KCET 2026

The mean and standard deviation of $100$ items are $50$ and $4$, respectively then the sum of all squares of the items is

The line $L_2$ passing through $(3, -1)$ divides the line segment $L_1$ joining the points $(-1, 2)$ and $(3, 6)$ in the ratio $1 : 3$ internally. The equation of line $L_2$ is:

The three points $A(2, 4, 3), B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of "a" is

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = \dfrac{y - 2}{1} = \dfrac{z - 3}{1}$ is

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

If $\alpha$ and $\beta$ are acute angles such that $\alpha - \beta$ and $\alpha + \beta$ satisfy the equation $\tan^2\theta - 4\tan\theta + 1 = 0$, then $\alpha$ and $\beta$ are respectively,

The maximum value of $\sin\left(x + \dfrac{\pi}{6}\right) + \cos\left(x + \dfrac{\pi}{6}\right)$ is attained at $x = $

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to