List of top Questions asked in KEAM- 2019

If \( z^2 + z + 1 = 0 \), where \( z \) is a complex number, then the value of \[ \left( z + \frac{1}{z} \right)^2 + \left( z^2 + \frac{1}{z^2} \right)^2 + \left( z^3 + \frac{1}{z^3} \right)^2 + \cdots + \left( z^6 + \frac{1}{z^6} \right)^2 \] is

The value of \( \tan\left[ \sin^{-1}\left(\frac{-1}{\sqrt{2}}\right) \right] \) is

If \( \sin^{-1} x + \cos^{-1} 2x = \frac{\pi}{6} \), then the value of \( x \) is

If \[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \] is the inverse of the matrix \[ \begin{pmatrix} 1 & 5 \\ 7 & -3 \end{pmatrix}, \] then \( d \) equals

If \( a, b \) and \( c \) are distinct reals and the determinant \[ \begin{vmatrix} a^3+1 & a^2 & a \\ b^3+1 & b^2 & b \\ c^3+1 & c^2 & c \end{vmatrix} = 0, \] then the product \( abc \) is

Consider the set \( M = \{1,2,3\} \) along with the relation \( R = \{(1,2), (1,1), (3,1), (3,4), (3,3), (4,3)\ \). Which of the following statements is true?

If \( f : \mathbb{R} \to \mathbb{R} \) is a function defined by \( f(x) = \sin x \), then which of the following is true?

If \( (x,y,z) \) is the solution of the equations \[ x - y - 2z = 3, 2x + y + 4z = 5, 4x - y - 2z = 11, \] then the value of \( y \) equals

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

A particle is displaced from the point \( (2,1,-1) \) to \( (4,3,-4) \) by the force \( 2i + 4j - 5k \). Then the work done by the force is

The value of \( m \) if the vectors \( 4i - 3j + 5k \) and \( mi - 4j + k \) are perpendicular, is

If \( A \) and \( B \) are two matrices such that \[ 3A + B = \begin{pmatrix} 9 & 11 & 3 \\ 12 & 14 & 19 \end{pmatrix} \] and \[ 2A - 3B = \begin{pmatrix} -16 & 11 & 2 \\ -3 & -22 & 9 \end{pmatrix}, \] then the matrix \( B \) is

The circle passing through \( (1, -2) \) and touching the \(x\)-axis at \( (3, 0) \) also passes through the point:

The axis of the parabola \( x^2 + 6x + 4y + 5 = 0 \) is:

The value of \( k \), if the circles \( 2x^2 + 2y^2 - 4x + 6y = 3 \) and \( x^2 + y^2 + kx + y = 0 \) cut orthogonally is:

A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. The bulk modulus of the material of the ball is

A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5\, kg$. The coefficient of kinetic friction between the block and the surface is 0.5. Tension in the cord is : $(g = 9.8 \,m/sec^2)$

A wave along a string has the following equation $y = 0.05 \sin (28t - 1.78x)\, m$ (where t is in seconds and x is in meters). What are the amplitude, (A) frequency (f) and wavelength $(\lambda)$ of the wave?

A body undergoing simple harmonic motion has a maximum acceleration of $8\,m / s ^{2}$ and maximum speed of $1.6\,m / s$. What is the time period $T$ ?

The radius of gyration about an axis through the center of a hollow sphere with external radius a and internal radius b is

A vehicle moving at $36\, km/hr$ is to be stopped by applying brakes in the next $5\, m$. If the vehicle weighs $2000\, kg,$ determine the average force that must be applied on it

Maximum number of photons emitted by a bulb capable of producing monochromatic light of wavelength $550\, nm$ is ..........., if $100\, V$ and $1\, A$ is supplied for one hour.

The standard heat of formation of $CH_4, CO_2$ and $H_2O (I)$ are $ -76.2, -394.8$ and $-285.82\, kJ\, mol^{-1}$, respectively. Heat of vaporization of water is $44\, kJ\, mol^{-1}$. Calculate the amount of heat eveolved when $22.4\, L$ of $CH _4$, kept under normal conditions, is oxidized into its gaseous products

The standard of length is maintained by a 1 meter long bar made up of a material having coefficient of linear expansion $\alpha = 0.00001 {^{\circ}C^{-1}}$. If the length of the bar were to be preserved to an accuracy of 1 part per million, what would be maximum allowed temperature variation?

The Henry�s law constant for $O_2$ dissolved in water is $4.34 \times 10^4$ atm at certain temperature. If the partial pressure of $O_2$ in a gas mixture that is in equilibrium with water is 0.434 atm, what is the mole fraction of $O_2$ in the solution?