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JEE MAIN_2022
26-07-2022_S1
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The number of distinct real roots of the equation $x^5\left(x^3-x^2-x+1\right)+x\left(3 x^3-4 x^2-2 x+4\right)-1=0$ is
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Showing 18 questions
QJEE Advance 20112011
Let $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots, \mathrm{a}_{100}$ be an arithmetic progression with $\mathrm{a}_1=3$ and $\mathrm{S}_{\mathrm{p}}=\sum_{\mathrm{i}=1}^{\mathrm{p}} \mathrm{a}_{\mathrm{i}}, 1 \leq \mathrm{p} \leq 100$....
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QJEE Advance2007
Let $f(x)=2+\cos x$ for all real $x$. STATEMENT -1 : For each real $t$, there exists a point $c$ in...
JEE AdvanceMathematicsEasy
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QJEE Advance 20092009
A metal rod AB of length 10 x has its one end A in ice at $0^{\circ} \mathrm{C}$ and the...
JEE AdvancePhysicsEasy
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QJEE Advance 20112011
The positive integer value of $\mathrm{n}>3$ satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{\mathrm{n}}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{\mathrm{n}}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{\mathrm{n}}\right)}$ is
JEE AdvanceMathematicsEasy
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QJEE Advance 20082008
A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as...
JEE AdvancePhysicsEasy
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QJEE Advance2007
Let $\mathrm{E}^{\mathrm{c}}$ denote the complement of an event E . Let $\mathrm{E}, \mathrm{F}, \mathrm{G}$ be pairwise independent events with $\mathrm{P}(\mathrm{G})>0$...
JEE AdvanceMathematicsEasy
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QJEE Advance 20112011
Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function such that $f(1)=2$. If $6 \int_1^x f(t) d t=3 x f(x)-x^3$...
JEE AdvanceMathematicsEasy
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QJEE Advance 20092009
A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=\mathrm{kr}^{\mathrm{a}}$, where...
JEE AdvancePhysicsEasy
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QJEE Advance 20112011
Let $f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)$, where $-\frac{\pi}{4}<\theta<\frac{\pi}{4}$. Then the value of $\frac{d}{d(\tan \theta)}(f(\theta))$ is
JEE AdvanceMathematicsEasy
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QJEE Advance2007
The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with
JEE AdvanceMathematicsEasy
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QJEE Advance 20092009
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of...
JEE AdvancePhysicsEasy
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QJEE Advance 20082008
Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use...
JEE AdvancePhysicsEasy
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QJEE Advance 20112011
Consider the parabola $y^2=8 x$. Let $\Delta_1$ be the area of the triangle formed by the end points of its...
JEE AdvanceMathematicsEasy
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QJEE Advance2007
Let $\mathrm{O}(0,0), \mathrm{P}(3,4), \mathrm{Q}(6,0)$ be the vertices of the triangle OPQ . The point R inside the triangle OPQ is...
JEE AdvanceMathematicsEasy
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QJEE Advance 20092009
A steady current I goes through a wire loop PQR having shape of a right angle triangle with $...
JEE AdvancePhysicsEasy
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QJEE Advance 20112011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
JEE AdvanceMathematicsEasy
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QJEE Advcance 20082008
The balls, having linear momenta $\overrightarrow{\mathrm{p}}_1=\mathrm{p} \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{p}}_2=-\mathrm{p} \hat{\mathrm{i}}$, undergo a collision in free space. There is no external...
JEE AdvancePhysicsEasy
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QJEE Advance2007
Let ABCD be a quadrilateral with area 18 , with side AB parallel to the side CD and $\mathrm{AB}=2 \mathrm{CD}$....
JEE AdvanceMathematicsEasy
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