List of top Questions asked in KEAM- 2019

Which of the following is not a solution of the equation $3\tan^2\theta - \sin\theta = 0$?

If $\tan^{-1}x + 2\cot^{-1}x = \frac{\pi}{3}$, then the value of $x$ is

If $\sqrt{\frac{y}{x}} + \sqrt{\frac{x}{y}} = 1$, then $\frac{dy}{dx}$ equals

If $\begin{pmatrix} e & f \\ g & h \end{pmatrix}$ is the inverse of the matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ where $ad - bc = 1$, then $g$ equals

If $(-\sqrt{3} - i)^{30} = -4^k$, then the value of $k$ is

If $\omega$ is an imaginary cube root of unity, then $(1+\omega-\omega^2)^7$ is equal to

If $f : \mathbb{R} \to \mathbb{R}$ is a function defined by $f(x) = x^2$, then which of the following is true?

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

The unit vector in the direction of the vector \( \overrightarrow{AB} \) if \( A=(-2,-1,3) \) and \( B=(1,1,0) \) is \( \alpha i + \beta j + \gamma k \), then \( \alpha+\beta \) is

The area enclosed within the curve \( |x| + |y| = 1 \) is

If the product \( abc = 1 \), then the value of the determinant \( \begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} \) is

The points with position vectors \(60\hat{i}+3\hat{j}, 40\hat{i}-8\hat{j}, a\hat{i}-52\hat{j}\) are collinear if

If $(x,y,z)$ is the solution of the equations $4x + y = 7$, $3y + 4z = 5$, $5x + 3z = 2$, then the value of $x + y + z$ equals

If \( \begin{pmatrix} 3x-y & x+3y \\ 2x-z & 2y+z \end{pmatrix} = \begin{pmatrix} 7 & 9 \\ 5 & 5 \end{pmatrix} \), then \( x+y+z \) equals

One of the foci of the hyperbola \( \frac{x^2}{9} - \frac{y^2}{16} = 1 \) is

The number of solutions of \( \frac{dy}{dx} = y^{1/3} \) passing through origin is

The differential equation which represents the family \( y^2 = 2c(x+\sqrt{c}) \) is

If the circles \( x^2+y^2-8x-6y+c=0 \) and \( x^2+y^2-2y+d=0 \) cut orthogonally, then \( c+d \) equals

If \( \frac{dy}{dx} = \frac{2}{x+y} \) and \( y(1)=0 \), then \( x+y+2 \) equals

The length of the latus rectum of the parabola \( (x+2)^2 = -14(y-5) \) is

If the lines \( \frac{x+3}{-3} = \frac{y-1}{k} = \frac{z-5}{5} \) and \( \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z-5}{5} \) are coplanar, then the value of \( k \) is

If \( M \) and \( N \) are square matrices of order 3 where \( \det(M)=2 \) and \( \det(N)=3 \), then \( \det(3MN) \) is

A plane passes through the point \( (1,-2,1) \) and is perpendicular to planes \(2x-2y+z=0\) and \(x-y+2z=4\). Then the equation of the plane is

The values of \(k\) for which the system \[ (k+1)x + 8y = 0 \] \[ kx + (k+3)y = 0 \] has unique solution, are

Let \( A = \begin{pmatrix} \alpha & 0 \\ 1 & 1 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 0\\ 5 & 1 \end{pmatrix} \) be two matrices where \( \alpha \) is a real number. Then