$ \text{If the points with position vectors } \alpha\hat{i}+10\hat{j}+13\hat{k},; 6\hat{i}+11\hat{j}+11\hat{k},; \dfrac{9}{2}\hat{i}+\beta\hat{j}-8\hat{k} \text{ are collinear, then } (19\alpha-6\beta)^2 \text{ is equal to:} $

1

If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation :

Topic: JEE Main 2023 (8 April Morning Shift)

2

Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], …

Topic: JEE Main 2023 (8 April Morning Shift)

3

$ \text{Let } S_K=\dfrac{1+2+\cdots+K}{K} \text{ and } \displaystyle\sum_{j=1}^{n} S_j^{2}=\dfrac{n}{A}\big(Bn^{2}+Cn+D…

Topic: JEE Main 2023 (8 April Morning Shift)

4

Let the number of elements in sets  and  be five and two respectively. Then the number of subsets o…

Topic: JEE Main 2023 (8 April Morning Shift)

5

$ \text{Let } \alpha,\beta,\gamma \text{ be the three roots of } x^{3}+bx+c=0. \text{ If } \beta\gamma=1=-\alpha,\ \tex…

Topic: JEE Main 2023 (8 April Morning Shift)

6

$ \text{Let } I(x)=\int \frac{x+1}{x,(1+x e^{x})^{2}},dx,; x>0.\ \text{If } \lim_{x\to\infty} I(x)=0,\ \text{then } I(1…

Topic: JEE Main 2023 (8 April Morning Shift)

7

$ \text{Let } C(\alpha,\beta) \text{ be the circumcenter of the triangle formed by the lines } 4x+3y=69,; 4y-3x=17,; x+…

Topic: JEE Main 2023 (8 April Morning Shift)

8

$ \text{The area of the region } {(x,y): x^{2}\le y \le 8-x^{2},; y\le 7} \text{ is:} $

Topic: JEE Main 2023 (8 April Morning Shift)

9

$ \text{Let } R \text{ be the focus of the parabola } y^{2}=20x \text{ and the line } y=mx+c \text{ intersect the parab…

Topic: JEE Main 2023 (8 April Morning Shift)

10

$ \text{The shortest distance between the lines } \dfrac{x-4}{4}=\dfrac{y+2}{5}=\dfrac{z+3}{3} \text{ and } \dfrac{x-1}…

Topic: JEE Main 2023 (8 April Morning Shift)