Between the following two statements: Statement I: Let $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$. Then the vector $\vec{r}$ satisfying $\vec{a} \times \vec{r} = \vec{a} \times \vec{b}$ and $\vec{a} \cdot \vec{r} = 0$ is of magnitude $\sqrt{10}$. Statement II: In a triangle $ABC$, $\cos 2A + \cos 2B + \cos 2C \geq -\dfrac{3}{2}$.
Previous 10 Questions — JEE Main 2024 (9 April Evening Shift)
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The value of the integral
$\displaystyle \int_{-1}^{2} \log_e \big(x + \sqrt{x^2 + 1}\big),dx$ is
Topic: JEE Main 2024 (9 April Evening Shift)
$\lim _\limits{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos…
Topic: JEE Main 2024 (9 April Evening Shift)
If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text{th}}$ roll than…
Topic: JEE Main 2024 (9 April Evening Shift)
If $\log_{e} y = 3\sin^{-1}x$, then $,(1-x^{2})y''-xy',$ at $x=\dfrac{1}{2}$ is equal to:
Topic: JEE Main 2024 (9 April Evening Shift)
Let $\alpha,\beta;\ \alpha>\beta,$ be the roots of the equation $x^{2}-\sqrt{2},x-\sqrt{3}=0$.
Let $P_{n}=\alpha^{n}-\b…
Topic: JEE Main 2024 (9 April Evening Shift)
The integral $\displaystyle \int_{1/4}^{3/4} \cos\left( 2\cot^{-1}\sqrt{\frac{1-x}{1+x}} \right),dx$ is equal to:
Topic: JEE Main 2024 (9 April Evening Shift)
Two vertices of a triangle $ABC$ are $A(3,-1)$ and $B(-2,3)$, and its orthocentre is $P(1,1)$.
If the coordinates of $C…
Topic: JEE Main 2024 (9 April Evening Shift)
Let $\displaystyle \int_{0}^{x}\sqrt{1-\big(y'(t)\big)^{2}},dt=\int_{0}^{x}y(t),dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0$.
The…
Topic: JEE Main 2024 (9 April Evening Shift)
Let the range of the function $f(x)=\dfrac{1}{2+\sin3x+\cos3x},\ x\in\mathbb{R}$ be $[a,b]$. If $\alpha$ and $\beta$ ar…
Topic: JEE Main 2024 (9 April Evening Shift)
Let $z$ be a complex number such that the real part of $\displaystyle \frac{z-2i}{z+2i}$ is zero. Then, the maximum val…
Topic: JEE Main 2024 (9 April Evening Shift)
Next 10 Questions — JEE Main 2024 (9 April Evening Shift)
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If the variance of the frequency distributionis $160$, then the value of $c\in\mathbb{N}$ is:
Topic: JEE Main 2024 (9 April Evening Shift)
Let $B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$ and $A$ be a $2 \times 2$ matrix such that $A B^{-1}=A^…
Topic: JEE Main 2024 (9 April Evening Shift)
$\displaystyle \lim_{x\to 0}\ \frac{e^{-(1+2x)^{\tfrac{1}{2x}}}}{x}$ is equal to:
Topic: JEE Main 2024 (9 April Evening Shift)
Consider the line $L$ passing through the points $(1,2,3)$ and $(2,3,5)$.
The distance of the point $\left(\dfrac{11}{3…
Topic: JEE Main 2024 (9 April Evening Shift)
The area (in square units) of the region enclosed by the ellipse $x^{2}+3y^{2}=18$ in the first quadrant below the line…
Topic: JEE Main 2024 (9 April Evening Shift)
Let $a,ar,ar^{2},\ldots$ be an infinite G.P. If $\displaystyle \sum_{n=0}^{\infty} a r^{n}=57$ and $\displaystyle \sum_…
Topic: JEE Main 2024 (9 April Evening Shift)
The sum of the coefficients of $x^{2/3}$ and $x^{-2/5}$ in the binomial expansion of
$\big(x^{2/3}+\tfrac{1}{2}x^{-2/5}…
Topic: JEE Main 2024 (9 April Evening Shift)
Let $\vec a=2\hat i+\alpha\hat j+\hat k,\ \vec b=-\hat i+\hat k,\ \vec c=\beta\hat j-\hat k$, where $\alpha,\beta$ are …
Topic: JEE Main 2024 (9 April Evening Shift)
