KCET 2021

Given that, \(A\) and \(B\) are two events such that \(P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2}\) and \(P(A \cup B)=\frac{4}{5}\), then \(P(A)\) is equal to

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

If \(P(A)=0.59, P(B)=0.30\) and \(P(A \cap B)=0.21\) then \(P\left(A^{\prime} \cap B^{\prime}\right)\) is equal to

If \(A, B\) and \(C\) are three independent events such that \(P(A)=P(B)=P(C)=P\), then \(P\) (at least two of \(A, B\) and \(C\) occur) is equal to

A car manufacturing factory has two plants \(X\) and \(Y\). Plant \(X\) manufactures \(70 \%\) of cars and plant \(Y\) manufactures \(30 \%\) of cars. \(80 \%\) of cars at plant \(X\) and \(90 %\) of cars at plant \(Y\) are rated as standar...

If the middle term of the AP is 300, then the sum of its first 51 terms is

In a certain two \(65 \%\) families own cell phones, 15000 families own scooter and \(15 \%\) families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

The standard deviation of the numbers \(31,32,33 \ldots 46,47\) is

The equation of straight line which passes through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to \(x \sec \theta+y \operatorname{cosec} \theta=a\) is

If a plane meets the coordinate axes at \(A, B\) and \(C\) in such a way that the centroid of \(\triangle A B C\) is at the point \((1,2,3)\), then the equation of the plane is

The equation of the line joining the points \((-3,4,11)\) and \((1,-2,7)\) is

The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\)

The mid points of the sides of triangle are \((1,5,-1)(0,4,-2)\) and \((2,3,4)\) then centroid of the triangle

The area of the quadrilateral \(A B C D\) when \(A(0,4,1), B(2,3,-1), C(4,5,0)\) and \(D(2,6,2)\) is equal to

The value of \(\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ}\) is

The value of \(\cos 1200^{\circ}+\tan 1485^{\circ}\) is

If the area of the parallelogram with \(\mathbf{a}\) and \(\mathbf{b}\) as two adjacent sides is 15 sq units, then the area of the parallelogram having \(\mathrm{3 a+2 b}\) and \(\mathbf{a}+3 \mathbf{b}\) as two adjacent sides in sq units i...

A vector a makes equal acute angles on the coordinate axis. Then the projection of vector \(\mathbf{b}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on \(\mathbf{a}\) is

If \(\mathbf{a} \cdot \mathbf{b}=0\) and \(\mathbf{a}+\mathbf{b}\) makes an angle \(60^{\circ}\) with \(a\), then

The diagonals of a parallelogram are the vectors \(3 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). and \(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-8 \hat{\mathbf{k}}\). Then the length of the shorter side of parallelogram is

In an oscillating \(L C\)-circuit, \(L=3 \mathrm{mH}\) and \(C=2.7 \mu \mathrm{F}\). At \(t=0\), the charge on the capacitor is zero and the current is \(2 \mathrm{~A}\). The maximum charge that will appear on the capacitor will be

LC-oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

What will be the reading in the voltmeter and ammeter of the circuit shown?

Energy of an electron in the second orbit of hydrogen atom is \(E_2\). The energy of electron in the third orbit of \(\mathrm{He}^{+}\) will be

An electron in an excited state of \(\mathrm{Li}^{2+}\) ion has angular momentum \(\frac{3 h}{2 \pi}\). The de-Broglie wavelength of electron in this state is \(p \pi a_0\) (where, \(a_0=\) Bohr radius). The value of \(p\) is

In a nuclear reactor heavy nuclei is not used as moderators because

Which graph in the following diagram correctly represents the potential energy of a pair of nucleons as a function of their separation?

The figure shows standing de-Broglie waves due to the revolution of electron in a certain orbit of hydrogen atom. Then, the expression for the orbit radius is (All notations have their usual meanings)

If a slab of insulating material (conceptual). \(4 \times 10^{-3} \mathrm{~m}\) thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by $$3.5 \times 10^{-3} \mathrm{~m}$...

An electrician requires a capacitance of \(6 \mu \mathrm{F}\) in a circuit across a potential difference of \(1.5 \mathrm{~kV}\). A large number of \(2 \mu \mathrm{F}\) capacitors which can withstand a potential difference of not more than ...

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is

In figure, charge on the capacitor is plotted against potential difference across the capacitor. The capacitance and energy stored in the capacitor are respectively.

A \(1 \mathrm{~kg}\) ball moving at \(12 \mathrm{~ms}^{-1}\) collides with a \(2 \mathrm{~kg}\) ball moving in opposite direction at \(24 \mathrm{~ms}^{-1}\). If the coefficient of restitution is \(2 / 3\), then their velocities after the c...

A ball hits the floor and rebounds after an inelastic collision. In this case

A coin placed on a rotating turn table just slips if it is placed at a distance of \(4 \mathrm{~cm}\) from the centre. If the angular velocity of the turn table is doubled it will just slip at a distance of

A copper wire of length \(1 \mathrm{~m}\) and uniform cross-sectional area \(5 \times 10^{-7} \mathrm{~m}^2\) carries a current of \(1 \mathrm{~A}\). Assuming that, there are \(8 \times 10^{28}\) free electrons per \(\mathrm{m}^3\) in coppe...

A wire of resistance \(3 \Omega\) is stretched to twice its original length. The resistance of the new wire will be

Consider an electrical conductor connected across a potential difference \(V\). Let \(\Delta q\) be a small charge moving through it in time \(\Delta t\). If \(I\) is the electric current through it,
I. the kinetic energy of the charge incr...

In the given arrangement of experiment on meter bridge, if \(A D\) corresponding to null deflection of the galvanometer is \(X\), what would be its value if the radius of the wire \(A B\) is doubled?

A proton moving with a momentum \(p_1\) has a kinetic energy \(1 / 8\)th of its rest mass-energy. Another light photon having energy equal to the kinetic energy of the possesses a momentum \(p_2\). Then, the ratio \(\frac{p_1-p_2}{p_1}\) is...

The work-function of a metal is 1 eV. Light of wavelength \(3000 \mathop A\limits^o\) is incident on this metal surface. The velocity of emitted photoelectrons will be

According to Einstein's photoelectric equation to the graph between kinetic energy of photoelectrons ejected and the frequency of incident radiation is

The physical quantity which is measure in the unit of wb \(\mathrm{A}^{-1}\) is

The current following through an inductance coil of self-inductance \(6 \mathrm{~mH}\) at different time instants is as shown. The emf induced between \(t=20 \mathrm{~s}\) and \(t=40 \mathrm{~s}\) is nearly

Suppose that the electric field amplitude of electromagnetic wave is \(E_0=120 \mathrm{~NC}^{-1}\) and its frequency \(f=50 \mathrm{~MHz}\). Then, which of the following value is incorrectly computed?

The source of electromagnetic wave can be a charge

A \(2 \mathrm{~g}\) object, located in a region of uniform electric field \(\mathrm{E}=\left(300 \mathrm{NC}^{-1}\right) \hat{\mathbf{i}}\) carries a charge \(Q\). The object released from rest at \(x=0\), has a kinetic energy of $$0.12 \ma...

Electric field due to infinite, straight uniformly charged wire varies with distance \(r\) as

Which of the following statements is false in the case of polar molecules?

Two capillary tubes \(P\) and \(Q\) are dipped vertically in water. The height of water level in capillary tube \(P\) is \(\frac{2}{3}\) of the height in capillary tube \(Q\). The ratio of their diameter is