AP EAPCET 2022 - 4th July Evening Shift

If the difference between the roots of \(x^2+a x+b=0\) and that of the roots of \(x^2+b x+a=0\) is same and \(a \neq b\), then

For what values of \(a \in Z\), the quadratic expression \((x+a)(x+1991)+1\) can be factorised as \((x+b)(x+c)\), where \(b, c \in Z\) ?

If the mean of the data \(p, 6,6,7,8,11,15,16\), is 3 times \(p\), then the mean deviation of the data from its mean is

If the pair of straight lines \(9 x^2+a x y+4 y^2+6 x+b y-3=0\) represents two parallel lines, then

A line passing through \(P(2,3)\) and making an angle of \(30^{\circ}\) with the positive direction of \(X\)-axis meets \(x^2-2 x y-y^2=0\) at \(A\) and \(B\). Then the value of \(P A: P B\) is

Suppose, in \(\triangle A B C, x-y+5=0, x+2 y=0\) are respectively the equations of the perpendicular bisectors of the sides \(A B\) and \(A C\). If \(A\) is \((1,-2)\), the equation of the line joining \(B\) and \(C\) is

Suppose \(P\) and \(Q\) are the mid-points of the sides \(A B\) and \(B C\) of a triangle where \(A(1,3), B(3,7)\) and \(C(7,15)\) are vertices. Then, the locus of \(R\) satisfying \(A C^2+Q R^2=P R^2\) is

If the points of intersection of the coordinate axes and \(|x+y|=2\) form a rhombus, then its area is

If the equation of the plane which is at a distance of \(1 / 3\) units from the origin and perpendicular to a line whose directional ratios are \((1,2,2)\) is \(x+p y+q z+r=0\), then \(\sqrt{p^2+q^2+r^2}=\)

If the equation of the plane passing through the point \(A(-2,1,3)\) and perpendicular to the vector \(3 \hat{i}+\hat{j}+5 \hat{k}\) is \(a x+b y+c z+d=0\), then \(\frac{a+b}{c+d}=\)

If \(x\)-coordinate of a point \(P\) on the line joining the points \(Q(2,2,1)\) and \(R(5,2,-2)\) is 4, then the \(y\)-coordinate of \(P=\)

If \((2,3, c)\) are the direction ratios of a ray passing through the point \(C(5, q, 1)\) and also the mid-point of the line segment joining the points \(A(p,-4,2)\) and \(B(3,2,-4)\), then \(c \cdot(p+7 q)=\)

\(D, E, F\) are respectively the points on the sides \(B C, C A\) and \(A B\) of a \(\triangle A B C\) dividing them in the ratio \(2: 3,1: 2,3: 1\) internally. The lines \(\mathbf{B E}\) and \(\mathbf{C F}\) intersect on the line $$\mathbf...

If \(A+B+C=\pi, \cos B=\cos A \cos C\), then \(\tan A \tan C=\)

A true statement among the following identities is

The value of \(\tan \left(\frac{7 \pi}{8}\right)\) is

\(1+\sec ^2 x \sin ^2 x=\)

If \(P\) and \(Q\) are two points on the curve \(y=2^{x+2}\) in the rectangular cartesian coordinate system such that \(\mathbf{O P} \cdot \hat{i}=-1, \mathrm{OQ} \cdot \hat{i}=2\), then \(\mathrm{OQ}-4 \mathrm{OP}=\)

If \(\mathbf{a}+\mathbf{b}+\mathbf{c}=0\) and \(|\mathbf{a}|=7,|\mathbf{b}|=5,|\mathbf{c}|=3\) then the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is

\(O A B C\) is a tetrahedron. If \(D, E\) are the mid-points of \(O A\) and \(B C\) respectively, then \(\mathbf{D E}=\)

Capacitive reactance of a capacitor in an AC circuit is \(3 \mathrm{k} \Omega\). If this capacitor is connected to a new AC source of double frequency, the capacitive reactance will become.

A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in the excited state is

The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 6 fermi is

As shown in the figure, an iron block \(A\) of volume \(0.25 \mathrm{~m}^3\) is attached to a spring \(S\) of unstretched length 1.0 m and hanging to the ceiling of a roof. The spring gets stretched by 0.2 m . This block is removed and anot...

Two balls \(A\) and \(B\), of masses \(M\) and \(2 M\) respectively collide each other. If the ball \(A\) moves with a speed of \(150 \mathrm{~ms}^{-1}\) and collides with ball \(B\), moving with speed \(v\) in the opposite direction. After...

The electrons take \(40 \times 10^3\) s to dirift from one end of a metal wire of length 2 m to its other end. The area of cross-section of the wire is \(4 \mathrm{~mm}^2\) and it is carrying a current of 1.6 A. The number density of free e...

