KCET 2020

If \(A, B, C\) are three mutually exclusive and exhaustive events of an experiment such that \(P(A)=2 P(B)=3 P(C)\), then \(P(B)\) is equal to

A die is thrown 10 times, the probability that an odd number will come up at least one time is

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{6}\), then \(P\left(A^{\prime} / B\right)\) is

If the sum of \(n\) terms of an AP is given by \(S_n=n^2+n\), then the common difference of the \(\mathrm{AP}\) is

If \(n(A)=2\) and total number of possible relations from Set A to set B is 1024, then \(n(B)\) is

If \(A=\{a, b, c\}\), then the number of binary operations on \(A\) is

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,1)\}\), then \(R\) is

If \(A=\{1,2,3,4,5,6\}\), then the number of subsets of A which contain at least two elements is

The standard deviation of the data 6, 7, 8, 9, 10 is

The two lines \(l x+m y=n\) and \(l^{\prime} x+m^{\prime} y=n^{\prime}\) are perpendicular if

The distance of the point \((1,2,-4)\) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) is

The point \((1,-3,4)\) lies in the octant

The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}\) and the plane \(2 x-2 y+z=5\) is

If a line makes an angle of with each of \(X\) and \(Y\)-axis, then the acute angle made by Z-axis is

The value of \(\sin ^2 51^{\circ}+\sin ^2 39^{\circ}\) is

If \(\tan A+\cot A=2\), then the value of \(\tan ^4 A+\cot ^4 A=\)

If \(|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6\), then \(|\mathbf{b}|\) is equal to

If \(\mathbf{a}\) and \(\mathbf{b}\) are unit vectors and \(\theta\) is the angle between \(\mathbf{a}\) and \(\mathbf{b}\), then \(\sin \frac{\theta}{2}\) is equal to

If the vectors \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are coplanar, then the value of $$\lambda...

The two vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) represent the two sides \(\overline{A B}\) and \(\overline{A C}\) respectively of a \(\triangle A B C\). Th...

The power factor of \(R-L\) circuit is \(\frac{1}{\sqrt{3}}\). If the inductive reactance is \(2 \Omega\). The value of resistance is

A \(220 \mathrm{~V}\) AC supply is connected between points \(A\) and \(B\) as shown in figure, what will be the potential difference \(V\) across the capacitor?

In the given circuit, the resonant frequency is

In the given circuit the peak voltage across \(C, L\) and \(R\) are \(30 \mathrm{~V}, 110 \mathrm{~V}\) and \(60 \mathrm{~V}\), respectively. The rms value of the applied voltage is

The period of revolution of an electron revolving in nth orbit of \(\mathrm{H}\)-atom is proportional to

Two protons are kept at a separation of \(10 \mathrm{~nm}\). Let \(F_n\) and \(F_e\) the nuclear force and the electromagnetic force between them

Angular momentum of an electron in hydrogen atom is \(\frac{3 h}{2 \pi}\) (\(h\) is the Planck's constant). The KE of the electron is

During a \(\beta^{-}\)-decay

A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years?

A beam of fast moving alpha particles were directed towards a thin film of gold. The parts \(A, B\) and \(C\) of the transmitted and reflected beams corresponding to the incident parts \(A, B\) and \(C\) of the beam are shown in the adjoini...

The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is \(6 \mu \mathrm{F}\). The value of capacitance of each capacitor is

One end of a string of length \(l\) is connected to a particle of mass \(m\) and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the ...

The colour code for a carbon resistor of resistance \(0.2 \mathrm{k} \Omega \pm 10 \%\) is

A metal rod of length \(10 \mathrm{~cm}\) and a rectangular cross-section of \(1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}\) is connected to a battery across opposite faces. The resistance will be

A car has a fresh storage battery of emf \(12 \mathrm{~V}\) and internal resistance \(2 \times 10^{-2} \Omega\). If the starter motor draws a current of \(80 \mathrm{~A}\). Then, the terminal voltage when the starter is On is

A potentiometer has a uniform wire of length \(5 \mathrm{~m}\). A battery of emf \(10 \mathrm{~V}\) and negligible internal resistance is connected between its ends. A secondary cell connected to the circuit gives balancing length at $$200 ...

Each resistance in the given cubical network has resistance of \(1 \Omega\) and equivalent resistance between \(A\) and \(B\) is

\(I-V\) characteristic of a copper wire of length \(L\) and area of cross-section \(A\) is shown in figure. The slope of the curve becomes

The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is

A hot filament liberates an electron with zero initial velocity. The anode potential is \(1200 \mathrm{~V}\). The speed of the electron when it strikes the anode is

The following graph represents the variation of photocurrent with anode potential for a metal surface. Here \(I_1, I_2\) and \(I_3\) represents intensities and \(\gamma_1, \gamma_2, \gamma_3\) represent frequency for curves \(1,2\) and $$3$...

Young's modulus of a perfect rigid body is

The current in a coil of inductance \(0.2 \mathrm{H}\) changes from \(5 \mathrm{~A}\) to \(2 \mathrm{~A}\) in \(0.5 \mathrm{~s}\). The magnitude of the average induced emf in the coil is

A rod of length \(2 \mathrm{~m}\) slides with a speed of \(5 \mathrm{~ms}^{-1}\) on a rectangular conducting frame as shown in figure. There exists a uniform magnetic filed of \(0.04 \mathrm{~T}\) perpendicular to the plane of the figure. I...

A light beam of intensity \(20 \mathrm{~W} / \mathrm{cm}^2\) is incident normally on a perfectly reflecting surface of sides \(25 \mathrm{~cm} \times 15 \mathrm{~cm}\). The momentum imparted to the surface by the light per second is

An infinitely long thin straight wire has uniform charge density of \(\frac{1}{4} \times 10^{-2} \mathrm{~cm}^{-1}\). What is the magnitude of electric field at a distance \(20 \mathrm{~cm}\) from the axis of the wire?

When a soap bubble is charged?

A dipole moment \(p\) and moment of inertia \(I\) is placed in a uniform electric field \(\mathbf{E}\). If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is

A point charge \(q\) is placed at the corner of a cube of side \(a\) as shown in the figure. What is the electric flux through the face \(A B C D\) ?

Figure shows three points \(A, B\) and \(C\) in a region of uniform electric field \(\mathbf{E}\). The line \(A B\) is perpendicular and \(B C\) is parallel to the field lines. Then, which of the following holds good ? (\(V_A, V_B\) and $$V...