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QJEE MAIN 2025
If $\int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} \mathrm{~d} x=\frac{1}{\mathrm{~m}}\left(\left(\sqrt{1+x^2}+x\right)^0\left(\pi \sqrt{1+x^2}-x\right)\right)+\mathrm{C}$ where C is the constant of integration and $m, n \in \mathbf{N}$, then $m+n$ is equal to $\_\_\_\_$ .
JEE MainMathematicsMedium
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QJEE MAIN 2025
Let the area of the triangle formed by a straight line $L: x+b y+c=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn...
JEE MainMathematicsMedium
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QJEE MAIN 2025
Butane reacts with oxygen to produce carbon dioxide and water following the equation given below. If 174.0 kg of butane is mixed with 320.0 kg...
JEE MainChemistryEasy
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QJEE MAIN 2025
JEE MainChemistryMedium
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QJEE MAIN 2025
If $A$ and $B$ are two events such that $P(A)=0.7, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, where $\bar{B}$ denotes the complement of $B$, then $...
JEE MainMathematicsMedium
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QJEE MAIN 2025
A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades....
JEE MainMathematicsHard
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QJEE MAIN 2025
' $X$ ' is the number of electrons in $t_{2 g}$ orbitals of the most stable complex ion among $\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{FeCl}_6 \mathrm{I}^{3-},\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}\right.$ and $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$....
JEE MainChemistryEasy
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QJEE MAIN 2025
If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{k=1}^n\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20$, then n is equal to
$\_\_\_\_$ .
JEE MainMathematicsMedium
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QJEE MAIN 2025
The number of paramagnetic metal complex species among $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$, $\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{FeF}_6\right]^{3-}$ with same number of unpaired electrons is $\_\_\_\_$ ↓
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