JEE MAIN 2023 Previous Year Questions (PYQs) – Page 31 of 34
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The range of the function $f(x)=\sqrt{\,3-x\,}+\sqrt{\,2+x\,}$ is:
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The solution of the differential equation $\dfrac{dy}{dx}=-\left(\dfrac{x^{2}+3y^{2}}{3x^{2}+y^{2}}\right),\ y(1)=0$ is:
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Let $x=(8\sqrt{3}+13)^{13}$ and $y=(7\sqrt{2}+9)^{9}$. If $[t]$ denotes the greatest integer $\le t$, then:
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The number of real roots of the equation $\sqrt{x^{2}-4x+3}+\sqrt{x^{2}-9}=\sqrt{4x^{2}-14x+6}$ is:
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A bag contains $6$ balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least $5$ black balls is:
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If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is
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If $\sin^{-1}\!\left(\dfrac{\alpha}{17}\right)+\cos^{-1}\!\left(\dfrac{4}{5}\right)-\tan^{-1}\!\left(\dfrac{77}{36}\right)=0,\ 0<\alpha<13$, then $\sin^{-1}(\sin\alpha)+\cos^{-1}(\cos\alpha)$ is equal to:
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Let $\mathrm{R}$ be a relation on $\mathbb{N}\times\mathbb{N}$ defined by $(a,b)\,\mathrm{R}\,(c,d)$ if and only if $ad(b-c)=bc(a-d)$. Then $\mathrm{R}$ is:
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$ \textbf{Q:}$ For the system of linear equations $x + y + z = 6,\ \alpha x + \beta y + 7z = 3,\ x + 2y + 3z = 14$, which of the following is **NOT true**?
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$ \text{If the domain of } f(x)=\dfrac{\lfloor x\rfloor}{1+x^{2}},\ \text{where } \lfloor x\rfloor \text{ is greatest integer } \le x,\ \text{is } [2,6),\ \text{then its range is:} $
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