The current 'I' in the circuit shown in the figure is

In a photoelectric experiment light of wavelength 800 nm produces photoelectrons with the smallest de-Broglie wavelength of 1 nm . Light of 400 nm produces photoelectrons with smallest de-Broglie wavelength of 0.5 nm. Then the work function...

A circular coil has 100 turns, radius 3 cm and resistance \(4 \Omega\). This coil is co-axial with a solenoid of 200 turns/\(\mathrm{cm}\) and diameter 4 cm . If the solenoid current is decreased from 2 A to zero in 0.04 s , then the curren...

A light of intensity \(12 \mathrm{Wm}^{-2}\) incidents on a black surface of area \(4 \mathrm{~cm}^2\). The radiation pressure on the surface is

A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by \(1 \%\) and \(3 \%\) respectively, the modulation index is changed by

The electric field \((E)\) and magnetic field \((B)\) of an electromagnetic wave passing through vacuum are given by
$$\begin{aligned} & E=E_0 \sin (k x-\omega t) \\ & B=B_0 \sin (k x-\omega t) \end{aligned}$$
Then the correct statement amo...

Assertion (A) In a region of constant potential, the electric field is zero and there can be no charge inside the region.
Reason (R) According to Gauss law, charge inside the region should be zero if electric field is zero.

A solid sphere of radius \(R\) carries a positive charge \(Q\) distributed uniformly throughout its volume. A very thin hole is drilled through it's centre. A particle of mass \(m\) and charge \(-\)q performs simple harmonic motion about th...

Statement (A) Inside a charged hollow metal sphere, \(E=0, V \neq 0\), (where, \(E=\) electric field, \(V=\) electric potential).
Statement (B) The work done in moving a positive charge on an equipotential surface is zero.
Statement (C) Whe...

In a hydraulic lift, compressed air exerts a force \(F\) on a small piston of radius 3 cm . Due to this pressure the second piston of radius 5 cm lifts a load of 1875 kg . The value of \(F\) is (Acceleration due to gravity $$=10 \mathrm{~ms...

In a \(U\)-shaped tube the radius of one limb is 2 mm and that of other limb is 4 mm . A liquid of surface tension \(0.03 \mathrm{~Nm}^{-1}\), density \(1500 \mathrm{~kg} \mathrm{~m}^{-3}\) and angle of contact zero is taken in the tube. Th...

A steady flow of a liquid of density \(\rho\) is shown in figure. At point 1, the area of cross-section is \(2 A\) and the speed of flow of liquid is \(\sqrt{2} \mathrm{~ms}^{-1}\). At point 2 , the area of cross-section is \(A\). Between t...

A uniform solid sphere of radius \(R\) produces a gravitational acceleration of \(a_0\) on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes \(\frac{a_0}{4}\) is

In non-rigid diatomic molecule with an additional vibrational mode

The temperature of the sink of a Carnot engine is 250 K . In order to increase the efficiency of the Carnot engine from \(25 \%\) to \(50 \%\), the temperature of the sink should be increased by

A metal tape is calibrated at \(25^{\circ} \mathrm{C}\). On a cold day when the temperature is \(-15^{\circ} \mathrm{C}\), the percentage error in the measurement of length is
(Coefficient of linear expansion of metal $$=1 \times 10^{-5}{ }...

A gas is expanded from an initial state to a final state along a path on a \(p\)-\(V\) diagram. The path consists of (i) an isothermal expansion of work 50 J , (ii) an adiabatic expansion and (iii) an isothermal expansion of work 20 J . If ...

A cricket ball of mass 50 g having velocity \(50 \mathrm{~cm} \mathrm{~s}^{-1}\) to stopped in 0.5 s. The force applied to stop the ball is

Two masses \(M_1\) and \(M_2\) are arranged as shown in the figure. Let \(a\) be the magnitude of the acceleration of the mass \(M_1\). If the mass of \(M_1\) is doubled and that of \(M_2\) is halved, then the acceleration of the system is
...

A steel wire of length \(l\) and magnetic moment \(M\) is bent into a semicircular arc of radius \(R\). The new magnetic moment is

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at \(30^{\circ}\) with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3 G . The...

A force \(\mathbf{F}_1\) of magnitude 4 N acts on an object of mass 1 kg , at origin in a direction \(30^{\circ}\) above the positive \(X\)-axis. A second \(F_2\) of magnitude 4 N acts on the same object in the direction of the positive $$Y...

\(y=\left(P t^2-Q t^3\right) \mathrm{~m}\) is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

An object moving along \(X\)-axis with a uniform acceleration has velocity \(\mathbf{v}=\left(12 \mathrm{cms}^{-1}\right) \hat{\mathbf{i}}\) at \(x=3 \mathrm{~cm}\). After 2 s if it is at \(x=-5 \mathrm{~cm}\), then its acceleration is