dimension
with a stationary particle of mass m. During
the collision, they remain in contact with
each other for an extremely small time T.
Their force of cont...

The sum of moments of all the particles in a
system about its centre of mass is always

Assertion (A) Two identical trains move in
opposite senses in equatorial plane with
same speeds relative to the Earth’s surface.
They have equal magnitude of normal
reaction.
Reason (R) The trains have different
centripetal accelerations du...

A cell of emf 1.8 V gives a current of 17 A when directly connected to an ammeter of resistance 0.06 \(\Omega\). Internal resistance of the cell is

Radiation of wavelength \(300 \mathrm{~nm}\) and intensity \(100 \mathrm{~W}-\mathrm{m}^{-2}\) falls on the surface of a photosensitive material. If \(2 \%\) of the incident photons produce photoelectron, the number of photoelectrons emitte...

The Young's modulus of a rubber string of length \(12 \mathrm{~cm}\) and density \(1.5 ~\mathrm{kgm}^{-3}\) is \(5 \times 10^8 ~\mathrm{Nm}^{-2}\). When this string is suspended vertically, the increase in its length due to its own weight i...

An electric generator is based on

Assertion (A) It is more difficult to move a
magnet into a coil with more loops.
Reason (R) This is because emf induced in
each current loop resists the motion of the
magnet.

Two inductors A and B when connected in
parallel are equivalent to a single inductor of
inductance 1.5 H and when connected in
series are equivalent to a single inductor of
inductance 8H. Find the difference in the
inductances of A and B.

The law which states that a variation in an
electric field causes magnetic field, is

Which statement(s) among the following are
incorrect?
(i) A negative test charge experiences a force
opposite to the direction of the field.
(ii) The tangent drawn to a line of force
represents the direction of electric field.
(iii) The ele...

The lower end of a capillary tube is dipped
into water and it is observed that the water
in capillary tube rises by 7.5 cm. Find the
radius of the capillary tube used, if surface
tension of water is 7.5 \(\times\) 10\(^{-2}\) Nm\(^{-1}\). A...

An ideal liquid flows through a horizontal
tube of variable diameter. The pressure is
lowest where the

A particle is kept on the surface of a uniform
sphere of mass 1000 kg and radius 1 m. The
work done per unit mass against the
gravitational force between them is
[G = 6.67 \(\times\) 10\(^{-11}\) Nm\(^2\) kg\(^{-2}\)]

The acceleration due to gravity at a height (1/20)th of the radius of Earth above the Earth's surface is 9 ms\(^{-2}\). Its value at an equal depth below the surface of earth is

In a steady state, the temperature at the end \(A\) and end \(B\) of a \(20 \mathrm{~cm}\) long rod \(A B\) are \(100 \Upsilon\) and \(0^{\circ} \mathrm{C}\). The temperature of a point \(9 \mathrm{~cm}\) from \(A\) is

If two rods of length \(L\) and \(2 L\), having coefficients of linear expansion \(\alpha\) and \(2 \alpha\) respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

A system is taken from state-A to state-B
along two different paths. The heat absorbed
and work done by the system along these
two paths are Q\(_1\), Q\(_2\) and W\(_1\), W\(_2\) respectively, then

A gas (\(\gamma\) = 1.5 ) is suddenly compressed to
(1/4 )th its initial volume. Then, find the ratio
of its final to initial pressure.

A cylinder has a piston at temperature of \(30 \Upsilon\)C. There is all round clearance of \(0.08 \mathrm{~mm}\) between the piston and cylinder wall if internal diameter of the cylinder is \(15 \mathrm{~cm}\). What is the temperature at w...

A balloon contains 1500 m\(^3\) of He at 27\(\Upsilon\)C and 4 atmospheric pressure, the volume of He at \(-3\Upsilon\)C temperature and 2 atmospheric pressure will be

An object dropped in a stationary lift takes time \(t_1\) to reach the floor. It takes time \(t_2\) when lift is moving up with constant acceleration. Then,

When a body is placed on a rough plane (coefficient of friction \(=~\propto\) ) inclined at an angle \(\theta\) to the horizontal, its acceleration is (acceleration due to gragvity \(=g\) )

The plane of a dip circle is set in the geographic meridian and the apparent dip is \(\delta_1\). It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is \(\delta_2\). The declination $$\theta$...

When a ball is thrown with a velocity of 50 ms\(^{-1}\) at an angle 30\(\Upsilon\) with the horizontal, it remains in the air for ......... s.
(Take, g = 10 ms\(^{-2}\))

Which of the following decreases, in motion
on a straight line, with constant retardation?