Let the system of linear equations $x + y + \alpha z = 2$, $3x + y + z = 4$, $x + 2z = 1$ have a unique solution $(x^*, y^*, z^*)$. If $(\alpha, x^*)$, $(y^*, \alpha)$ and $(x^*, -y^*)$ are collinear points, then the sum of absolute values of all possible values of $\alpha$ is ?

1

The sum of all the real roots of the equation $({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$ is

Topic: JEE Main 2022 (24 June Evening Shift)

2

Let $x * y = {x^2} + {y^3}$ and $(x * 1) * 1 = x * (1 * 1)$.Then a value of $2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2…

Topic: JEE Main 2022 (24 June Evening Shift)

1

Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is

Topic: JEE Main 2022 (24 June Evening Shift)

2

Let $$f(x) = \left\{ {\matrix{ {{{\sin (x - [x])} \over {x - [x]}}} & {,\,x \in ( - 2, - 1)} \cr {\max \{ 2x,3[|x…

Topic: JEE Main 2022 (24 June Evening Shift)

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The value of the integral $\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {(1 + {e^x})({{\sin }^6}x + {{\cos }^6}x)}}} $…

Topic: JEE Main 2022 (24 June Evening Shift)

4

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at th…

Topic: JEE Main 2022 (24 June Evening Shift)

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Let the maximum area of the triangle that can be inscribed in the ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} …

Topic: JEE Main 2022 (24 June Evening Shift)

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Let the area of the triangle with vertices $A(1,\alpha)$, $B(\alpha,0)$ and $C(0,\alpha)$ be $4$ sq. units. If the poin…

Topic: JEE Main 2022 (24 June Evening Shift)

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The number of distinct real roots of the equation x7 $-$ 7x $-$ 2 = 0 is

Topic: JEE Main 2022 (24 June Evening Shift)

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A random variable X has the following probability distribution :The value of P(1 < X < 4 | X $\le$ 2) is equal to…

Topic: JEE Main 2022 (24 June Evening Shift)

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If the shortest distance between the lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{\lambda}$ and $\dfrac{x-2}{1}…

Topic: JEE Main 2022 (24 June Evening Shift)

10

If the shortest distance between the lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{\lambda}$ and $\dfrac{x-2}{1}…

Topic: JEE Main 2022 (24 June Evening Shift)