Let $\vec a=\hat i+\hat j+\hat k,;\vec b=2\hat i+4\hat j-5\hat k$ and $\vec c=x\hat i+2\hat j+3\hat k,;x\in\mathbb R$. If $\vec d$ is the unit vector in the direction of $(\vec b+\vec c)$ such that $\vec a\cdot\vec d=1$, then $(\vec a\times\vec b)\cdot\vec c$ equals:

1

Let a relation $R$ on $\mathbb N\times\mathbb N$ be defined by $(x_1,y_1),R,(x_2,y_2)$ iff $x_1\le x_2$ or $y_1\le y_2$…

Topic: JEE Main 2024 (4 April Evening Shift)

2

If $a,b,c$ are in AP and $a+1,; b,; c+3$ are in GP. Given $a>10$ and the arithmetic mean of $a,b,c$ is $8$, then the cu…

Topic: JEE Main 2024 (4 April Evening Shift)

3

If $\displaystyle \int_{-1}^{1}\frac{\cos(\alpha x)}{1+3x^{2}},dx=\frac{2}{\pi}$, then a value of $\alpha$ is:

Topic: JEE Main 2024 (4 April Evening Shift)

4

The area (in sq. units) of the region $S = \{\, z \in \mathbb{C} : |z - 1| \le 2,\ (z + \bar{z}) + i(z - \bar{z}) \le …

Topic: JEE Main 2024 (4 April Evening Shift)

5

Let $PQ$ be a chord of the parabola $y^{2}=12x$ and the midpoint of $PQ$ be at $(4,1)$. Then, which of the following …

Topic: JEE Main 2024 (4 April Evening Shift)

6

Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersect the circle…

Topic: JEE Main 2024 (4 April Evening Shift)

7

The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.

Topic: JEE Main 2024 (4 April Evening Shift)

8

Let $y=y(x)$ be the solution of the differential equation $(x^{2}+4)^{2}\,dy+(2x^{3}y+8xy-2)\,dx=0.$ If $y(0)=0$, then …

Topic: JEE Main 2024 (4 April Evening Shift)

9

For $\lambda>0$, let $\theta$ be the angle between the vectors $\vec a=\hat i+\lambda\hat j-3\hat k$ and $\vec b=3\ha…

Topic: JEE Main 2024 (4 April Evening Shift)

10

Given that the inverse trigonometric functions assume principal values only. Let $x,y\in[-1,1]$ such that $\cos^{-1}x…

Topic: JEE Main 2024 (4 April Evening Shift)

1

Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2…

Topic: JEE Main 2024 (4 April Evening Shift)