List of top Mathematics Questions asked in KEAM

$\int\frac{\cos \theta}{2-\sin^{2}\theta}d \theta=$ ________.

$\int\frac{\log(1+x)}{(1+x)}dx=$ ________.

$\int\frac{\sin 2x}{\sin x}dx=$ ________.

The maximum value of the function $f(x)=x\sqrt{4x-x^{2}}$ is ________.

The distance travelled by a moving particle is given by $s=t^{2}-6t+10$. The particle is at rest when $t=$ ________.

If $g(x)=x^{2}-x, x\in\mathbb{R},$ then $g(x)$ is increasing in ________.

The minimum of $f(x)=|x+2|$, $x\in\mathbb{R}$ occurs at ________.

If $y=(\tan x)^{x}$, then $\frac{1}{y}\frac{dy}{dx}=$ ________.

If $e^{y}+x^{2}y+xy^{2}=e^{1}$, then $\frac{dy}{dx}$ at (0,1) is equal to ________.

The function $f(x)=|x^{2}-3x+2|,x\in\mathbb{R}$ is not differentiable at ________.

Let \([a]\) denote the greatest integer less than or equal to \(a\). Then \[ \lim_{x\to 0^{+}} x\left( \left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] \right) \] is equal to ________.

$\lim_{x\rightarrow0}\frac{x \cos^{2}x}{\sin x}$ is equal to ________.

$\lim_{x\rightarrow2}\frac{(x^{3}-8)\sin(x-2)}{x^{2}-4x+4}$ is equal to ________.

$\lim_{x\rightarrow0}\frac{\sin(\pi \sin^{2}x)}{x^{2}} = $ ________.

Four unbiased coins are tossed simultaneously. Probability of getting at most two heads is ________.

The variance of 240, 260, 270, 280 is ________.

If $P(A)=0.7, P(B)=0.5$ and $P(A\cup B)=0.9$, then $P(A/B)$ is ________.

A straight line through the point (1,-1,0) meets the line $\frac{x-1}{1}=\frac{y+1}{1}=\frac{z-1}{-1}$ at right angle. Its equation is ________.

Which one of the following is a vector parallel to the straight line $\vec{r}=(\hat{i}-11\hat{j}+101\hat{k})+\lambda(3\hat{i}-5\hat{j}+2\hat{k}),\lambda\in\mathbb{R}$? ________.

The equation of the line passing through (0, 0, 1) and (1, 1, 0) is ________.

The point of intersection of the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-11}{4}$ and $\frac{x-3}{1}=\frac{y-\frac{9}{2}}{2}=\frac{z}{1}$ is ________.

Let $\vec{a}\times(2\hat{i}+3\hat{j}+4\hat{k})=(2\hat{i}+3\hat{j}+4\hat{k})\times\vec{b}$. If $|\vec{a}+\vec{b}|=\sqrt{29}$, then $\vec{a}+\vec{b} = $ ________.

The line $x-y+4=0$ touches the ellipse $x^{2}+3y^{2}=12$ at ________.

The centre of the ellipse $4x^{2}+24x+9y^{2}-18y+9=0$ is ________.

The length of the latus rectum of the ellipse \[ \frac{x^2}{9}+\frac{y^2}{16}=1 \] is ________.