KCET 2022

If \(A\) and \(B\) are two independent events such that \(P(\bar{A})=0.75, P(A \cup B)=0.65\) and \(P(B)=x\), then find the value of \(x\).

If \(A=\{1,2,3, \ldots, 10\}\), then number of subsets of \(A\) containing only odd numbers is

If \(a_1, a_2, a_3, \ldots, a_{10}\) is a geometric progression and \(\frac{a_3}{a_1}=25\), then \(\frac{a_9}{a_5}\) equals

If the set \(x\) contains 7 elements and set \(y\) contains 8 elements, then the number of bijections from \(x\) to \(y\) is

Suppose that the number of elements in set \(A\) is \(p\), the number of elements in set \(B\) is \(q\) and the number of elements in \(A \times B\) is 7, then \(p^2+q^2=\)

Let the relation \(R\) is defined in \(N\) by \(a R b\), if \(3 a+2 b=27\) then \(R\) is

If the standard deviation of the numbers \(-1, 0,1, k\) is \(\sqrt{5}\) where \(k>0\), then \(k\) is equal to

If the straight line \(2 x-3 y+17=0\) is perpendicular to the line passing through the points \((7,17)\) and \((15, \beta)\), then \(\beta\) equals

If the vertices of a triangle are \((-2,6),(3,-6)\) and \((1,5)\), then the area of the triangle is

The octant in which the point (2, \(-\)4, \(-7\)) lies is

The coordinates of foot of the perpendicular drawn from the origin to the plane \(2 x-3 y+4 z=29\) are

The angle between the pair of lines \(\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}\) and \(\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}\) is

The distance of the point whose position vector is \((2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) from the plane \(\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=4\) is

The trigonometric function \(y=\tan x\) in the II quadrant

The degree measure of \(\frac{\pi}{32}\) is equal to

The value of \(\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}\) is

\(\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}=\)

If \(|\mathbf{a}|=2\) and \(|\mathbf{b}|=3\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then the length of the vector \(\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|\) is

If \(|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36\) and \(|\mathbf{a}|=3\), then \(|\mathbf{a}|\) is equal to

If \(\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\), then express \(\beta\) in the form \(\beta=\beta_1+\beta_2\) where \(\beta_1\) is parallel to \(\alpha\) and \(\beta_2\) is perpe...

In a series \(L C R\) circuit, \(R=300 \Omega, L=0.9 \mathrm{H}, C=2.0 \mu \mathrm{F}\) and \(\omega=1000 \mathrm{~rad} / \mathrm{s}\), then impedance of the circuit is

A series resonant \(\mathrm{AC}\) circuit contains a capacitance \(10^{-6} \mathrm{~F}\) and an inductor of \(10^{-4} \mathrm{H}\). The frequency of electrical oscillations will be

A fully charged capacitor \(C\) with initial charge \(q_0\) is connected to a coil of self inductance \(L\) at \(t=0\). The time at which the energy is stored equally between the electric and the magnetic field is

An alternating current is given by \(i=i_1 \sin \omega t+i_2 \cos \omega t\). The rms current is given by

The radius of hydrogen atom in the ground state is 0.53\(\mathop A\limits^o\). After collision with an electron, it is found to have a radius of 2.12\(\mathop A\limits^o\), the principal quantum number \(n\) of the final state of the atom...

In accordance with the Bohr's model, the quantum number that characterises the Earth's revolution around the Sun in an orbit of radius \(1.5 \times 10^{11} \mathrm{~m}\) with orbital speed \(3 \times 10^4 \mathrm{~ms}^{-1}\) is
[given, mass...

If an electron is revolving in its Bohr orbit having Bohr radius of 0.529\(\mathop A\limits^o\), then the radius of third orbit is

Binding energy of a nitrogen nucleus \(\left[{ }_7^{14} \mathrm{~N}\right]\), given \(m\left[{ }_7^{14} \mathrm{~N}\right]=14.00307 \mathrm{u}\)

Which of the following radiations is deflected by electric field?

