Matrices_JEE-Main 310124(S2) - Competishun – Live JEE & NEET Courses and Exam Prep

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Jee Main 2024

31-01-2024

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Let $A$ be a $3 \times 3$ matrix and $\operatorname{det}(A)=2$. If $\mathrm{n}=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots \ldots}(\operatorname{adj} A))))$ Then the remainder when n is 2024-times divided by 9 is equal to

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Given the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[-1,1]$ such...

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Let P Q be a chord of the parabola $y^2=12 x$ and the midpoint of PQ be at $(4,1)$. Then,...

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Consider a hyperbola $H$ having centre at the origin and foci and the $x$-axis. Let $C_1$ be the circle touching...

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If the coefficients of $x^4, x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the...

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Let f(x) = 3 $ \sqrt{\mathrm{x}-2}+\sqrt{4-\mathrm{x}}$ be a real valued function. If $\alpha$ and $\beta$ are respectively the minimum and...

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If the value of the integral $\int_{-1}^1 \frac{\cos \alpha x}{1+3^x} d x$ is $\frac{2}{\pi}$. Then, a value of $\alpha$ is

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The area (in sq. units) of the region $S=\{z \in \mathbb{C} ;|z-1| \leq 2 ;(z+\bar{z})+i(z-\bar{z}) \leq 2, \operatorname{lm}(z) \geq 0\}$...

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The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $...

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Let $f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}$. Then $\lim _{x \rightarrow 0} \frac{f(x)}{x^3}$ is equal to

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The value of $\frac{1 \times 2^2+2 \times 3^2+\cdots+100 \times(101)^2}{1^2 \times 2+2^2 \times 3+\cdots+100^2 \times 101}$ is

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Let ABC be an isosceles triangle in which A is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$...

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If $\frac{d x}{d y}=\frac{1+x-y^2}{y}, x(1)=1$, then $5 x(2)$ is equal to :

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Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\cdots+(\operatorname{adj} A)^{10}$. Then, the sum of all the elements of...

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Let three real numbers 𝑎, 𝑏, 𝑐 be in arithmetic progression and a +1, b, c +3 be in geometric...

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The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas...

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Let a relation R on N x N be defined as : $\left(x_1, y_1\right) R\left(x_2, y_2\right)$ if and only if...

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Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of...

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QJEE MAIN 20242024

The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{I}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to...

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