$ \text{Let A, B, C be three points whose position vectors respectively are } \vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}, ; \vec{b} = 2\hat{i} + \alpha \hat{j} + 4\hat{k}, ; \alpha \in \mathbb{R}, ; \vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}. ; \text{If } \alpha \text{ is the smallest positive integer for which } \vec{a}, \vec{b}, \vec{c} \text{ are non-collinear, then the length of the median in } \triangle ABC \text{ through A is :}$
Previous 10 Questions — JEE Main 2022 (29 June Evening Shift)
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The distance of the origin from the centroid of the triangle whose two sides have the equations $x - 2y + 1 = 0$ and $2…
Topic: JEE Main 2022 (29 June Evening Shift)
Let a triangle ABC be inscribed in the circle ${x^2} - \sqrt 2 (x + y) + {y^2} = 0$ such that $\angle BAC = {\pi \over…
Topic: JEE Main 2022 (29 June Evening Shift)
If y = y(x) is the solution of the differential equation $\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 +…
Topic: JEE Main 2022 (29 June Evening Shift)
If $\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^…
Topic: JEE Main 2022 (29 June Evening Shift)
Let f be a real valued continuous function on [0, 1] and $f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $.Then, which of t…
Topic: JEE Main 2022 (29 June Evening Shift)
Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = ${…
Topic: JEE Main 2022 (29 June Evening Shift)
Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $-$ 1) $-$ arg(z + 1) = ${…
Topic: JEE Main 2022 (29 June Evening Shift)
Let $\alpha$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $\alpha$1011 + $\alpha$2022 $-$ $\alpha$3033…
Topic: JEE Main 2022 (29 June Evening Shift)
Next 10 Questions — JEE Main 2022 (29 June Evening Shift)
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The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :
Topic: JEE Main 2022 (29 June Evening Shift)
The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :
Topic: JEE Main 2022 (29 June Evening Shift)
