AP EAPCET 2022 - 5th July Morning Shift

If the mean deviation of the data \(1,1+d 1+2 d, \ldots, 1+100 d,(d>0)\) from their mean is 255, then '\(d\)' is equal to

Suppose the slopes \(m_1\) and \(m_2\) of the lines represented by \(a x^2+2 h x y+b y^2=0\) satisfy \(3\left(m_1-m_2\right)-7=0\) and \(m_1 m_2-2=0\). Then, which of the following is true?

Suppose that the sides passing through the vertex \((\alpha, \beta)\) of a triangle are bisected at right angles by the lines \(y^2-8 x y-9 x^2=0\). Then, the centroid of the triangle is

Suppose \(P\) and \(Q\) lie on \(3 x+4 y-4=0\) and \(5 x-y-4=0\) respectively. If the mid-point of \(P Q\) is \((1,5)\), then the slope of the line passing through \(P\) and \(Q\) is

The length of intercept of \(x+1=0\) between the lines \(3 x+2 y=5\) and \(3 x+2 y=3\) is

If P divides the line segment joining the points \(A(1,2,-1)\) and \(B(-1,0,1)\) externally in the ratio 1 : 2 and \(Q=(1,3,-1)\), then \(PQ=\)

If the direction cosines of a line are \(\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)\) and \(c-a=4\), then \(ca=\)

Let the plane \(\pi\) pass through the point (1, 0, 1) and perpendicular to the planes \(2x + 3y - z = 2\) and \(x - y + 2z = 1\). Let the equation of the plane passing through the point (11, 7, 5) and parallel to the plane \(\pi\) be $$ax ...

\(\text { If } \sin \theta+\operatorname{cosec} \theta=4, \text { then } \sin ^2 \theta+\operatorname{cosec}^2 \theta=\)

If \(2 \cosh 2 x+10 \sinh 2 x=5\), then \(x=\)

If \(\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta\), then the least \(n\) for which \(a_{2 n}=0\) is

If \(\sin \theta=-\frac{3}{4}\), then \(\sin 2 \theta=\)

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$$

Which of the following trigonometric values are negative?
I. \(\sin \left(-292^{\circ}\right)\)
II. \(\tan \left(-190^{\circ}\right)\)
III. \(\cos \left(-207^{\circ}\right)\)
IV. \(\cot \left(-222^{\circ}\right)\)

\(\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=\)

a, b, c are non-coplanar vectors. If
\(\mathbf{a}+3 \mathbf{b}+4 \mathbf{c}=x(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c})+y(\mathbf{a}+5 \mathbf{b}-2 \mathbf{c}) +z(6 \mathbf{a}+14 \mathbf{b}+4 \mathbf{c}) \text {, then } x+y+z=\)

Three vectors of magnitudes \(a, 2 a, 3 a\) are along the directions of the diagonals of 3 adjacent faces of a cube that meet in a point. Then, the magnitude of the sum of those diagonals is

If \(\mathbf{a}\) is collinear with \(\mathbf{b}=3 \hat{i}+6 \hat{j}+6 \hat{k}\) and \(\mathbf{a} \cdot \mathbf{b}=27\), then \(|\mathbf{a}|=\)

Let \(a, b\) and \(c\) be unit vectors such that \(a\) is perpendicular to the plane containing \(\mathbf{b}\) and \(\mathbf{c}\) and angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\). Then, $$|\mathbf{a}+\mathbf{b}+\math...

Let \(\mathbf{F}=2 \hat{i}+2 \hat{j}+5 \hat{k}, A=(1,2,5), B=(-1,-2,-3)\) and \(\mathbf{B A} \times \mathbf{F}=4 \hat{i}+6 \hat{j}+2 \lambda \hat{k}\), then \(\lambda=\)

An \(R-L-C\) circuit consists of a \(150 \Omega\) resistor, \(20 \mu \mathrm{F}\) capacitor and a 500 mH inductor connected in series with a 100 V AC supply. The angular frequency of the supply voltage is $$400 \mathrm{rad} \mathrm{s}^{-1}$...

An electron in the hydrogen atom excites from 2nd orbit to 4th orbit then the change in angular momentum of the electron is (Planck's constant \(h=6.64 \times 10^{-34} \mathrm{~J}-\mathrm{s}\))

Choose the correct statement of the following

A ancient discovery found a sample, where \(75 \%\) of the original carbon (\(\mathrm{C}^{14}\)) remains. Then the age of the sample is
\(\binom{T_{\frac{1}{2}}\left(C^{14}\right)=5730 \text { years, } \ln 0.5=-0.7}{\ln (0.75)=-0.3}\)

The capacitance between the points A and B in the following figure.

Ball \(A\) of mass 1 kg moving along a straight line with a velocity of \(4 \mathrm{~ms}^{-1}\) hits another ball \(B\) of mass 3 kg which is at rest. After collision, they stick together and move with the same velocity along the same strai...

