If $f(x)= \begin{vmatrix} x^{3} & 2x^{2}+1 & 1+3x\\ 3x^{2}+2 & 2x & x^{3}+6\\ x^{3}-x & 4 & x^{2}-2 \end{vmatrix} \ \text{for all } x\in\mathbb{R},\ \text{then } 2f(0)+f'(0)$ is equal to:
Previous 10 Questions — JEE Main 2024 (31 January Morning Shift)
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Let $a$ be the sum of all coefficients in the expansion of
$\big(1-2x+2x^{2}\big)^{2023}\big(3-4x^{2}+2x^{3}\big)^{2024…
Topic: JEE Main 2024 (31 January Morning Shift)
If the system of linear equations
$\begin{aligned}
& x-2 y+z=-4 \\
& 2 x+\alpha y+3 z=5 \\
& 3 x-y+\beta z=3
\end{align…
Topic: JEE Main 2024 (31 January Morning Shift)
The solution curve of the differential equation
$y\dfrac{dx}{dy}=x(\log_e x-\log_e y+1),\ x>0,\ y>0,$
passing through…
Topic: JEE Main 2024 (31 January Morning Shift)
The area of the region
$\Big\{(x,y): y^{2}\le4x,\ x0,\ x\ne3\Big\}$
is:
Topic: JEE Main 2024 (31 January Morning Shift)
Let $g(x)$ be a linear function and
$
f(x)=
\begin{cases}
g(x), & x\le 0,\\[2mm]
\left(\dfrac{1+x}{2+x}\right)^{\tfrac{…
Topic: JEE Main 2024 (31 January Morning Shift)
The distance of the point $Q(0,2,-2)$ from the line passing through the point
$P(5,-4,3)$ and perpendicular to the line…
Topic: JEE Main 2024 (31 January Morning Shift)
Two marbles are drawn in succession from a box containing $10$ red, $30$ white,
$20$ blue and $15$ orange marbles, with…
Topic: JEE Main 2024 (31 January Morning Shift)
The sum of the series
$\displaystyle \frac{1}{1-3\cdot1^{2}+1^{4}}+\frac{2}{1-3\cdot2^{2}+2^{4}}+\frac{3}{1-3\cdot3^{2}…
Topic: JEE Main 2024 (31 January Morning Shift)
Let $\vec a=3\hat i+\hat j-2\hat k,\ \vec b=4\hat i+\hat j+7\hat k$ and $\vec c=\hat i-3\hat j+4\hat k$ be three vector…
Topic: JEE Main 2024 (31 January Morning Shift)
Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random
variable $x$ to be the number …
Topic: JEE Main 2024 (31 January Morning Shift)
Next 10 Questions — JEE Main 2024 (31 January Morning Shift)
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If one of the diameters of the circle $x^{2}+y^{2}-10x+4y+13=0$ is a chord of another
circle $C$, whose center is the p…
Topic: JEE Main 2024 (31 January Morning Shift)
If the foci of a hyperbola are the same as those of the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{25}=1$
and the eccentri…
Topic: JEE Main 2024 (31 January Morning Shift)
