List of top Questions asked in KEAM

In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

The maxima and minima of the function $2x^3 - 15x^2 + 36x + 10$ occur respectively at

If $x = \frac{3t}{1+t^3}$ and $y = \frac{3t^2}{1+t^3}$, then $\frac{dy}{dx}$ at $t=1$ equals

A point of inflection of the curve given by $y = x^3 - 6x^2 + 12x + 50$ occurs when

The area enclosed between the curve $y = 11x - 24 - x^2$ and the line $y = x$ is

The value of the integral $\int_{0}^{\frac{\pi}{2}} \log(\tan \theta)\, d\theta$ is

The solution of the differential equation $\frac{dy}{dx} = \frac{y^2}{x}$ passing through the point $(1,-1)$ is

The equation of the normal to the curve given by $x^2 + 2x - 3y + 3 = 0$ at the point $(1,2)$ is

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

The value of $\tan\left[\sin^{-1}\left(\frac{5}{13}\right) + \cot^{-1}\left(\frac{4}{3}\right)\right]$ is

If $\arg(z_1) = \arg(z_2)$, then

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

The value of $\left[\cos\frac{\pi}{8} + i\sin\frac{\pi}{8}\right]^{-4}$ is

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

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

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

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

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 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

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

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

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