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JEE MAIN 2023
13-4-2023 S1
Question
Let for $\mathrm{x} \in \mathbb{R}, \mathrm{So}(\mathrm{x})=\mathrm{x}$, $S_k(x)=C_k x+k \int_0^x S_{k-1}(t) d t$, where $C_0=1, C_k=1-\int_0^x S_{k-1}(x) d x, k=1,2,3 \ldots .$. Then $S_2(3)+6 C_3$ is equal to
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Showing 18 questions
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The unit vector perpendicular to...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
Suppose four distinct positive numbers $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ are in G.P. Let $\mathrm{b}_1=\mathrm{a}_1, \mathrm{~b}_2=\mathrm{b}_1+\mathrm{a}_2, \mathrm{~b}_3=\mathrm{b}_2+ \mathrm{a}_3$ and $\mathrm{b}_4=\mathrm{b}_3+\mathrm{a}_4$. STATEMENT-1:...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
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QJEE ADVANCE 20112011
Match the statements given in Column I with the intervals/union of intervals given in Column II
JEE AdvanceMathematicsEasy
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QJEE ADVANCE 20112011
Match the statements given in Column I with the values given in Column II
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0$ satisfy $y(2)=\frac{2}{\sqrt{3}}$. STATEMENT-1 : $...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
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QJEE Advance 20082008
Consider $$ \begin{aligned} & L_1: 2 x+3 y+p-3=0 \\ & L_2: 2 x+3 y+p+3=0 \end{aligned} $$ where $p$ is a...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
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QJEE ADVANCE 20112011
Let M be a $3 \times 3$ matrix satisfying $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...
JEE AdvanceMathematicsEasy
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QJEE ADVANCE 20112011
Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...
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QJEE Advance 20082008
STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...
JEE AdvanceChemistryEasy
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QJEE Advance 20082008
STATEMENT-1: Bromobenzene upon reaction with $\mathrm{Br}_2 / \mathrm{Fe}$ gives 1,4 - dibromobenzene as the major product. and STATEMENT-2: In bromobenzene,...
JEE AdvanceChemistryEasy
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QJEE ADVANCE 20112011
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
JEE AdvanceMathematicsEasy
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QJEE ADVANCE 20112011
Let $\omega=\mathrm{e}^{\mathrm{i} \mathrm{x} / 3}$, and $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{x}, \mathrm{y}, \mathrm{z}$ be non-zero complex numbers such that $$ \begin{aligned}...
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
STATEMENT-1: The plot of atomic number ( y -axis) versus number of neutrons ( x -axis) for stable nuclei shows...
JEE AdvanceChemistryEasy
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QJEE ADVANCE 20112011
The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If $$ S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2},...
JEE AdvanceMathematicsEasy
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