Let $\overrightarrow a = \alpha \widehat i + 2\widehat j - \widehat k$ and $\overrightarrow b = - 2\widehat i + \alpha \widehat j + \widehat k$, where $\alpha \in R$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\overrightarrow a $ and $\overrightarrow b $ is $\sqrt {15({\alpha ^2} + 4)} $, then the value of $2{\left| {\overrightarrow a } \right|^2} + \left( {\overrightarrow a \,.\,\overrightarrow b } \right){\left| {\overrightarrow b } \right|^2}$ is equal to :
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Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola ${{{x^2}…
Topic: JEE Main 2022 (28 June Evening Shift)
Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $-$4x + 3y = 12 and the line L3, which passes through th…
Topic: JEE Main 2022 (28 June Evening Shift)
Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $\tan x(\cos x - y)$. If the curve passes thro…
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Let x = x(y) be the solution of the differential equation $2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \righ…
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The area of the bounded region enclosed by the curve $y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$ and the x-axi…
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Let f : R $\to$ R be a continuous function satisfying f(x) + f(x + k) = n, for all x $\in$ R where k > 0 and n is a po…
Topic: JEE Main 2022 (28 June Evening Shift)
Let f : R $\to$ R be a differentiable function such that $f\left( {{\pi \over 4}} \right) = \sqrt 2 ,\,f\left( {{\pi …
Topic: JEE Main 2022 (28 June Evening Shift)
Let f, g : R $\to$ R be functions defined by$f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x …
Topic: JEE Main 2022 (28 June Evening Shift)
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 an…
Topic: JEE Main 2022 (28 June Evening Shift)
The term independent of x in the expansion of $(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \rig…
Topic: JEE Main 2022 (28 June Evening Shift)
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If vertex of a parabola is (2, $-$1) and the equation of its directrix is 4x $-$ 3y = 21, then the length of its latus …
Topic: JEE Main 2022 (28 June Evening Shift)
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Topic: JEE Main 2022 (28 June Evening Shift)
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Let $\overrightarrow a $ be a vector which is perpendicular to the vector $3\widehat i + {1 \over 2}\widehat j + 2\wide…
Topic: JEE Main 2022 (28 June Evening Shift)
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Topic: JEE Main 2022 (28 June Evening Shift)
