$ \text{If [t] denotes the greatest integer } \le t, \text{ then the value of } \frac{3(e-1)}{e} \int_{1}^{2} x^2 e^{\lfloor x \rfloor + \lfloor x^3 \rfloor} dx \text{ is:} $

1

Let the system of linear equations \[ \begin{cases} x + y + kz = 2,\\ 2x + 3y - z = 1,\\ 3x + 4y + 2z = k \end{cases} \…

Topic: JEE Main 2023 (30 January Morning Shift)

2

The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c)\}$ on the set $\{a,b,c\}$ so that it…

Topic: JEE Main 2023 (30 January Morning Shift)

3

Let the solution curve $y=y(x)$ of the differential equation \[ \frac{dy}{dx}=\frac{3x^5\tan^{-1}(x^3)}{(1+x^6)^{3/2}}\…

Topic: JEE Main 2023 (30 January Morning Shift)

1

$ \text{Suppose } f:\mathbb{R}\to(0,\infty) \text{ be a differentiable function such that } 5f(x+y)=f(x)\cdot f(y),\ \f…

Topic: JEE Main 2023 (30 January Morning Shift)

2

If the solution of the equation $\log_{\cos x}\!\big(\cot x\big) + 4\log_{\sin x}\!\big(\tan x\big) = 1,\ x\in\left(0,\…

Topic: JEE Main 2023 (30 January Morning Shift)

3

If $\tan 15^\circ + \dfrac{1}{\tan 75^\circ} + \dfrac{1}{\tan 105^\circ} + \tan 195^\circ = 2a$, then the value of $(a+…

Topic: JEE Main 2023 (30 January Morning Shift)

4

If the coefficient of $x^{15}$ in the expansion of $\left(a x^{3}+\dfrac{1}{b x^{1/3}}\right)^{15}$ is equal to the coe…

Topic: JEE Main 2023 (30 January Morning Shift)

5

Let a unit vector $\overrightarrow{OP}$ make angles $\alpha,\beta,\gamma$ with the positive directions of the coordinat…

Topic: JEE Main 2023 (30 January Morning Shift)

6

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the produ…

Topic: JEE Main 2023 (30 January Morning Shift)