Let $\overrightarrow a = \alpha \widehat i + 3\widehat j - \widehat k$, $\overrightarrow b = 3\widehat i - \beta \widehat j + 4\widehat k$ and $\overrightarrow c = \widehat i + 2\widehat j - 2\widehat k$ where $\alpha ,\,\beta \in R$, be three vectors. If the projection of $\overrightarrow a $ on $\overrightarrow c $ is ${{10} \over 3}$ and $\overrightarrow b \times \overrightarrow c = - 6\widehat i + 10\widehat j + 7\widehat k$, then the value of $\alpha + \beta $ is equal to :
Previous 10 Questions — JEE Main 2022 (29 June Morning Shift)
Nearest first
1
2
3
Let $f:R \to R$ be a function defined by :$f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2…
Topic: JEE Main 2022 (29 June Morning Shift)
Let the solution curve of the differential equation$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $, $y(1) = 3$ be $…
Topic: JEE Main 2022 (29 June Morning Shift)
The probability that a randomly chosen 2 $\times$ 2 matrix with all the entries from the set of first 10 primes, is sin…
Topic: JEE Main 2022 (29 June Morning Shift)
Next 10 Questions — JEE Main 2022 (29 June Morning Shift)
Ascending by ID
1
2
3
4
5
6
7
8
9
10
The area enclosed by y2 = 8x and y = $\sqrt2$ x that lies outside the triangle formed by y = $\sqrt2$ x, x = 1, y = 2$\…
Topic: JEE Main 2022 (29 June Morning Shift)
If the system of linear equations2x + y $-$ z = 7x $-$ 3y + 2z = 1x + 4y + $\delta$z = k, where $\delta$, k $\in$ R has…
Topic: JEE Main 2022 (29 June Morning Shift)
Let $\alpha$ and $\beta$ be the roots of the equation x2 + (2i $-$ 1) = 0. Then, the value of |$\alpha$8 + $\beta$8| is…
Topic: JEE Main 2022 (29 June Morning Shift)
Let $A = [{a_{ij}}]$ be a square matrix of order 3 such that ${a_{ij}} = {2^{j - i}}$, for all i, j = 1, 2, 3. Then, th…
Topic: JEE Main 2022 (29 June Morning Shift)
Let a set $A = A_1 \cup A_2 \cup \cdots \cup A_k$, where $A_i \cap A_j = \phi$ for $i \ne j$, $1 \le i, j \le k$. Defin…
Topic: JEE Main 2022 (29 June Morning Shift)
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B i…
Topic: JEE Main 2022 (29 June Morning Shift)
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an…
Topic: JEE Main 2022 (29 June Morning Shift)
The domain of the function ${\cos ^{ - 1}}\left( {{{2{{\sin }^{ - 1}}\left( {{1 \over {4{x^2} - 1}}} \right)} \over \pi…
Topic: JEE Main 2022 (29 June Morning Shift)
If the constant term in the expansion of ${\left( {3{x^3} - 2{x^2} + {5 \over {{x^5}}}} \right)^{10}}$ is 2k.l, where l…
Topic: JEE Main 2022 (29 June Morning Shift)
$\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx} $,where [t] denotes greatest …
Topic: JEE Main 2022 (29 June Morning Shift)
