KCET 2019

If \(A\) and \(B\) are two events of a sample space \(S\) such that \(P(A)=0.2, P(B)=0.6\) and \(P(A \mid B)=0.5\) then \(P\left(A^{\prime} \mid B\right)=\)

If '\(X\)' has a binomial distribution with parameters \(n=6, p\) and \(P(X=2)=12\), \(P(X=3)=5\) then \(P=\)

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set \(S=\{1,2,3,4,5,6,7\}\) and reports that it is even. The probability that is actually even is

If \(\alpha\) and \(\beta\) are roots of the equation \(x^2=x+1=0\), then \(\alpha^2+\beta^2\) is

The third term of a GP is 9. The product of its first five terms is

If \(A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}\), then the number of onto functions from \(A\) to \(B\) is

On the set of positive rational, a binary operation * is defined by \(a * b=\frac{2 a b}{5}\). If \(2 * x=3^{-1}\), then \(x=\)

If \(U\) is the universal set with 100 elements; \(A\) and \(B\) are two set such that \(n(A)=50, n(B)=60, n(A \cap B)=20\) then \(n\left(A^{\prime} \cap B^{\prime}\right)=\)

Mean and standard deviation of 100 items are 50 and 4 , respectively. The sum of all squares of the items is

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of \(X\)-axis is

Foot of the perpendicular drawn from the point \((1,3,4)\) to the plane \(2 x-y+z+3=0\) is

Acute angel between the line \(\frac{(x-5)}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and the plane \(3 x-4 y-z+5=0\) is

\(X Y\) plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

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

If \(\cos x=|\sin x|\) then, the general solution is

\(\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=\)

If \(|\mathbf{a}|=16,|\mathbf{b}|=4\), then \(\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=\)

If the angle between \(\mathbf{a}\) & \(\mathbf{b}\) is \(\frac{2 \pi}{3}\) and the projection of \(\mathbf{a}\) in the direction of \(\mathbf{b}\) is \(-\)2 , the \(|\mathbf{a}|=\)

A unit vector perpendicular to the plane containing the vector \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is

\([\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=\)

The frequency of an alternating current is \(50 \mathrm{~Hz}\). What is the minimum time taken by current to reach its peak value from rms value?

An inductor of inductance \(L\) and resistor \(R\) are joined together in series and connected by a source of frequency \(\omega\). The power dissipated in the circuit is

In Rutherford experiment, for head-on collision of \(\alpha\)-particles with a gold nucleus, the impact parameter is

Frequency of revolution of an electron revolving in \(n\)th orbit of \(\mathrm{H}\)-atom is proportional to

A hydrogen atom is ground state absorbs \(10.2 \mathrm{~eV}\) of energy. The orbital angular momentum of the electron is increased by

The end product of decay of \({ }_{90} \mathrm{Th}^{232}\) is \({ }_{82} \mathrm{~Pb}^{208}\). The number of \(\alpha\) and \(\beta\) particles emitted are respectively

Which one of the following nuclei has shorter mean life?

A capacitor of capacitance \(C\) charged by an amount \(Q\) is connected in parallel with an uncharged capacitor of capacitance \(2 C\). The final charges on the capacitors are

The equivalent capacitance between A and B is

During inelastic collision between two objects, which of the following quantity always remains conserved?

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are \(v\) and \(2 v\) at any instant, then the speed of centre of mass of the system is

Though the electron drift velocity is small and electron charge is very small, a conductor can carry an appreciably large current because

Masses of three wires of copper are in the ratio \(1: 3: 5\) and their lengths are in the ratio \(5: 3: 1\). The ratio of their electrical resistance are

Kirchhoff 's junction rule is a reflection of

In a potentiometer experiment, the balancing point with a cell is at a length \(240 \mathrm{~cm}\). On shunting the cell with a resistance of \(2 \Omega\), the balancing length becomes \(120 \mathrm{~cm}\). The internal resistance of the ce...

The readings of ammeter and voltmeter in the following circuit are respectively

In the given circuit, the current through 2\(\Omega\) resistor is

The variation of terminal potential difference \(V\) with current flowing through a cell is as shown. The emf and internal resistance of the cell are

An electron is moving with an initial velocity \(\mathbf{v}=v_0 \hat{\mathbf{i}}\) and is in a uniform magnetic field \(\mathbf{B}=B_0 \hat{\mathbf{j}}\). Then its de-Broglie wavelength

Light of certain frequency and intensity incident on a photosensitive material causes photoelectric effect. If both the frequency and intensity are doubled, the photoelectric saturation current becomes

A wire is stretched such that its volume remains constant. The poission's ratio of the material of the wire is

Consider the situation given in figure. The wire \(A B\) is slid on the fixed rails with a constant velocity. If the wire \(A B\) is replaced by a semicircular wire, the magnitude of the induced current will

An antenna uses electromagnetic waves of frequency \(5 \mathrm{~MHz}\).
For proper working, the size of the antenna should be

Due to Doppler's effect the shift in wavelength observed is \(0.1 \mathop A\limits^o\) for a star producing wavelength \(6000 \mathop A\limits^o\). Velocity of recession of the star will be

An electromagnetic wave is travelling in \(x\)-direction with electric field vector given by, \(\mathbf{E}_y=E_0 \sin (k x-\omega t) \hat{\mathbf{j}}\). The correct expression for magnetic field vector is

The phenomenon involved in the reflection of radio-waves by ionosphere is similar to

Two metal plates are separated by \(2 \mathrm{~cm}\). The potentials of the plates are \(-10 \mathrm{~V}\) and \(+30 \mathrm{~V}\). The electric field between the two plates is

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

A certain charge \(2 Q\) is divided at first into two parts \(q_1\) and \(q_2\). Later the charges are placed at a certain distance. If the force of interaction between two chagrges is maximum then \(\frac{Q}{q_1}\) is

A particle of mass \(m\) and charge \(q\) is placed at rest in uniform electric field \(E\) and then released. The kinetic energy attained by the particle after moving a distance \(y\) is