The resistance of wire at \(0^{\circ} \mathrm{C}\) is \(20 \Omega\). If the temperature coefficient of the resistance is \(5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\). The temperature at which the resistance will be double of that at $$0^...

In the given circuit values of \(I_1, I_2, I_3\) are respectively

The following statement is correct in the case of photoelectric effect

Two wires \(A\) and \(B\) of same cross-section are connected end to end. When same tension is created in both wires, the elongation in \(B\) wire is twice the elongation in \(A\) wire. If \(L_A\) and \(L_B\) are the initial lengths of the ...

A circular loop of wire of radius 14 cm is placed in magnetic field directed perpendicular to the plane of the loop. If the field decreases at a steady rate of \(0.05 \mathrm{~Ts}^{-1}\) in some interval, then the magnitude of the emf induc...

The magnetic field in a plane electromagnetic wave is given as
\(\mathbf{B}=\left(3 \times 10^{-7} \mathrm{~T}\right) \sin \left(3 \times 10^4 x+9 \times 10^{12} t\right) \hat{j}\)
The electric field of this wave is given as

Frequencies in the UHF range normally propagate by means of

A large number of positive charges each of magnitude \(q\) are placed along the \(X\)-axis at the origin and at every 1 cm distance in both the directions. The electric flux through a spherical surface of radius 2.5 cm centred at the origin...

The electric field in a region of space is given as \(\mathbf{E}=\left(5 \mathrm{NC}^{-1}\right) x \hat{i}\). Consider point \(A\) on the \(Y\)-axis at \(y=5 \mathrm{~m}\) and point \(B\) on the \(X\)-axis at \(x=2 \mathrm{~m}\). If the pot...

A hydraulic lift is shown in the figure. The movable pistons \(A, B\) and \(C\) are of radius \(10 \mathrm{~cm}, 100 \mathrm{~m}\) and 5 cm respectively. If a body of mass 2 kg is placed on piston \(A\), the maximum masses that can be lifte...

Statement (A) Two artificial satellites revolving in the same circular orbit have same period of revolution.
Statement (B) The orbital velocity is inversely proportional to the square root of radius of the orbit.
Statement (C) The escape ve...

5 g of ice at \(-30^{\circ} \mathrm{C}\) and 20 g of water at \(35^{\circ} \mathrm{C}\) are mixed together in a calorimeter.
The final temperature of the mixture is (Neglect heat capacity of the calorimeter, specific heat capacity of ice $$...

An iron sphere having diameter \(D\) and mass \(M\) is immersed in hot water so that the temperature of the sphere increases by \(\delta T\). If \(\alpha\) is the coefficient of linear expansion of the iron then the change in the surface ar...

The work done by a Carnot engine operating between 300 K and 400 K is 400 J. The energy exhausted by the engine is

The slopes of the isothermal and adiabatic \(p-V\) graphs of a gas are by \(S_I\) and \(S_A\) respectively. If the heat capacity ratio of the gas is \(\frac{3}{2}\), then \(\frac{S_I}{S_A}=\)

The number of rotational degrees of freedom of a diatomic molecule

A body is travelling with \(10 \mathrm{~ms}^{-1}\) on a rough horizontal surface. It's velocity after 2 s is \(4 \mathrm{~ms}^{-1}\). The coefficient of kinetic friction between the block and the plane is (acceleration due to gravity $$=10 ...

Two short magnets of equal dipole moments \(M\) are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance \(d\) from the centre on the bisector of the right angle is
(\(\mu_0=\) Permeability of free sp...

A projectile is launched from the ground, such that it hits a target on the ground which is 90 m away. The minimum velocity of projectile to hit the target is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\))

A student is at a distance 16 m from a bus when the bus begins to move with a constant acceleration of \(9 \mathrm{~m} \mathrm{~s}^{-2}\). The minimum velocity with which the student should run. towards the bus so as the catch it is $$\alph...

An electron having kinetic energy of 100 eV circulates in a path of radius 10 cm in a magnetic field. The magnitude of magnetic field \(|\mathbf{B}|\) is approximately
[Mass of electron \(=0.5 \mathrm{~MeV} \mathrm{c}^{-2}\), where c is the...

A particle of mass \(2.2 \times 10^{-30} \mathrm{~kg}\) and charge \(1.6 \times 10^{-19} \mathrm{C}\) is moving at a speed of \(10 \mathrm{~km} \mathrm{~s}^{-1}\) in a circular path of radius 2.8 cm inside a solenoid. The solenoid has $$25 ...

A needle is lying at the bottom of a water tank of height 12 cm. The apparent depth of the needle measured by a microscope is 9 cm . If the water is replaced by a liquid of refractive index of 1.5 of same height, the distance through which ...

A solid cylinder of radius \(R\) is at rest at a height \(h\) on an inclined plane. If it rolls down then its velocity on reaching the ground is