Let $\vec a=\hat i+2\hat j+\hat k$ and $\vec b=2\hat i+\hat j-\hat k$. Let $\vec c$ be a unit vector in the plane of the vectors $\vec a$ and $\vec b$ and be perpendicular to $\vec a$. Then such a vector $\vec c$ is:

1

If $A$ and $B$ are two events such that $P(A)=0.7,\ P(B)=0.4$ and $P(A\cap \overline{B})=0.5$, where $\overline{B}$ den…

Topic: JEE Main 2025 (8 April Evening Shift)

2

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. T…

Topic: JEE Main 2025 (8 April Evening Shift)

3

Let $f(x)$ be a positive function and $I_{1}=\int_{-\tfrac{1}{2}}^{1} 2x,f\left(2x(1-2x)\right),dx$ and $I_{2}=\int_{-1…

Topic: JEE Main 2025 (8 April Evening Shift)

4

Let $A={0,1,2,3,4,5}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ iff $\max{x,y}\in{3,4}$. Then among the sta…

Topic: JEE Main 2025 (8 April Evening Shift)

5

Let $ A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix} $.If $ \det(\text…

Topic: JEE Main 2025 (8 April Evening Shift)

6

The integral $\displaystyle \int_{-1}^{\tfrac{3}{2}} \left( |\pi^2 x \sin(\pi x)| \right) dx$ is equal to

Topic: JEE Main 2025 (8 April Evening Shift)

7

Given below are two statements: Statement I: $\displaystyle \lim_{x \to 0} \left( \tan^{-1}x + \log_e \dfrac{\sqrt{1+x…

Topic: JEE Main 2025 (8 April Evening Shift)

8

Let $A = {\theta \in [0,2\pi] : 1 + 10,\mathrm{Re}\left(\dfrac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta}\ri…

Topic: JEE Main 2025 (8 April Evening Shift)

9

The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \ta…

Topic: JEE Main 2025 (8 April Evening Shift)

10

The sum of the squares of the roots of $|x - 2|^2 + |x - 2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x - 3| - …

Topic: JEE Main 2025 (8 April Evening Shift)

1

Let the function $f(x)=\dfrac{x}{3}+\dfrac{3}{x}+3,\ x\ne0$ be strictly increasing in $(-\infty,\alpha_1)\cup(\alpha_2,…

Topic: JEE Main 2025 (8 April Evening Shift)

2

The number of integral terms in the expansion of $\left(5^{\tfrac{1}{2}}+7^{\tfrac{1}{8}}\right)^{1016}$ is:

Topic: JEE Main 2025 (8 April Evening Shift)

3

Let α be a solution of $x^2 + x + 1 = 0$, and for some a and b in $R, \begin{bmatrix} 4 & a & b \end{bmatrix} \begin{bm…

Topic: JEE Main 2025 (8 April Evening Shift)