Let $\vec a,\vec b,\vec c$ be three non-zero vectors such that $\vec b$ and $\vec c$ are non-collinear. If $\vec a+5\vec b$ is collinear with $\vec c$, $\ \vec b+6\vec c$ is collinear with $\vec a$ and $\vec a+\alpha\vec b+\beta\vec c=\vec 0$, then $\alpha+\beta$ is equal to:

1

Suppose $f(x)=\dfrac{(2^{x}+2^{-x})\tan x\,\sqrt{\tan^{-1}(x^{2}-x+1)}}{(7x^{2}+3x+1)^{3}}$. Then the value of $f'(0)$ …

Topic: JEE Main 2024 (29 January Morning Shift)

1

Let $\left(5,\dfrac{9}{4}\right)$ be the circumcenter of a triangle with vertices $A(a,-2)$, $B(a,6)$ and $C\!\left(\df…

Topic: JEE Main 2024 (29 January Morning Shift)

2

If $\alpha,\;-\dfrac{\pi}{2}

Topic: JEE Main 2024 (29 January Morning Shift)

3

If in a G.P. of $64$ terms, the sum of all the terms is $7$ times the sum of the odd terms of the G.P., then the common…

Topic: JEE Main 2024 (29 January Morning Shift)

4

A fair die is thrown until $2$ appears. Then the probability that $2$ appears in an even number of throws is:

Topic: JEE Main 2024 (29 January Morning Shift)

5

In an A.P., the sixth term $a_6=2$. If the product $a_1a_4a_5$ is the greatest, then the common difference of the A.P. …

Topic: JEE Main 2024 (29 January Morning Shift)

6

Let $A=\begin{bmatrix} 1&0&0\\ 0&\alpha&\beta\\ 0&\beta&\alpha \end{bmatrix}$ and $\;|2A|^{3}=2^{21}$ where $\alpha,\b…

Topic: JEE Main 2024 (29 January Morning Shift)

7

Let $R$ be a relation on $\mathbb{Z}\times\mathbb{Z}$ defined by $(a,b)R(c,d)$ iff $ad-bc$ is divisible by $5$. Then $R…

Topic: JEE Main 2024 (29 January Morning Shift)

8

If $f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\b…

Topic: JEE Main 2024 (29 January Morning Shift)

9

Let $O$ be the origin and the position vectors of $A$ and $B$ be $2\hat i+2\hat j+\hat k$ and $2\hat i+4\hat j+4\hat k$…

Topic: JEE Main 2024 (29 January Morning Shift)

10

In $\triangle ABC$, suppose $y=x$ is the equation of the bisector of the angle $B$ and the equation of the side $AC$ is…

Topic: JEE Main 2024 (29 January Morning Shift)