Let $\beta(m,n)=\displaystyle\int_{0}^{1}x^{m-1}(1-x)^{,n-1},dx,; m,n>0$. If $\displaystyle\int_{0}^{1}(1-x^{10})^{20},dx=a\times \beta(b,c)$, then $100(a+b+c)$ equals:

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. If $y(\theta)=\dfrac{2\cos\theta+\cos2\theta}{\cos3\theta+\cos2\theta+5\cos\theta+2}$, then at $\theta=\dfrac{\pi}{2}…

Topic: JEE Main 2024 (5 April Evening Shift)

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The values of $m, n$, for which the system of equations $\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\ma…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $A(-1,1)$ and $B(2,3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $\triang…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $\vec a=2\hat i+5\hat j-\hat k$, $\vec b=2\hat i-2\hat j+2\hat k$ and $\vec c$ be three vectors such that $(\vec c+…

Topic: JEE Main 2024 (5 April Evening Shift)

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If the constant term in the expansion of $\left(\dfrac{\sqrt{3}}{x}+\dfrac{2x}{\sqrt{5}}\right)^{12}$, $x\ne 0$, is $\a…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $(\alpha,\beta,\gamma)$ be the image of the point $(8,5,7)$ in the line $\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-2}{…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $ABCD$ and $AEFG$ be squares of side $4$ and $2$ units, respectively. The point $E$ is on the line segment $AB$ and…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $f, g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as : $f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle with centre $(-1,0)$ and radius $2$. If the line of the …

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $f:[-1,2]\to\mathbb{R}$ be given by $f(x)=2x^{2}+x+\lfloor x^{2}\rfloor-\lfloor x\rfloor$, where $\lfloor t\rfloor$…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let the set $S={2,4,8,16,\ldots,512}$ be partitioned into three sets $A,B,C$ having equal number of elements such that …

Topic: JEE Main 2024 (5 April Evening Shift)

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For $x\ge0$, the least value of $K$ for which $4^{,1+x}+4^{,1-x},\ \dfrac{K}{2},\ 16^{x}+16^{-x}$ are three consecutive…

Topic: JEE Main 2024 (5 April Evening Shift)

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Let $\alpha \beta \neq 0$ and $A=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alp…

Topic: JEE Main 2024 (5 April Evening Shift)

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The area enclosed between the curves $y=x|x|$ and $y=x-|x|$ is:

Topic: JEE Main 2024 (5 April Evening Shift)

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60 words can be formed using all the letters of the word BHBJO (with or without meaning). If these words are arranged i…

Topic: JEE Main 2024 (5 April Evening Shift)

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Consider three vectors $\vec a,\vec b,\vec c$. Let $|\vec a|=2$, $|\vec b|=3$ and $\vec a=\vec b\times\vec c$. If $\alp…

Topic: JEE Main 2024 (5 April Evening Shift)

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The differential equation of the family of circles passing through the origin and having centre on the line $y=x$ is:

Topic: JEE Main 2024 (5 April Evening Shift)