If $A$ is a square matrix of order $3$ such that $\det(A) = 3$ and $\det(\text{adj}(-4,\text{adj}(-3,\text{adj}(3,\text{adj}((2A)^{-1}))))) = 2^m 3^n$, then $m + 2n$ is equal to:

1

Find the value of $ \displaystyle \lim_{n \to \infty} \frac{(1^2 - 1)(n - 1) + (2^2 - 2)(n - 2) + \cdots + (n^2 - n)(n …

Topic: JEE Main 2024 (6 April Evening Shift)

2

Let $f(x)=\dfrac{1}{7-\sin5x}$ be a function defined on $\mathbb{R}$. Then the range of the function $f(x)$ is equal to:

Topic: JEE Main 2024 (6 April Evening Shift)

3

Let $A={1,2,3,4,5}$. Let $R$ be a relation on $A$ defined by $xRy$ iff $4x \le 5y$. Let $m$ be the number of elements i…

Topic: JEE Main 2024 (6 April Evening Shift)

4

If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$, t…

Topic: JEE Main 2024 (6 April Evening Shift)

5

If the function $f(x)=\left(\dfrac1x\right)^{2x},; x>0$ attains its maximum at $x=\dfrac1e$, then:

Topic: JEE Main 2024 (6 April Evening Shift)

1

If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters a…

Topic: JEE Main 2024 (6 April Evening Shift)

2

Let $\vec a=2\hat i+\hat j-\hat k,\quad \vec b=\big((\vec a\times(\hat i+\hat j))\times\hat i\big)\times\hat i.$ Then t…

Topic: JEE Main 2024 (6 April Evening Shift)

3

Let $\vec a=6\hat i+\hat j-\hat k$ and $\vec b=\hat i+\hat j$. If $\vec c$ is a vector such that $|\vec c|\ge 6$, $\ \v…

Topic: JEE Main 2024 (6 April Evening Shift)

4

Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\dfrac{x-0}{1}=\dfrac{y-3}{1}=\dfrac{z-…

Topic: JEE Main 2024 (6 April Evening Shift)

5

Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the midpoints of all sides of $\triangle ABC$…

Topic: JEE Main 2024 (6 April Evening Shift)

6

If the area of the region $\left\{(x, y): \frac{\mathrm{a}}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2,0

Topic: JEE Main 2024 (6 April Evening Shift)

7

Suppose the solution of the differential equation $ \displaystyle \frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\…

Topic: JEE Main 2024 (6 April Evening Shift)

8

A software company sets up $n$ computer systems to finish an assignment in $17$ days. If $4$ systems crash at the start…

Topic: JEE Main 2024 (6 April Evening Shift)

9

If $P(6,1)$ is the orthocentre of the triangle whose vertices are $A(5,-2)$, $B(8,3)$ and $C(h,k)$, then the point $C$ …

Topic: JEE Main 2024 (6 April Evening Shift)

10

If all words (with or without meaning) formed using all the letters of the word NAGPUR are arranged in dictionary order…

Topic: JEE Main 2024 (6 April Evening Shift)