List of top Mathematics Questions asked in KEAM

If \( x^3=\sin\theta,\ y^3=\cos\theta \), then \( x\dfrac{dy}{dx} \) is

If $(f(x))^n=f(nx)$, then $\frac{f'(nx)}{f'(x)}$ is:

If $y=\sin x\sin 2x$ and $t=\cos x$, then $\frac{dy}{dt}$ is:

The function $f(x)=\begin{cases}\dfrac{3x^2-12}{x-2}, & x\neq 2 \\ \lambda, & x=2 \end{cases}$ is continuous for $x\in\mathbb{R}$, then the value of $\lambda$ is:

If $(xe)^y-e^x=0$, then $\frac{dy}{dx}$ at $x=1$ is:

The set of all points where the function $f(x)=\frac{x}{x^2-4},\ x\in\mathbb{R}$ is discontinuous, is:

If \(y=\sin^{-1}(2x\sqrt{1-x^2})\), then \(\frac{dy}{dx}\) at \(x=0\) is

If the standard deviation of six numbers \(x_1,x_2,x_3,x_4,x_5,x_6\) is \(4\), then the variance of \(2x_1+3,2x_2+3,2x_3+3,2x_4+3,2x_5+3,2x_6+3\) is

If \(f(x)+3f(1-x)=x+4\), then \(f(x)=\)

A die is rolled once. If the die shows odd number, then the probability of getting other than \( 5 \) is

If \( P(A)=0.4 \) and \( P(B|A)=0.9 \), then \( P(A \cap B) \) is equal to

If $f(x)=\sqrt{10-x}$, then $\lim_{x\to 1}\frac{f(x)-f(1)}{x-1}$ is equal to:

The value of $\lim\limits_{x \to 0} \frac{(x-\sin 2x)(2x-\sin x)}{x^2}$ is equal to:

The shortest distance between the point \( (2,3,4) \) and the line \( \dfrac{x-4}{-2}=\dfrac{y-4}{2}=\dfrac{z-6}{1} \) is

If a point \( P \) with \( x \)-coordinate \( 7 \) lies on the line joining the points \( A(1,2,3) \) and \( B(4,6,8) \), then the coordinates of the point \( P \) are

If the point \( (3,6,k) \) lies on the line \( \dfrac{x-1}{1}=\dfrac{y-2}{2}=\dfrac{z-3}{3} \), then the value of \( k \) is

The projections of a line segment on the coordinate axes are \(5,6,8\). Then the length of the line segment is

The equation of the straight line joining the points \((1,2,3)\) and \((3,4,k)\) is \(\frac{x-3}{1}=\frac{y-4}{1}=\frac{z-k}{5}\). Then the value of \(k\) is

The mean deviation from mean of the five numbers \(2,4,6,8,10\) is

Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be the sides of a triangle \( ABC \) such that \( \overrightarrow{BC}=\vec{a}, \overrightarrow{CA}=\vec{b} \) and \( \overrightarrow{AB}=\vec{c} \). If \( BC=AC=3 \) and \( \vec{b}\cdot\vec{c}=-9 \), then \( \vec{a}\cdot\vec{b} \) is equal to

If \( \vec{a}=\hat{i}+2\hat{j}-2\hat{k} \) and \( \vec{b}=2\hat{i}+\hat{j}+2\hat{k} \), then a unit vector perpendicular to \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) is

If one end of the latus rectum of the parabola \(y^2=16x\) is \((4,8)\), then the coordinates of the other end of the latus rectum are

If the length of the latus rectum of an ellipse is one-fourth of the major axis, then the eccentricity of the ellipse is

The distance between the foci of the hyperbola \( x^2-4y^2=16 \), is

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors, and \(\theta\) be the angle between them. If \(\vec{a}-\vec{b}\) is a unit vector, then \(\theta\) is equal to