List of top Questions asked in KCET

If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point

If \(x\begin{bmatrix}     3 \\  2 \end{bmatrix}+y\begin{bmatrix}     1 \\     -1 \end{bmatrix}=\begin{bmatrix}     15 \\     5\end{bmatrix}\) then the value of x and y are

A charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes increase in its speed

A square loop of side 2 cm enters a magnetic field with a constant speed of 2 cm s^-1 as shown. The front edge enters the field at t = 0s. Which of the following graph correctly depicts the induced emf in the loop?
( Take clockwise direction positive )

A stretched wire of a material whose Young's modulus Y = 2 × 10¹¹ Nm^-2 has Poisson's ratio of 0.25. Its lateral strain ε_l = 10^-3. The elastic energy density of the wire is

A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field B_H = 3 × 10^-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms^-2 )

The modulus of the complex number \(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\) is

The equivalent resistance between the points A and B in the following circuit is

The current in a coil changes from 2A to 5A in 0.3s. The magnitude of emf induced in the coil is 1.0V. The value of self-inductance of the coil is

A weak acid with pKa 5.9 and weak base with pKb 5.8 are mixed in equal proportions. pH of the resulting solution is

A sample of water is found to contain 5.85% \((\frac{w}{w})\) of AB (molecular mass 58.5) and 9.50% \((\frac{w}{w})\) XY₂ (molecular mass 95). Assuming 80% ionisation of AB and 60% ionisation of XY₂ , the freezing point of water sample is
[Given : K_f for water 1.86 K kg mol^-1 , Freezing point of pure water is 273 K and A, B and Y are monovalent ions]

A positively charged particle of mass m is passed through a velocity selector. It moves horizontally rightward without deviation along the line y = \(\frac{2mv}{qB}\) with a speed v. The electric field is vertically downwards and magnetic field is into the plane of the paper. Now, the electric field is switched off at t = 0. The angular momentum of the charged particle about origin O at t = \(\frac{\pi m}{qB}\) is

A uniform electric field vector \(\vec{E}\) exists along horizontal direction as shown. The electric potential at A is V_A . A small point charge q is slowly taken from A to B along the curved path as shown. The potential energy of the charge when it is at point B is

The distance ‘s’ in meters travelled by a particle in ‘t’ seconds is given by s = \(\frac{2t^3}{3}-18t+\frac{5}{3}.\) The acceleration when the particle comes to rest is

If y = a sin x + b cos x, then y² + \((\frac{dy}{dx})^2\) is a

In the following equation representing β^- decay, the number of neutrons in the nucleus X is
\(_{83}^{210}\text{Bi}\rightarrow X+e^{-1}+\bar{v}\)

The Curie temperatures of Cobalt and iron are 1400K and 1000K respectively. At T = 1600K , the ratio of magnetic susceptibility of Cobalt to that of iron is

The P-V diagram of a Carnot's engine is shown in the graph below. The engine uses 1 mole of an ideal gas as working substance. From the graph, the area enclosed by the P-V diagram is
[ The heat supplied to the gas is 8000 J ]

A gas at a pressure of 2 atm is heated from 25 °C to 323 °C and simultaneously compressed to \(\frac{2^{rd}}{3}\) of its original value. Then the final pressure is

The swelling in feet and ankles of an aged person due to sitting continuously for long hours during travel, is reduced by soaking the feet in warm salt water. This is because of:

For a given pair of transparent media, the critical angle for which colour is maximum?

A point object is moving at a constant speed of 1 ms^-1 along the principal axis of a convex lens of focal length 10cm. The speed of the image is also 1 ms^-1 , when the object is at _______ cm from the optic centre of the lens.

Three energy levels of hydrogen atom and the corresponding wavelength of the emitted radiation due to different electron transition are as shown. Then

A cubical Gaussian surface has side of length a = 10 cm. Electric field lines are parallel to x-axis as shown. The magnitudes of electric fields through surfaces ABCD and EFGH are 6kNC^-1 and 9kNC^-1 respectively. Then the total charge enclosed by the cube is
[Take ε₀ = 9 × 10^-12 Fm^-1]

An enemy fighter jet is flying along the curve given by y = x² + 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is