List of top Mathematics Questions asked in KCET

A die is thrown 10 times. The probability that an odd number will come up at least once is:

Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:

If a random variable $X$ follows the binomial distribution with parameters $n = 5$, $p$, and $P(X = 2) = 9P(X = 3)$, then $p$ is equal to:

A random variable $X$ has the following probability distribution: \[ \begin{array}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & \frac{25}{36} & k & \frac{1}{36} \\ \hline \end{array} \] If the mean of the random variable $X$ is $\frac{1}{3}$, then the variance is:

The plane containing the point $(3, 2, 0)$ and the line $\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}$ is

The equation $xy = 0$ in three-dimensional space represents:

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is:

If lines $\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5}$ are mutually perpendicular, then $k$ is equal to:

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{p}, \vec{q}, \vec{r}$ are vectors defined by:}\\ \[ \vec{p} = \frac{\vec{a} \times \vec{c}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{q} = \frac{\vec{c} \times \vec{b}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{r} = \frac{\vec{b} \times \vec{a}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \] then $(\vec{i} + \vec{b}) \cdot \vec{p} + (\vec{b} + \vec{c}) \cdot \vec{q} + (\vec{c} + \vec{a}) \cdot \vec{r}$ is:

Let $\vec{a}$ and $\vec{b}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{a} + \vec{b}$ is a unit vector if:

The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$. The length of the median through $A$ is:

The volume of the parallelepiped whose co-terminous edges are $\hat{i} + \hat{j}, \hat{i} + \hat{k}, \hat{i} + \hat{j}$ is:

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is:

The solution of $e^{\frac{dy}{dx}} = x + 1, \, y(0) = 3$ is:

The area of the region bounded by the line $y = x$ and the curve $y = x^3$ is:

The area of the region bounded by the line $y = 3x$ and the curve $y = x^3$ in sq. units is:

$\lim_{n \to \infty} \left(\frac{n}{n^2 + 1^2} + \frac{n}{n^2 + 2^2} + \dots + \frac{n}{n^2 + 3^2 + \dots + \frac{1}{5n}} \right) =$

$\int_{1}^{5} \left(|x - 3| + |1 - x|\right) \, dx =$

$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} \, dx =$

$\int \frac{1}{x \left(6(\log x)^2 + 7\log x + 2\right)} \, dx =$

$\int_{-\pi}^\pi (1 - x^2)\sin x \cos^2 x \, dx =$

$\int \frac{\sin x}{3 + 4\cos^2 x} \, dx =$

If $f(x) = x e^{x^{1-x}}$, then $f(x)$ is:

The maximum volume of the right circular cone with slant height $6$ units is: