Let α be a solution of $x^2 + x + 1 = 0$, and for some a and b in
$R, \begin{bmatrix} 4 & a & b \end{bmatrix} \begin{bmatrix} 1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix}$. If $\frac{4}{\alpha^4} + \frac{m}{\alpha^a} + \frac{n}{\alpha^b} = 3$, then m + n is equal to _______
Previous 10 Questions — JEE Main 2025 (8 April Evening Shift)
Nearest first
1
2
3
4
5
6
7
8
9
10
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)
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)
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 th…
Topic: JEE Main 2025 (8 April Evening Shift)
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)
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)
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)
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)
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)
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)
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)
