If the system of equations $x+\big(\sqrt{2}\sin\alpha\big)y+\big(\sqrt{2}\cos\alpha\big)z=0$ $x+(\cos\alpha)y+(\sin\alpha)z=0$ $x+(\sin\alpha)y-(\cos\alpha)z=0$ has a non-trivial solution, then $\alpha\in\left(0,\frac{\pi}{2}\right)$ is equal to:

1

Let the sum of the maximum and the minimum values of the function $f(x)=\dfrac{2x^{2}-3x+8}{2x^{2}+3x+8}$ be $\dfrac{m…

Topic: JEE Main 2024 (4 April Morning Shift)

2

If $2$ and $6$ are roots of the equation $ax^{2}+bx+1=0$, then the quadratic equation whose roots are $\dfrac{1}{2a+b}$…

Topic: JEE Main 2024 (4 April Morning Shift)

3

The sum of all rational terms in the expansion of $\left(2^{\frac15}+5^{\frac13}\right)^{15}$ is equal to:

Topic: JEE Main 2024 (4 April Morning Shift)

4

Let the first three terms $2,\,p,\,q$ with $q\ne 2$ of a G.P. be respectively the $7^{\text{th}},\,8^{\text{th}}$ and $…

Topic: JEE Main 2024 (4 April Morning Shift)

5

If the solution $y = y(x)$ of the differential equation $(x^{4}+2x^{3}+3x^{2}+2x+2)\,dy-(2x^{2}+2x+3)\,dx=0$ satisfies …

Topic: JEE Main 2024 (4 April Morning Shift)

6

Three urns $A$, $B$ and $C$ contain $(7\text{ red}, 5\text{ black})$, $(5\text{ red}, 7\text{ black})$ and $(6\text{ re…

Topic: JEE Main 2024 (4 April Morning Shift)

7

The vertices of a triangle are $A(-1,3)$, $B(-2,2)$ and $C(3,-1)$. A new triangle is formed by shifting the sides of …

Topic: JEE Main 2024 (4 April Morning Shift)

8

Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$, farther from the origin and at a di…

Topic: JEE Main 2024 (4 April Morning Shift)

9

If the domain of the function $\sin^{-1}\!\left(\dfrac{3x-22}{2x-19}\right)+\log_e\!\left(\dfrac{3x^2-8x+5}{x^2-3x-10}…

Topic: JEE Main 2024 (4 April Morning Shift)

10

Let a unit vector which makes an angle of $60^\circ$ with $\,2\hat i+2\hat j-\hat k\,$ and an angle of $45^\circ$ with …

Topic: JEE Main 2024 (4 April Morning Shift)

1

Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\overline{z})^2 + …

Topic: JEE Main 2024 (4 April Morning Shift)

2

Let $f:\mathbb{R}\to\mathbb{R}$ be a function given by $ f(x)= \begin{cases} \dfrac{1-\cos 2x}{x^2}, & x0, \end{cases} …

Topic: JEE Main 2024 (4 April Morning Shift)