A nuclear reactor delivers a power of \(10^9 \mathrm{~W}\), the amount of fuel consumed by the reactor in one hour is

A parallel place capacitor is charged by connecting a \(2 \mathrm{~V}\) battery across it. It is then disconnected from the battery and a glass slab is introduced between plates. Which of the following pairs of quantities decrease?

The centre of mass of an extended body on the surface of the earth and its centre of gravity

A car is moving in a circular horizontal track of radius \(10 \mathrm{~m}\) with a constant speed of \(10 \mathrm{~ms}^{-1}\). A bob is suspended from the roof of the car by a light wire of length \(1.0 \mathrm{~m}\). The angle made by the ...

A charged particle is moving in an electric field of \(3 \times 10^{-10} \mathrm{Vm}^{-1}\) with mobility \(2.5 \times 10^6 \mathrm{~m}^2 / \mathrm{V}-\mathrm{s}\), its drift velocity is

Wire bound resistors are made by winding the wires of an alloy of

10 identical cells each potential \(E\) and internal resistance \(r\) are connected in series to form a closed circuit.

Determine the potential difference across three cells using an ideal voltmeter.

In an atom electrons revolve around the nucleus along a path of radius \(0.72\mathop A\limits^o\) making \(9.4 \times 10^{18}\) revolutions per second. The equivalent currents is [given, \(e=1.6 \times 10^{-19} \mathrm{C}\)]

When a metal conductor connected to left gap of a meter bridge is heated, the balancing point

A wire of a certain material is stretched slowly by \(10 \%\). Its new resistance and specific resistance becomes respectively

A galvanometer of resistance \(50 \Omega\) is connected to a battery \(3 \mathrm{~V}\) along with a resistance \(2950 \Omega\) in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this defle...

If voltage across a bulb rated \(220 \mathrm{~V}, 100 \mathrm{~W}\) drops by \(2.5 \%\) of its rated value, then the percentage of the rated value by which the power would decrease is

The kinetic energy of the photoelectrons increases by \(0.52 \mathrm{~eV}\) when the wavelength of incident light is changed from \(500 \mathrm{~nm}\) to another wavelength which is approximately

The de-Broglie wavelength of a particle of kinetic energy \(K\) is \(\lambda\), the wavelength of the particle, if its kinetic energy \(\frac{K}{4}\) is

In a photo electric experiment, if both the intensity and frequency of the incident light are doubled, then the saturation photoelectric current

A metallic rod breaks when strain produced is \(0.2 \%\). The Young's modulus of the material of the \(\operatorname{rod} 7 \times 10^9 \mathrm{~N} / \mathrm{m}^2\). The area of crosssection to support a load of \(10^4 \mathrm{~N}\) is

A long solenoid has 500 turns, when a current of \(2 \mathrm{~A}\) is passed through it, the resulting magnetic flux linked with each turn of the solenoid is \(4 \times 10^{-3} \mathrm{~Wb}\), then self induction of the solenoid is

A magnetic field of flux densiity \(1.0 \mathrm{~Wb} \mathrm{~m}^{-2}\) acts normal to a 80 turn coil of \(0.01 \mathrm{~m}^2\) area. If this coil is removed from the field in \(0.2 \mathrm{~s}\), then the emf induced in it is

Which of the following radiations of electromagnetic waves has the highest wavelength ?

A tiny spherical oil drop carrying a net charge \(q\) is balanced in still air, with a vertical uniform electric field of strength \(\frac{81}{7} \pi \times 10^5 \mathrm{~V} / \mathrm{m}\). When the field is switched OFF, the drop is observ...

Four charges \(+q_1+2 q_1+q\) and \(-2 q\) are placed at the corners of a square \(A B C D\) respectively. The force on a unit positive charge kept at the centre \(O\) is